BIBLIOGRAPHY
MENZI, MELANIE B., NGOABAN, RHEA B. March 2008. Analysis of
Queueing of Customers Serviced at Landbank-La Trinidad, Benguet. Benguet State
University, La Trinidad, Benguet.
Adviser: Marycel H. Toyhacao
ABSTRACT
The study was conducted to determine the arrival distribution, the service time
distribution, the operating characteristics and the economic analysis of customers
serviced at Landbank-La Trinidad, Benguet. There were 3116 customers who composed
the respondents of the study.
The average number of customers who arrived at Landbank-La Trinidad, Benguet
were 22/hour and the average customer that the teller can serviced per hour were 14, thus
the discrepancy between the customers arrivals and the number of customers serviced by
the teller results to the existence of queueing of customers.

In Landbank-La Trinidad, customer arrivals were not scheduled and occurred in
an unpredictable manner, a random pattern appeared to exist. Thus to determine the
customer arrivals at Landbank-La Trinidad, the Poisson distribution provides a good
description of the arrival pattern. The Poisson probability
x e λ
λ −
distribution is defined by: P(X ≤ x) =
for x = 0, 1, 2,…….. where λ = 22 and e =
!
x
2.71828.

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Customers of Landbank-La Trinidad demand different services. They either
deposit, withdraw, update accounts, exchange funds, or pay BIR tax thus, the teller’s
service time varies. The exponential probability distribution was used to describe the
service time. The exponential probability distribution is defined by
t
f (x


)
e μ
μ −
=
for x ≥
0 where μ = 14 and e = 2.71828.
Using the assumptions of Poisson arrival and exponential service time, a first-
come-first-served queue discipline and two identical servers the operating characteristics
were computed. On the average, there were 5 customers in the system (L), the average
time a customer spends in the system is 13 minutes (W), on the average, there were 3
customers in the queue waiting for the service (Lq), the average time, a unit spends in the
queue waiting for service is 8 minutes (Wq) and the probability that an arriving customer
has to wait for service is 69% (Pw).
Adding another teller using the same arrival rate and service rate, three identical
servers and a first-in first-out queue discipline. On the average, the number of customers
in the system was reduced from 5 to 2 (L), the average time a customer spends in the
system is reduced from 13 minutes to 5 minutes (W), on the average, the number of
customers in the queue waiting for the service is reduced from 3 to 0.27 (Lq), the average
time a unit spends in the queue waiting for service is reduced from 8 minutes to 0.6
minutes (Wq) and the probability that an arriving customer has to wait for service was
reduced from 69% to 26% (Pw).
The three-teller system will greatly improve the operating characteristics of the
system.

ii

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TABLE OF CONTENTS
Page
Bibliography ……………………………………………….……………...... i
Abstract …………...………………………………………………………... i
Table of Contents ………………………………………….......….….……. iii
INTRODUCTION
Background of the Study ………………………………………….…. 1
Objectives of the Study ……………………………………………… 3
Importance of the Study ……………………………………….….… 3
Scope and Delimitation of the Study ………………………………… 4
REVIEW OF LITERATURE

Studies on Queueing …………………………………………….…. 5
THEORETICAL FRAMEWORK
Multiserver Queueing Model ……………..…………………………. 10
Arrival distribution ………………………………………………...… 11
Service Time Probability …………………………………………….. 12
Queue Discipline ……………………………………………………... 12
Multiserver Single-Line Queueing Model ……………………….… 12
Definition of Terms ……………………………………...………… 15
METHODOLOGY

Respondents of the Study ………………………………………….. 17

Data Gathered …………………………………..………………..… 17
Data Used ……………………...……………………………..……. 17
iii

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Statistical Analysis ……………………...…………………………. 17
RESULTS AND DISCUSSION
The Arrival Distributions of Customers Serviced at
Landbank-La Trinidad, Benguet ...………………………………… 19
The Service Time Distributions of Customers Serviced at
Landbank-La Trinidad, Benguet …………….…………..………… 22
Operating Characteristics of Customers Serviced at
Landbank-La Trinidad, Benguet …….……………….…...……….. 25
SUMMARY, CONCLUSION, AND RECOMMENDATIONS
Summary …………………………………………...……………… 28
Conclusion ……………………………………………………....… 30
Recommendations …...……………….……………………………. 31
LITERATURE CITED …………………………….……………………… 32
APPENDICES
A. Request Letter to the Manager of Landbank-La Trinidad,
Benguet to Gather Data ……………………...………..………... 34
B. Application for Oral Defense ……………………...……….…… 35
C. Raw Data …………………………………...…………...………. 36
D. Arrival Time and Service Time Probability …………………..... 76

E. Multiple-Server Operating Characteristics of Customers Serviced at

Landbank-La Trinidad, Benguet ………………………………… 77

iv

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1

INTRODUCTION


Background of the Study

Waiting line is part of everyday life. Whether it is waiting at a teller
window of a bank, waiting in line at the registrars office during enrollment,
waiting in line at a fast food outlet’s service counter or cars waiting in line at a
traffic light, we spend a lot of waiting. Waiting line situations are undesirable to
both parties concerned. This may result to customer’s dissatisfaction with the
service and may be root of economic losses in business.

Waiting lines form because customers arrive at the servicing function
faster than they can be served every single time. This does not mean that the
service function is understaffed, rather it means that waiting lines form because
customers do not arrive at a constant rate, nor are they all served in an equal
amount of time. A waiting line is continually increasing and decreasing in length,
and in the long run approaches an average rate of customer arrivals and an
average time to serve the customers.

Landbank-La Trinidad, Benguet which is the focus of the study is one of
the business establishments that deal with the problems involving in queueing. It
is a bank branch under the Landbank of the Philippines. It provides services on
financial transactions to the customers with the need of human teller machine
based service. It provides financial services, including check encashment or
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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issuing money in various forms, receiving deposits of money, lending money,
updating of account balances and receives payment of BIR tax.

Landbank-La Trinidad illustrates the transient nature of waiting lines.
Waiting line occurs at the bank daily and doubles during peak hour that falls on
the time interval of 9:00AM-10:00AM; peak day which is Friday and peak date
that falls every 20th of the month. The existence of long waiting lines is due to the
large number of customers demanding for the teller’s service. Customers either
deposit, withdraw, update balances, exchange funds or pay BIR tax. However,
there are only two tellers who render the service or there is limited number of
servers. Since customers demand a different service, it also requires a different
service time, the amount of time it takes to serve each individual customer adds to
the long waiting lines. This results to a situation where arriving customers at
random points in time, enter a bank, joins the line of customers and wait until a
teller is free then turn for one of the two tellers available. This describes the
queueing system.
It is therefore important to understand the different elements of a waiting
line system. These elements include the customer population source, the service
system, the arrival and service patterns, and the queue discipline used for
controlling the customer. A queueing system is considered the waiting line or the
queue as well as the available service facility that contains one or more servers.
The queue is the place where customers spend most of their time. Queueing
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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systems can have single or multiple lines. In Landbank-La Trinidad, it has a
single line of customers. In general, we shall consider the term customer as any
entity demanding or requiring service within a queuing system. In this study, a
customer is a person waiting in line for the bank teller’s service. The term service,
as applied to queuing system, will refer to the facility. In the study, it refers to the
teller’s service. The last component is the server who makes up the service
facility.

Objectives of the Study

The study sought to determine the variables that cause the queueing of
customers serviced at Landbank-La Trinidad, Benguet. Specifically, the study
aimed to:
1) Determine the arrival distribution of customers of Landbank-La Trinidad,
Benguet who deposit, withdraw, update/check balances, exchange funds and pay
BIR tax
2) Determine the service time distribution of customers of Landbank-La
Trinidad, Benguet who deposit, withdraw, update/check balances, exchange funds
and pay BIR tax
3) Determine the operating characteristics of queuing of customers at
Landbank-La Trinidad, Benguet
4) Determine the economic analysis of the operating characteristics of
queuieng of customers at Landbank-La Trinidad, Benguet
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Importance of the Study
The study helps in making effective decisions whether or not to make
changes, or several alternatives about situation that involves waiting lines.
Results will provide information to the management of Landbank-La Trinidad,
Benguet, and other business establishment or commercial institution on the proper
management of queues and the importance of balance between services to
customers, to what level of service to offer. The study is very important to
Landbank-La Trinidad, Benguet and other business establishment in their
immediate but appropriate solution to prevent the existence of long waiting lines
that may cause losses in the business.
The study provides information to the customers on proper understanding
on the reasons for queueing.

Scope and Delimitation of the Study
This study was focused on the application of analysis of queueing of the
customers serviced at Landbank-La Trinidad, Benguet who deposit, withdraw,
update/check of account balance, exchange funds and pay BIR tax.
The variables that were gathered were the arrival time, waiting time and
the service time. The gathered data were observed and tallied on December 17-21,
2007 and January 7-11, 2008. The data gathered were observed in two different
weeks because December was the peak times while January was the normal
operation of the bank.
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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REVIEW OF LITERATURE

Queueing is a daily encounter. Existence of long queues is undesirable to
the customers and also to the management, thus management scientist has
formulated a study on queueing.

Studies on Queueing
Wang Zenghua (2007) conducted a study on Local Banks Line up To
Tackle Queueing Times in Shanghai China. Results required the domestic banks
in the city to devise measure to deal with long queues at their outlets amid
growing complains from customers and threats the regulator. Analysts said
domestic banks cannot ignore their lower-end customers as they court a higher-
end group.
The recent outcry from customers over long waiting times at bank outlets
prompted the regulator to urge domestic institutions to find solutions and threaten
punishment. Bank of Communications (BoCom) suggested on the “making
effective steps” and regards the issue as a priority as it quickens the expansion and
optimizes the structure of its customer base. The bank will add more staff during
rush hours like lunchtime and peak times when new mutual funds and treasury
bond are issued.
Other banks in Shanghai said “they would add more ATMs and self
service-machines and guide their customers to use them”. Banks also said that
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they would add more staff during rush hours like lunchtime and peak times. They
would use counters reserved for VIP clients for regular customers when queues
are long. BoCom pledge to install water dispensers, newspaper stands and TV sets
as its major outlets in a bid to improve the environment.
Furthermore, Zughbur (2005) conducted a study of GAZA Seaport
Berthing Facilities Using Simulation. Queuieng model of the logistic activities to
the arrival, berthing, and departure of ships in GAZA Seaport in Palestine was
presented in the study. Non standard service stations, time dependent priority
mechanism, and complex resource allocation policies prevent the use of analytical
approach, to the solution. By adopting the process approach, a simulation model
for the queuing model has been developed for GAZA Seaport. This requires a
limited effort when using graphical objects of the Arena program for discrete –
event simulation. Good validations of results against measures on a real system
are obtained using aggregated data related to finite time horizon. Steady state
simulation results illustrate the use of the model.
Garroppo, Giordano, and Pagano (1998), conducted a study on Stochastic
Traffic Features and Queueing Working Conditions: A Simulation Study. The
paper presents an extended simulation study aimed to the evaluation of the impact
on queueing performance of different statistical features of actual traffic data. In
particular, the relevance of marginal distribution (PDF of the arrival rate) and
memory properties (LRD-SRD) is considered, highlighting the impact of these
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features in different queueing scenarios, varying queue length and loading
conditions. The study is carried out by means of discrete event simulation driven
by actual traces (collected during measurement sessions) and synthetic sequences
generated according to different models. The choice of the generation procedures
is motivated by model adequacy in capturing the considered statistical features of
actual traffic. The analysis emphasizes the need of a proper methodology (which
takes into account working conditions) in model selection for realistic queueing
performance evaluation
Banks and Dai (1996) in their study on Simulation Studies of Multiclass
Queueing Networks conclude that, researcher have been rather surprised to learn
that there are open networks that are unstable even though their traffic intensity at
each station is less than unity. This article described some of the network that
have exhibited this surprising behavior and further illustrated the instability or
conjecture about both stability and instability. In particular, it demonstrated that
some buffer priority dispatching rules as well as FIFO, shortest-mean-processing-
time-first, and shortest-remaining-processing-time-first dispatching rules can be
unstable. Researcher are continuing their investigation in this area, both
theoretical and application interest

Norros and Virtamo (2005) made a study on “Importance Sampling
Simulation Studies on the Discrete Time n{D}/{D}/1 Queue” they concluded that
the importance sampling simulation can be used as an effective tool also in the
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analysis of non-Markovian queueing systems. However, the use of the measure
transformation is difficult in general.
Al-Deek and Radwan(1995) in their case study on the Operational
Benefits of Electronic Toll Collection cited the improvements in traffic operations
at the electronic toll collection plazas of the Orlando-Orange Country Expressway
Authority. Service time, vehicle arrival times, and departure times, as well as
vehicle counts were collected before and after the installation of automatic vehicle
identification technology known as E-PASS. The findings indicate that, for the
dedicated E-PASS lane, the measured capacity has tripled, the service time has
decreased by five seconds per vehicle, the average queueing delay has decreased
by one minute per vehicle, the maximum queueing delay has decreased by 2.5-3
minutes per vehicle, and the total delay has decreased by 8.5-9.5 vehicle per
morning peak per hour for that lane. Also, variability in the headway has been
reduced significantly in the dedicated E-PASS lane. Capacity, headway, and
service times of the mixed (manual/E-PASS or automatic/E-PASS) lanes did not
change significantly. However, arrivals have shifted to the dedicated E-PASS
lanes, thus reducing delays at the mixed lanes and improving traffic operation for
the entire toll plaza.
Le Ny (2005) studied a queue with two classes of customers, a single
server and FIFO discipline. Class – I (I = 1, 2) customers arrive according to
Poisson processes; there is no priority between the two classes. The service of
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class-1 costumers is exponential whereas class-2 customers are served
instantaneously. We have obtained exact formulas of geometric form for the
stationary probability of each ordered state and for the steady-state distributions
of customer numbers in the system.
Krinik, Rubino, Marcus, Swift, Kasfy, and Lam (2005) using the concept
of duality between stochastic processes as defined in “ Continuous-Time Markov
Chains” (Anderson, 1991, Springer-Verlag), developed a new approach to obtain
closed-form expressions of transient distribution for basic Markovian queues. The
idea is to go to discrete time through uniformization, then to use duality to map
the problem into transient analysis of absorbing models and then, to use
combinatorial techniques to analyze these absorbing chains.
Belen (1988) fitted a stochastic time series model on the monthly recorded
rate of crimes. Two models, both adequate for forecasting were derived. The
second model which was derived from a logarithmic transformed differenced
series is more preferred with respect to some aspect than the first model which
was derived from a differenced series.






Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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THEORETICAL FRAMEWORK



Teller 1
Queue

Queue
Arrivals
Discipline
Departures


Teller2
Figure.1 Multiserver Single-Queue Diagram of Landbank-La Trinidad, Benguet

Multiserver Queuing Model
Multiserver single-line model is a logical extension of a single server
queueing model. It means that two or more service locations are present. Items
arriving for service wait in a single waiting line and they may move to the first
available server to be serviced.
For a waiting line problem, queueing model may be used to identify the
systems operating characteristics these are the:
1) probability of zero customers in the system at time t
2) probability of n customers in the system when n < k
3) probability of n customers in the system when n ≥ k
4) average waiting time in the queue
5) average waiting time in the system
6) average number of customers in the waiting line
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7) average number of customers in the system
In order to develop a waiting line model, we will need to identify some
important characteristics of the system:
1) the arrival distribution
2) the service time distribution
3) the queue discipline

Arrival Distribution
Arrival distribution for a waiting line involves determining how many
customers arrive and the pattern of arrivals over a given period of time. The
arrivals occurring in a given period of time appear to have a random pattern and
each arrival is independent of the other arrivals. The probability distribution
function which provides a good description of arrival pattern is the Poisson
process. One of the most useful applications of the Poisson distribution is in the
field of queueing theory. In many situations where queues occur, it has been
shown that the number of people joining the queue in a given time period follows
the Poisson model.
The Poisson probability distribution is defined as:
λ
λ −
P( )
e
x =
for x = 0, 1, 2………… (1)
!
x
Where in waiting line application:
x = number of arrivals in a specified period of time
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λ = average number of arrivals for the specific period of time
e = 2.71828

Service Time Probability
A service time probability distribution describes how long it takes a customer
to acquire the service needed. Since the customer demand a different service, the
teller’s service times will vary. Thus, the service process will follow an
exponential probability distribution.
The exponential probability distribution is defined as:
F(x)
−( t
μ )
= 1− e
for x ≥ 0 (2)
Where:
x = service time
μ = average number of units that the service facility can handle in a
specific period of time
e = 2.71828

Queue Discipline
Queue discipline is a manner in which the waiting customers are ordered for
service. In Landbank-La Trinidad, the waiting customers are ordered on a first
come first serve basis which is referred to us a first–in–first–out (FIFO) queue
discipline.

Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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Multiserver Single-Line Queueing Model
The model assumes that there are k identical servers, the service time
distribution for each k server is exponential and the arrival distribution can be
described by the Poisson distribution and that the queue discipline is a first in first
out basis.

Utilization Rate
This shows the percentage of time, the servers are busy or the probability
that the servers are busy. The utilization rate is defined as:
λ

ρ =
for kμ > λ (3)
μ
k
Where:
λ = average number of arrivals for the specific period of time
μ = average number of units that the service facility can handle in a
specific period of time
k = number of servers
Using these assumptions the operating characteristics can be described
with the following formulas: Let
λ = average arrival rate of the costumers

μ = average service rate of the k identical servers in the facility

k = number of available servers (1 < k < ∞)

Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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1) the probability that the k service channels are idle (zero customers
in the system at time t):
1

p t
( ) =
for kµ > λ (4)
0
⎡ 1 1 ⎛ λ n
k
⎤
⎞
1 ⎛ λ ⎞k
μ
⎢∑−
⎥ +
k
⎜
⎜ ⎟⎟
⎢n=0 n ⎝
! μ
⎜
⎜
⎠ ⎥ k!⎝ μ ⎟⎟⎠ ( μ
k − λ)
⎣
⎦
2) the probability of n customers in the system:
n
1
⎛ λ ⎞


p t
( ) =
p
for n > k (5)
n
− ⎜⎜
⎟
⎟ 0(t)
k!k n k ⎝ μ ⎠
n
1 ⎛ λ ⎞


p t
( ) =
p
for
n
≤ k
n
⎜
⎜ ⎟⎟ 0(t)
n! ⎝ μ ⎠
3) the average number of customers in the service system:
⎛ λ k
λμ
⎞
⎜
⎜
⎝ μ ⎟⎟⎠
λ


L =
P
(6)
2
0 (t )
(k − )1!(
+
μ
k − λ)
μ
4) the average time a customer spends in the system ( waiting time +
service time):
⎛ λ k
λμ
⎞
⎜
⎜
⎝ μ ⎟⎟⎠
1


W =
P t +
(7)
2
0 ( )
(k − )1!( μ
k − λ)
λ
L
=

λ
5) The average number of customers in the queue waiting for service:
λ

L = L −
(8)
q
μ
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6) The average time a customer spends in the queue waiting for the
service:
1

W = W −

q
μ
L

q
=
(9)
λ
7) The probability that an arriving unit has to wait for service:

k
1 ⎛ λ ⎞ ⎡
kμ
⎤


P =
(10)
w
k!⎜⎜ ⎟⎟ ⎢
⎝ μ ⎠ ⎣(kμ − λ) P
⎥ 0 (t)
⎦

Definition of Terms
Arrival Distribution involves determining how many units arrive and the
pattern of arrivals over a given period of time.
Arrival rate is the average number of customers arriving per time period
denoted by lambda (λ).
Bank is a business which provides financial services for profit.
Customer is any entity demanding or requiring service.
Exponential Distribution is a particular function form for a continuous
distribution with parameter k, a scalar real greater than zero. They are often used
to model the time between independent events that happen at a constant average
rate.
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Poisson distribution is a distribution that arises when you count a number
of events across time or over an area. The Poisson distribution involves counting
of events.
Queue means a waiting line, it represents a certain number of certain
number of customers waiting for service (of course the queue may be empty).
Queue Area is a place in which people in line wait for goods or services.
Queue Discipline represents the way the queue is organized (rules of
inserting and removing customers to/from the queue).
Queueing refers to waiting.
Queueing Theory is a mathematical study of waiting lines (or queues). It is
concerned in the factors relating to queues such as the distribution of arrivals, the
average time spent in the queues.
Server is the facility that provides service.
Service rate is the average number of customers that can be served per
time period denoted by mu (μ).
Service Time Distribution describes how long it takes a customer acquire
the service needed.
Utilization rate shows the probability that the server is busy, denoted by
rho (ρ).


Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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METHODOLOGY

Respondents of the Study
The respondents of the study were the customers of Landbank La
Trinidad, Benguet who deposit, withdraw, update account balances, exchange
funds and pay BIR tax. There were 3116 customers who composed the
respondents of the study. Due to confidential reasons, we were not able to get the
number of customers who deposit, withdraw, update account balances, exchange
funds and those who paid BIR tax.

Data Used
The data gathered were the arrival time, waiting time and the service
time. The arrival time was timed and tallied upon the entry of a customer to the
bank, waiting time was timed and tallied when customer joins the waiting line and
the service time was gathered and timed once the customer was there at the teller
window of the bank.

Statistical Analysis

The data gathered were encoded and summarized and were analyzed using
Microsoft Excel. Average number of customers arriving per hour (λ) and the
average number of customers that can be served per hour (μ) were computed
using the Microsoft excel.
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Poisson distribution was used in the description of the customer arrival
rate and Exponential distribution was used in the description of the customer
service rate. The queue discipline is a first-in-first-out basis (FIFO). Using these
assumptions, the operating characteristics of waiting line system were computed.
These were the probability that the service facilities are idle, probability of
specific number of customers in the system, the probability that an arriving
customer has to wait for service, the average number of customers in the system,
the average time each customer spends in the system, the average number of
customers in the queue waiting for the service and the average time each customer
spends in the queue waiting for the service.











Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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RESULTS AND DISCUSSION


The Arrival Distribution of Customers Serviced
at Landbank-La Trinidad, Benguet

Table 1 presents the summary for the arrivals of customers per hour
interval, the mean of the arrivals, the total number of arrivals and the over-all
mean.
The time interval between 8:30-9:30 had the highest customer arrival with
945. It had also the highest mean of 47 customers arrival per hour. This time
interval had the highest arrival because of the BIR tax payers. Since paying of
BIR tax was scheduled 8:30-12:00, most of the customers arrive in this time
interval. Where, time interval 2:31-3:00 had the lowest number of arrivals with
224 and had the lowest mean of 12. This is because the time interval that was
considered was 30 minutes or 0.5 hours which is the closing time for the bank.

Table 1. Summary of arrivals and arrival means
HOUR INTERVAL # OF CUSTOMER MEAN ARRIVAL/HOUR
8:30-9:30 945 47
9:31-10:30 514 26
10:3-11:30 391 20
11:31-12:30 337 17
12:31-1:30 314 16
1:31-2:30 371 19
2:31-3:00 224 12
Over-all mean 22




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The Arrival Distributions at Landbank-La Trinidad, Benguet
In Landbank-La Trinidad, customer arrivals were not scheduled and
occurred in an unpredictable manner, a random pattern appeared to exist. Thus, to
determine the customer arrivals at Landbank-La Trinidad, the Poisson distribution
provides a good description of the arrival pattern. The Poisson probability
x e λ
λ −
distribution is defined as: P(X ≤ x) =
for x = 0, 1, 2,……..
!
x
where from Table 1 the mean customers arrival per hour is λ = 22 and e =
2.71828.
Table 2 presents the Poisson customers arrival distribution of Landbank-
La Trinidad, Benguet, where we would expect 5 arrivals at 0.0012% of the time,
10 arrivals at 0.31%, 15 arrivals at 6.97% of the time or 4.18 minutes, 20 arrivals
at 36.64% of the time or 21.98 minutes, 25 arrivals at 76% of the time or 45.6
minutes, 30 arrivals at 95.42% of the arrivals or 57.25 minutes, 35 arrivals at
99.73% of the time or 59.73 minutes, 40 arrivals at 99.98% of the time or 59.99
minutes,45 arrivals at 99.99% of the time or 59.99 minutes and 50 arrivals at
100% of the time or exactly one hour.
Figure 2 presents the graph for the Poisson arrival distribution of
customers serviced at Landbank-La Trinidad, Benguet. It shows that as the
number of arrivals increases, the probability of having arrivals in an hour also
increases. This implies a positive relationship between the numbers of arrivals in
an hour and the probability that the arrival is expected in an hour of the time.
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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21

Table 2. Arrival distributions
NUMBER OF ARRIVALS P(X ≤ x)
5 0.0000
10 0.0031
15 0.0697
20 0.3664
25 0.7600
30 0.9542
35 0.9955
40 0.9998
45 1.0000
50 1.0000

1
P(X≤x)
.8
.6
.4
.2
0
0
10
20
30
40
50
x


Figure 2. Graph of the Poisson arrivals of customers serviced at Landbank-La
Trinidad (Cumulative Density Function)





Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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22

The Service Time of Customers Serviced
at Landbank-La Trinidad Benguet

Table 3 presents the summary for the number of customers serviced by the
teller of Landbank-La Trinidad who had either deposit, withdraw, update account
balances, exchange funds or pay BIR tax per one hour interval, the mean of the
customers serviced by the teller, the total number of customers who were serviced
and the over-all mean of the customers being served by the bank teller per day.
From Table 3 the time interval between 8:30-9:30 had the highest
customer serviced by the teller 1 and teller 2 with 18 and 13 customers serviced
per hour. It had also the highest over all total of 31 customers serviced per hour
by the two tellers. The over all mean of customers serviced per hour by the teller
is 14. This implies that from Table 1 the average number of arrivals per hour was
22 and from Table 3 the average number of customers that was served by the
bank teller per hour was 14. Thus, there was discrepancy between the arrivals of
customers per hour and the customer serviced by the bank teller per hour. This is
the reason for queueing. The time interval between 2:31-3:00 had the lowest
number of customers serviced by the Landbank-La Trinidad teller with 8
customers serviced per hour. This is because the time interval that was counted
was 30 minutes or 0.5 hours.



Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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23

Table 3. Summary of customers serviced per hour and service mean
HOUR INTERVAL TELLER 1 TELLER 2 SERVICED/HOUR
8:30-9:30 18 13 31
9:31-10:30 8 9 17
10:3-11:30 7 6 13
11:31-12:30 5 5 10
12:31-1:30 5 4 9
1:31-2:30 7 6 13
2:31-3:00 4 4 8
Over-all mean 14


Customers of Landbank-La Trinidad demanded different services. They
deposit, withdraw, update accounts, exchange funds, and pay BIR tax, thus the
teller’s service times varied. The exponential probability distribution was used to
describe the service time. The exponential probability distribution is defined by
t
f (x


)
e μ
μ −
=
for x ≥ 0 where μ = 14 and e = 2.71828. Table 4 presents the
exponential distribution for the service time thus, we would expect 75.34% of the
22 customers who arrived to be serviced in 6 minutes (t = 0.1), 93.92% of the
customers to be serviced at 12 minutes (t = 0.2), 98.50% of the customers to be
serviced at 18 minutes (t = 0.3), 99.63% of the customers to be serviced at 24
minutes (t = 0.4), 99.91% of the customers to be serviced at 32 minutes (t = 0.5),
99.98% of the customers to be serviced at 36 minutes (t = 0.6), 99.99% of the
customers to be serviced at 42 minutes (t = 0.7), 100% of the customers to be
serviced at 48 minutes (t = 0.8), 100% of the customers to be serviced at 54
minutes (t = 0.9), 100% of the customers to be serviced at 60 minutes (t = 1.0).
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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24

Figure 3 presents the graph for exponential of the service time of
Landbank-La Trinidad. As the value of the service time increases, the probability
of the customers being serviced also increases. Thus, it implies a positive
relationship between the service time and the probability of customers being
serviced.

Table 4. Service time distribution of assumed values of service time (in hours)
SERVICE TIME (IN HOURS) P ( st ≤ x)
0.1 0.7534
0.2 0.9392
0.3 0.9850
0.4 0.9963
0.5 0.9991
0.6 0.9998
0.7 0.9999
0.8 1.0000
0.9 1.0000
1.0 1.0000

Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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25

1
.95
p(st ≤ x)
.9
.85
.8
.75
0
.2
.4
.6
.8
1
x


Figure 3. Graph of the exponential service time of customers serviced at
Landbank-La Trinidad (Cumulative Density Function)


Operating Characteristics of Customers Serviced
at Landbank-La Trinidad, Benguet

Using the Poisson arrivals and exponential service times with identical
servers and a first in first out queue discipline, operating characteristics for the
multiserver single queue was presented in Table 5.
Table 5 presents the teller utilization rate which is the percentage of the
time a teller is busy. The total service rate must be greater than the arrival rate that
is kμ > λ. If kμ ≤ λ the average number of customers in the system (L) and the
average time a customer spends in the system (W) both become infinitely large. In
λ
Table 5, the utilization rate is clear, that the formula is applicable since the
< 1,
μ
k
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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26

thus the probability that the servers were busy is 79%. The probability that the
teller was idle is 12% which imply that the servers were free for 7.2 minutes upon
the start of the operation, thus most of the time the teller is busy. On the average,
there are 5 customers in the system. The average time a customer spends in the
system was 0.21 hour or 13 minutes. The average time a customer spends in the
queue before being served is 0.14 hours or 8 minutes. The average number of
customers in the waiting line was 3 and that 69% of the arriving customers had to
wait for the service.
Suppose we add another teller using the same arrival rate and service rate,
three identical servers and a first-in first-out queue discipline. Based on Table 5
the probability that the servers are busy is reduced from 79% to 52%. The
probability that the teller is idle increased from 12% (7.2 minutes) to 19% (11.4
minutes) which implies that teller is free at least 10.3 minutes. The average
number of customers in the system is reduced form 5 to 2. The average time a
customer spends in the system is reduced from 0.21 hours (13 minutes) to 0.08
hours (5 minutes). The average number of customers in the queue are reduced
from 3 to 0.27 and that the probability that arriving customers has to wait is
reduced from 69% to 26%. The result implies that an arriving customer will be
served directly or wait at least a minute or less.
The advantages are clear. The three-teller will greatly improve the
operating characteristics of the system.
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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27

Table 5. Economic analysis on the operating characteristics of the queuieng of
customers serviced at Landbank-La Trinidad, Benguet
Servers ρ=λ/kμ P(0) L W Lq Wq Pw
(k)
2 0.79 0.12 5 0.21 3 0.14 0.69
3 0.52 0.19 2 0.08 0.27 0.01 0.26


Legend:
ρ = probability that the teller is busy (utilization rate)
P(0) = probability that the teller is idle
L = average number of units in the system
W = the average time a unit spends in the system (waiting time + service)
Lq = the average number of units in the queue waiting for the service
Wq = the average time a unit spends in the queue waiting for service
Pw = the probability that an arriving customer has to wait for service













Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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28

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS


Summary
The study was conducted to determine the arrival distribution, the service
time distribution, the operating characteristics and the economic analysis of
customers serviced at Landbank-La Trinidad, Benguet. The respondents of the
study were the customers of Landbank-La Trinidad, Benguet who deposit,
withdraw, and update account balances, exchange funds and pay BIR tax. There
were 3116 customers who composed the respondents of the study.
The average number of customers who arrived at Landbank-La Trinidad,
Benguet were 22 customers/hour and the average customer that the teller can
serviced per hour were 14 customers, thus the discrepancy between the customers
arrivals and the number of customers serviced by the teller results to long queues
of customers.
In Landbank-La Trinidad customer arrivals were not scheduled and
occurred in an unpredictable manner, a random pattern appeared to exist. Thus to
determine the customer arrivals at Landbank-La Trinidad, the Poisson distribution
provides a good description of the arrival pattern. The Poisson probability
x e λ
λ −
distribution is defined as: P(X ≤ x) =
for x = 0, 1, 2,…….. where λ = 22
!
x
and e = 2.71828.
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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29

Customers of Landbank-La Trinidad demand different services. They
either deposit, withdraw, update accounts, exchange funds, pay BIR tax hence, the
teller’s service times vary. The exponential probability distribution was used to
describe the service time. The exponential probability distribution is defined by
t
f (x


)
e μ
μ −
=
for x ≥ 0 where μ = 14 and e = 2.71828.
Using the assumptions of Poisson arrival and exponential service time, a
first-come-first-served queue discipline and two identical servers, the operating
characteristics were computed. On the average, there were 5 customers in the
system (L); the average time a customer spends in the system is 13 minutes (W),
on the average, there were 3 customers in the queue waiting for the service (Lq),
the average time a unit spends in the queue waiting for service is 8 minutes (Wq)
and the probability that an arriving customer has to wait for service is 69% (Pw).
Adding another teller using the same arrival rate and service rate, three
identical servers and a first-in first-out queue discipline, On the average, the
number customers in the system was reduced from 5 to 2 (L); the average time a
customer spends in the system was reduced from 13 minutes to 5 minutes (W), on
the average 3 customers in the queue waiting for the service was reduced from
0.27 (Lq), the average time a unit spends in the queue waiting for service was
reduced from 8 minutes to 0.6 minutes (Wq) and the probability that an arriving
customer had to wait for service was reduced from 69% to 26% (Pw).
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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30

The advantages are clear. The three-teller system greatly improves the
operating characteristics of the system.

Conclusions

The arrival rate and service rate are the most important variables to be
considered in the analysis of queueing. It is the variability in arrival and service
patterns that causes the long queues of customers in the bank. They are used in
queueing formulas to compute the operating characteristics.
Based on the results of the operating characteristics of Landbank-La
Trinidad, Benguet, this indicates that customer wait an average of 0.21 hours or
13 minutes before being served. This appears to be undesirable. The fact that on
the average, there are 5 customers waiting in the line and that 69% of the arriving
customers have to wait for service are indicators that something should be done to
improve the efficiency of the bank teller of Landbank-La Trinidad.
Adding another teller improves the operating characteristics of the system;
based on the results of the operating characteristics, the advantages are clear that a
customer wait an average of 0.01 hours or 0.60 minutes. On the average, there are
2 customers waiting in line and that 26% of the arriving customer has to wait for
the service. Results of adding another teller greatly improves the operating
characteristics of the system.


Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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31

Recommendations
The results on the queuing analysis of customers serviced at Landbank-La
Trinidad may be utilized by the bank management and serve as basis on the need
to change the system to alter its performance. Since customer often link long
waits to poor quality service, types of changes can be made to the different
elements of waiting line system. In the arrival distribution of the customers at
Landbank-La Trinidad could be altered like running special promotions during the
non-peak times.
For the convenience of the customers in the queue, bank management can
improve its environment by installing water dispensers and news paper stands.
For service efficiency, the management could add more staff during peak times.
They may use especial counters for regular VIP clients and senior citizens. The
queue discipline or the priority rule can be altered like customers requiring short
service times will be the first to be serviced but the management must consider
the impact on those customers who will wait longer.
Lastly, management must consider the goal of having enough servers to
assure that waiting is within allowable limits. However cost effectiveness must be
considered before additional servers are hired.




Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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32

LITERATURE CITED


BANKS, J. and J.G. DAI. 1996. Simulation Studies of Multiclass Queueing
Networks. New York.

BOROVKOV, A.A.1980. Asymptotic Methods in Queueing Theory.

CHANG, W. 1970. “Single Server Queueing Processes in Computing Systems”.

IBM Systems Journal. New York: Wiley.

COHEN, J. W. 1989. Single Server Queue. North Holland, Amsterdam, New
York.

COX, D.R. and W. L. SMITH. 1963. Queues. New York: Wiley.

COOPER, R.B. 1981. Introduction to Queueing Theory. North Holland, New
York.

GARROPPO, R.G, GIORDANO, and S. M. PAGANO. 1998. Stochastic Traffic
Features and Queueing Working Conditions: A Simulation Study.

GROSS, and HARRIS.1998. Fundamentals of Queueing Theory.

KALASHNIKOV, V. V.1995. Mathematical Methods in Queueing Theory.

KENDALL, D. G. 1951. “Problems in the Theory of Queues”. Journal of the

Royal Statistical Society, Series B 13:151-85.

KLEINROCK, LEONARD. 1975. Queueing Systems Theory, Volume 1. New
York:
Wiley.

KRINIK A., G. RUBINO, D. MARCUS, R. SWIFT, H. KASFY, and H. LAM.
2005. “Dual Processes to Solve Single Server Systems”. Journal of
Statistical Planning and Inference Vol. 135.

LE NY L. M. 2005. Geometric Form Solution for a Two Class FIFO Queue with
Instantaneous Service for One Class. In Proceedings of the European
Simulation and Modeling Conference, Porto, Portugal

MOOD, A. M., F. A. GRAYBILL, and D. C. BOES.1993. Introduction to the
Theory of Statistics - 3rd Edition. McGraw-Hill,Milano.
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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33

NORROS, I. and VIRTAMO, J.2005. Importance Sampling Simulation Studies
on the Discrete Time N{D}/{D}/1 Queue. Finland.

PRAHBU, N. U.1965. Queues and Inventories. New York: Wiley.

SIGMAN. K. 2001. Queueing Course. Lecture Notes. Columbia University, New
York.

TANNER, M. 1995. Practical Queueing Analysis. New York, McGrow Hill.

















Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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34

APPENDIX A
Benguet State University
College of Arts and Sciences
MATH-PHYSICS-STATISTICS DEPARTMENT

December 11, 2007

Ms. Adeline M. Ramos
Manager
Landbank of the Philippines-La Trinidad
Benguet Branch

Ma’am:

Greetings!


The undersigned are conducting a thesis entitled “Analysis of Queueing of
Customers Serviced at Landbank La Trinidad, Benguet”. This is a partial
requirement in the degree Bachelor of Science in Applied Statistics.


In this connection, we would like to ask your permission to gather the necessary
data from your office, which includes the arrival time, service time and the
number of customers waiting at the teller windows from December 17-21, 2007
and January 7-11, 2008.

Your kind approval on this matter is highly appreciated. Rest assured that the data
gathered would be held confidential.

Thank you and more power.

Respectfully yours,

Melanie B. Menzi
Rhea B. Ngoaban

Noted By:

Ms. Marycel H. Toyhacao
Adviser

Maria Azucena B. Lubrica Ph. D
Chairman, MPS-Department
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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35

College of Arts and Sciences
MATH-PHYSICS-STATISTICS DEPARTMENT

APPLICATION FOR ORAL DEFENSE








Date:
March
17,
2008
Group Members:

Melanie B. Menzi
Major Field: Statistics

Rhea B. Ngoaban

Minor Field: Information Technology

Degree: Bachelor of Science in Applied Statistics

Title of Thesis: ANALYSIS OF QUEUEING OF CUSTOMERS SERVICED AT
LANDBANK-LA TRINIDAD, BENGUET.


Endorsed:
Marycel
H.
Toyhacao
Adviser

Date and Time of Defense: March 17, 2008 @ 4:00 pm
Place of Defense: CAS-An 210






Noted:

Maria
Azucena
B.
Lubrica,
Ph
D.



Department
Chairman

REPORT OF RESULT OF MANUSCRIPT/PROJECT DEFENSE
Name and Signature



Remarks*


Marycel H. Toyhacao








Adviser


Salvacion Z. Beligan








Member

Maria Azucena B. Lubrica







Member


Cristina B. Ocden









Member

*Passed/failed

Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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36

Appendix C. Raw Data

C1
C2
C3
C4 C5 C6 C1
C2
C3
C4 C5 C6
1 1 1 8:30 300 170 1 9 54 9:21 6442 624
1 1 2 8:30 430 50 1 9 55 9:21 6592 90
1 1 3 8:30 500 46 1 9 56 9:21 6720 172
1 1 4 8:30 574 51 1 9 57 9:24 7203 117
1 1 5 8:30 643 53 1 9 58 9:27 6636 147
1 1 6 8:30 710 115 1 9 59 9:27 6760 74
1 1 7 8:30 835 68 1 9 60 9:30 6034 77
1 1 8 8:30 887 362 1 9 61 9:32 6557 72
1 1 9 8:32 1185 62 1 9 62 9:36 6365 338
1 1 10 8:32 1123 62 1 9 63 9:37 7047 136
1 1 11 8:32 1181 64 1 9 64 9:39 6671 71
1 1 12 8:32 1237 67 1 9 65 9:44 6480 111
1 1 13 8:32 1290 57 1 9 66 9:45 6489 153
1 1 14 8:34 1233 93 1 9 67 9:46 6636 119
1 1 15 8:34 1320 74 1 9 68 9:46 6757 57
1 1 16 8:34 1426 65 1 9 69 9:51 6520 318
1 1 17 8:36 1361 655 1 9 70 9:55 6562 33
1 1 18 8:36 1620 66 1 9 71 10:09 6289 341
1 1 19 8:37 1669 130 1 9 72 10:14 5768 60
1 1 20 8:37 1779 72 1 9 73 10:22 5348 153
1 1 21 8:40 1647 31 1 9 74 10:22 5555 206
1 1 22 8:42 1088 58 1 9 75 10:24 5589 236
1 1 23 8:42 1620 51 1 9 76 10:34 5233 154
1 1 24 8:44 1509 58 1 9 77 10:38 5199 200
1 1 25 8:44 1571 64 1 9 78 10:38 5359 128
1 1 26 8:46 1507 48 1 9 79 10:49 4811 165
1 1 27 8:46 1579 114 1 9 80 10:51 4866 51
1 1 28 8:47 2280 52 1 9 81 10:55 4695 219
1 1 29 8:49 1593 62 1 9 82 10:56 4896 86
1 1 30 9:00 931 36 1 9 83 11:01 4630 97
1 1 31 9:01 960 55 1 9 84 11:12 4113 428
1 1 32 9:02 960 57 1 9 85 11:13 4467 142
1 1 33 9:04 843 75 1 9 86 11:17 4323 138
1 1 34 9:09 708 137 1 9 87 11:18 4485 136
1 1 35 9:09 811 108 1 9 88 11:24 4229 170
1 1 36 9:10 943 74 1 9 89 11:36 3699 74
1 1 37 9:11 929 55 1 9 90 11:46 3145 306


Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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37

1 1 37 9:11 929 55 1 9 90 11:46 3145 306
1 1 38 9:12 934 61 1 9 91 11:56 2849 73
1 1 39 9:15 900 79 1 9 92 12:00 2646 54
1 1 40 9:15 1001 62 1 9 93 12:43 132 53
1 1 41 9:18 960 75 1 9 94 12:43
199 51
1 1 42 9:18 1055 51 1 9 95 12:45 148 79
1 1 43 9:21 944 63 1 9 96 12:59 0
117
1 1 44 9:21 1001 248 1 9 97 1:02 0
218
1 1 45 9:23 1113 56 1 9 98 1:04 0
162
1 1 46 9:23 1177 83 1 9 99 1:05 120 178
1 1 47 9:24 1154 182 1 9 100 1:07 360 85
1 1 48 9:24 1392 48 1 9 101 1:09 335 61
1 1 49 9:26 1344 75 1 9 102 1:13 174 45
1 1 50 9:27 1869 42 1 9 103 1:13 229 103
1 1 51 9:28 1887 56 1 9 104 1:15 120 189
1 1 52 9:32 1951 56 1 9 105 1:16 240 149
1 1 53 9:33 1715 51 1 9 106 1:22 91 151
1 1 54 9:34 1724 65 1 9 107 1:24 60 60
1 1 55 9:34 1839 159 1 9 108 1:29 0
150
1 1 56 9:36 1860 130 1 9 109 2:08 560 42
1 1 57 9:37 1970 64 1 9 110 2:09 578 127
1 1 58 9:37 2026 242 1 9 111 2:11 91 109
1 1 59 9:40 2084 72 1 9 112 2:12 600 30
1 1 60 9:41 2072 66 1 9 113 2:14 492 192
1 1 61 9:44 1946 67 1 9 114 2:15 540 81
1 1 62 9:44 1999 37 1 9 115 2:16 579 59
1 1 63 9:48 1842 144 1 9 116 2:19 460 117
1 1 64 9:49 1878 48 1 9 117 2:22 427 69
1 1 65 9:52 1770 42 1 9 118 2:29 629 89
1 1 66 9:52 1800 275 1 9 119 2:36 1200 41
1 1 67 9:55 1813 86 1 9 120 2:42 1200 60
1 1 68 9:55 1967 50 1 9 121 2:44 1200 41
1 1 69 10:05 1380 53 1 9 122 2:56 499 139
1 1 70 10:05 1864 44 1 9 123 3:02 600 88
1 1 71 10:06 1400 51 1 9 124 3:12 92 212
1 1 72 10:06 1469 42 1 10 1 8:30 360 108
1 1 73 10:17 1007 71 1 10 2 8:30 432 174
1 1 74 10:18 996 207 1 10 3 8:30 618 68
1 1 75 10:20 1029 47 1 10 4 8:30 670 185
1 1 76 10:23 922 40 1 10 5 8:30 845 209
1 1 77 10:26 822 67 1 10 6 8:30 1116 202
1 1 78 10:28 755 84 1 10 7 8:30 1274 186
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
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38

1 1 79 10:29 731 50 1 10 8 8:30 1448 105
1 1 80 10:31 681 159 1 10 9 8:30 1583 323
1 1 81 10:31 863 66 1 10 10 8:30 1920 174
1 1 82 10:33 797 31 1 10 11 8:30 2046 43
1 1 83 10:33 840 67 1 10 12 8:30 2123 263
1 1 84 10:35 780 50 1 10 13 8:36 2040 129
1 1 85 10:40 483 44 1 10 14 8:40 1940 51
1 1 86 10:44 319 30 1 10 15 8:47 1560 60
1 1 87 10:44 409 87 1 10 16 8:53 1320 146
1 1 88 10:44 442 70 1 10 17 8:57 1294 173
1 1 89 10:44 432 34 1 10 18 9:04 1020 41
1 1 90 10:44 518 38 1 10 19 9:04 1080 79
1 1 91 10:46 420 42 1 10 20 9:09 881 57
1 1 92 10:46 396 63 1 10 21 9:12 764 236
1 1 93 10:46 495 20 1 10 22 9:12 1008 248
1 1 94 10:46 540 169 1 10 23 9:13 1060 145
1 1 95 10:50 486 106 1 10 24 9:19 795 135
1 1 96 10:50 620 34 1 10 25 9:19 960 95
1 1 97 10:50 706 160 1 10 26 9:21 925 85
1 1 98 10:55 486 55 1 10 27 9:21 1020 216
1 1 99 10:55 611 162 1 10 28 9:35 444 182
1 1 100
10:58 749 58 1 10 29 9:37 502 53
1 1 101
10:58 780 31 1 10 30 9:39 449 40
1 1 102
10:58 840 110 1 10 31 9:39 469 215
1 1 103
11:00 785 20 1 10 32 9:40 614 103
1 1 104
11:00 240 46 1 10 33 9:40 631 211
1 1 105
11:00 233 53 1 10 34 9:42 720 224
1 1 106
11:05 622 65 1 10 35 9:45 796 285
1 1 107
11:06 617 51 1 10 36 9:48 927 59
1 1 108
11:10 446 98 1 10 37 9:49 868 37
1 1 109
11:10 588 85 1 10 38 9:51 831 111
1 1 110
11:15 323 83 1 10 39 9:53 600 115
1 1 111
11:15 480 60 1 10 40 9:58 605 108
1 1 112
11:16 960 105 1 10 41 9:59 677 159
1 1 113
11:20
795 36 1 10 42 10:00
878 75
1 1 114
11:20
879 81 1 10 43 10:00
863 107
1 1 115
11:20
918 92 1 10 44 10:01
936 96
1 1 116 11:22 946 46 1 10 45 10:02 1029 93
1 1 117 11:25 720 108 1 10 46 10:04 1056 78
1 1 118 11:28 1130 146 1 10 47 10:06 858 119
1 1 119
11:30
672 36 1 10 48 10:10
799 191
1 1 120
11:32
636 83 1 10 49 10:13
968 89
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

39

1 1 121 11:34 553 53 1 10 50 10:14 1059 51
1 1 122 11:34 620 55 1 10 51 10:14 1128 104
1 1 123 11:34 685 52 1 10 52 10:16 1024 64
1 1 124 11:34 753 51 1 10 53 10:18 1020 120
1 1 125
11:36
702 47 1 10 54 10:21
987 83
1 1 126
11:38
600 50 1 10 55 10:22
964 44
1 1 127
11:40
485 74 1 10 56 10:25
860 65
1 1 128
11:40
651 67 1 10 57 10:29
675 296
1 1 129
11:42
584 65 1 10 58 10:32
799 118
1 1 130
11:45
459 49 1 10 59 10:35
741 582
1 1 131 11:47 410 79 1 10 60 10:36 1299 72
1 1 132 11:50 271 63 1 10 61 10:39 1167 319
1 1 133 11:50 328 51 1 10 62 10:42 1268 55
1 1 134 11:50 397 54 1 10 63 10:42 1325 223
1 1 135 11:52 343 137 1 10 64 10:49 1151 107
1 1 136 11:55 266 111 1 10 65 10:53 1044 204
1 1 137 11:57 275 47 1 10 66 10:53 1260 174
1 1 138 11:57 348 304 1 10 67 10:56 1206 59
1 1 139 12:00 464 68 1 10 68 10:56 1267 169
1 1 140 12:04 276 73 1 10 69 10:58 1338 88
1 1 141 12:05 263 51 1 10 70 11:00 1350 422
1 1 142 12:07 212 73 1 10 71 11:06 1408 305
1 1 143 12:07 259 51 1 10 72 11:12 1343 65
1 1 144 12:10 148 237 1 10 73 11:13 1338 898
1 1 145 12:10 391 123 1 10 74 11:14 2180 161
1 1 146 12:53 914 74 1 10 75 11:18 2139 250
1 1 147 12:54 1041 57 1 10 76 11:19 2309 62
1 1 148 1:01 684 45 1 10 77 11:22 2182 362
1 1 149 1:02 699 80 1 10 78 11:27 2540 380
1 1 150 1:05 578 190 1 10 79 11:34 2601 141
1 1 151 1:07 609 174 1 10 80 12:22 0
60
1 1 152 1:10 675 106 1 10 81 12:24 60 89
1 1 153 1:11 749 58 1 10 82 12:31 0
71
1 1 154 1:13 751 169 1 10 83 12:38 0
203
1 1 155
1:13 942 74 1 10 84 12:40
281 47
1 1 156
1:13 988 188 1 10 85 12:40
334 67
1 1 157 1:16 980 169 1 10 86 12:45 97 171
1 1 158
1:20 931 31 1 10 87 12:46
226 64
1 1 159 1:23 721 42 1 10 88 12:54 0
136
1 1 160
1:26 619 117 1 10 89 12:55
104 84
1 1 161 1:26 742 40 1 10 90 12:56 80 55
1 1 162
1:26 822 122 1 10 91 12:56
145 56
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

40

1 1 163
1:26 940 125 1 10 92 12:57
149 34
1 1 164
1:26 1055 127 1 10 93 1:00 0
58
1 1 165
1:27 1108 78 1 10 94 1:01 0
57
1 1 166
1:29 1030 61 1 10 95 1:01 60 136
1 1 167
1:29 1089 98 1 10 96 1:02 164 44
1 1 168
1:29 1231 71 1 10 97 1:03 120 170
1 1 169
1:30 1220 65 1 10 98 1:04 190 322
1 1 170
1:30 1275 178 1 10 99 1:05 528 63
1 1 171
1:31 1397 53 1 10 100
1:08 465 285
1 1 172
1:32 1404 404 1 10 101
1:20 0
141
1 1 173
1:32 1840 44 1 10 102
1:20 159 159
1 1 174
1:33 1803 50 1 10 103
1:20 300 270
1 1 175
1:33 1806 101 1 10 104
1:42 696 96
1 1 176
1:50 925 111 1 10 105
1:43 780 46
1 1 177
1:50 1054 63 1 10 106
1:46 614 125
1 1 178
1:51 1051 126 1 10 107
1:52 369 230
1 1 179
1:52 1105 470 1 10 108
1:59 199 79
1 1 180
1:54 1475 121 1 10 109
2:05 0
74
1 1 181
1:54 1594 177 1 10 110
2:07 0
262
1 1 182
1:56 1777 78 1 10 111
2:53 0
180
1 1 183 2:00 1459 57 2 1 1 8:30 0
142
1 1 184 2:03 1342 65 2 1 2 8:30 148 109
1 1 185 2:04 1337 143 2 1 3 8:30 279 48
1 1 186 2:05 1440 49 2 1 4 8:30 360 76
1 1 187 2:05 1445 79 2 1 5 8:30 464 121
1 1 188 2:05 1560 76 2 1 6 8:30 720 133
1 1 189 2:07 1590 135 2 1 7 8:30 887 61
1 1 190 2:09 1575 54 2 1 8 8:30 946 132
1 1 191 2:10 1581 33 2 1 9 8:30 1054 75
1 1 192 2:12 1548 50 2 1 10 8:30 1099 370
1 1 193 2:13 1500 57 2 1 11 8:32 1380 71
1 1 194 2:26 721 37 2 1 12 8:32 1489 58
1 1 195 2:27 744 46 2 1 13 8:32 1791 238
1 1 196 2:32 518 94 2 1 14 8:32 1793 71
1 1 197 2:35 364 52 2 1 15 8:32 1842 63
1 1 198 2:38 252 51 2 1 16 8:34 1779 56
1 1 199 2:40 201 108 2 1 17 8:34 1843 70
1 1 200 2:44 93 304 2 1 18 8:36 1773 66
1 1 201 2:44 449 69 2 1 19 8:36 1827 63
1 1 202 2:45 440 90 2 1 20 8:37 1824 105
1 1 203 2:46 360 42 2 1 21 8:37 1959 70
1 1 204 2:48 368 25 2 1 22 8:40 1829 80
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

41

1 1 205 2:48 463 69 2 1 23 8:42 1749 545
1 1 206 2:49 454 79 2 1 24 8:44 2164 89
1 1 207 2:50 435 116 2 1 25 8:44 2315 70
1 1 208 2:52 439 58 2 1 26 8:46 2245 97
1 1 209 2:53 441 57 2 1 27 8:46 2388 74
1 1 210 2:54 444 43 2 1 28 8:47 2434 84
1 1 211 2:55 521 380 2 1 29 8:47 2470 149
1 1 212 2:58 681 237 2 1 30 8:49 2561 45
1 1 213 2:59 864 42 2 1 31 9:00 1976 113
1 2 1 8:30 582 60 2 1 32 9:00 1983 73
1 2 2 8:30 642 73 2 1 33 9:01 2090 64
1 2 3 8:30 689 65 2 1 34 9:04 1966 153
1 2 4 8:30 744 51 2 1 35 9:04 2066 119
1 2 5 8:30 813 113 2 1 36 9:09 1874 47
1 2 6 8:30 940 146 2 1 37 9:09 2127 106
1 2 7 8:30 1034 65 2 1 38 9:11 2220 60
1 2 8 8:30 1089 35 2 1 39 9:12 2940 142
1 2 9 8:30 1164 77 2 1 40 9:14 2978 64
1 2 10 8:30 1217 54 2 1 41 9:15 2974 135
1 2 11 8:30 1283 40 2 1 42 9:16 3011 123
1 2 12 8:30 1363 65 2 1 43 9:18 3120 80
1 2 13 8:30 1418 100 2 1 44 9:18 3220 132
1 2 14 8:30 1500 49 2 1 45 9:21 3148 351
1 2 15 8:30 1509 23 2 1 46 9:23 3397 147
1 2 16 8:30 1606 64 2 1 47 9:23 3490 291
1 2 17 8:30 1620 50 2 1 48 9:24 3739 126
1 2 18 8:30 1630 14 2 1 49 9:26 3733 24
1 2 19 8:30 1680 56 2 1 50 9:26 3829 78
1 2 20 8:30 1740 200 2 1 51 9:28 3751 82
1 2 21 8:30 2020 102 2 1 52 9:29 3729 155
1 2 22 8:30 2100 56 2 1 53 9:33 3694 135
1 2 23 8:30 2102 279 2 1 54 9:34 3739 31
1 2 24 8:30 2423 115 2 1 55 9:34 3828 86
1 2 25 8:30 2548 372 2 1 56 9:35 3802 39
1 2 26 8:30 2896 54 2 1 57 9:36 3780 36
1 2 27 8:31 2902 49 2 1 58 9:37 3744 39
1 2 28 8:31 2973 63 2 1 59 9:41 3585 66
1 2 29 8:32 2970 42 2 1 60 9:44 3420 36
1 2 30 8:32 3048 64 2 1 61 9:44 3444 27
1 2 31 8:33 3044 166 2 1 62 9:48 3297 71
1 2 32 8:34 3178 86 2 1 63 9:49 3286 75
1 2 33 8:35 3152 133 2 1 64 9:49 3331 45
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

42

1 2 34 8:37 3139 52 2 1 65 9:52 3300 73
1 2 35 8:37 3207 53 2 1 66 9:52 3360 26
1 2 36 8:38 3214 61 2 1 67 9:55 3214 55
1 2 37 8:39 3213 52 2 1 68 9:56 3339 46
1 2 38 8:42 3161 85 2 1 69 10:05 3353 144
1 2 39 8:42 3196 49 2 1 70 10:05 3449 116
1 2 40 8:47 2967 48 2 1 71 10:06 2893 35
1 2 41 8:47 3039 69 2 1 72 10:16 2398 70
1 2 42 8:49 2198 72 2 1 73 10:17 2460 183
1 2 43 8:50 2958 105 2 1 74 10:20 2517 626
1 2 44 8:51 2553 65 2 1 75 10:23 2911 133
1 2 45 8:52 3028 6 2 1 76 10:23 3018 55
1 2 46 8:54 2967 80 2 1 77 10:28 2783 52
1 2 47 9:01 2587 84 2 1 78 10:29 2791 62
1 2 48 9:02 2683 91 2 1 79 10:29 2849 115
1 2 49 9:03 2652 46 2 1 80 10:30 2914 135
1 2 50 9:09 2366 44 2 1 81 10:31 2959 174
1 2 51 9:11 2322 52 2 1 82 10:33 3025 49
1 2 52 9:13 3830 81 2 1 83 10:33 3096 47
1 2 53 9:15 2189 195 2 1 84 10:40 2749 85
1 2 54 9:17 2234 72 2 1 85 10:41 2724 51
1 2 55 9:18 2522 66 2 1 86 10:44 2613 434
1 2 56 9:21 2460 51 2 1 87 10:44 3019 36
1 2 57 9:22 2405 44 2 1 88 10:55 3060 79
1 2 58 9:24 2361 54 2 1 89 11:15 3180 69
1 2 59 9:25 2367 129 2 1 90 12:00 591 247
1 2 60 9:26 2418 184 2 1 91 12:04 584 143
1 2 61 9:29 2414 35 2 1 92 12:05 681 403
1 2 62 9:29 2499 48 2 1 93 12:10 780 213
1 2 63 9:30 2460 44 2 1 94 12:15 840 110
1 2 64 9:32 2356 61 2 1 95 12:18 2880 19
1 2 65 9:34 2295 122 2 1 96 12:20 665 82
1 2 66 9:35 2353 37 2 1 97 12:25 449 188
1 2 67 9:36 2376 36 2 1 98 12:27 501 34
1 2 68 9:39 2280 112 2 1 99 12:30 377 118
1 2 69 9:43 2108 41 2 1 100 12:32 379 35
1 2 70 9:44 2127 49 2 1 101 12:33 404 64
1 2 71 9:49 1898 40 2 1 102 12:33 460 80
1 2 72 9:51 1858 59 2 1 103 12:34 440 85
1 2 73 9:56 1619 77 2 1 104 12:35 535 72
1 2 74 9:58 1542 55 2 1 105 12:42 240 81
1 2 75 10:00 1487 107 2 1 106 12:44 360 155
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

43

1 2 76 10:03 1440 47 2 1 107 12:46 385 66
1 2 77 10:06 1273 39 2 1 108 12:51 199 227
1 2 78 10:07 1294 36 2 1 109 12:51 420 122
1 2 79 10:08 1318 73 2 1 110 12:53 540 43
1 2 80 10:09 1305 111 2 1 111 12:54 660 91
1 2 81 10:13 1140 42 2 1 112 1:01 329 65
1 2 82 10:13 1218 108 2 1 113 1:05 144 153
1 2 83 10:19
990 52 2 1 114
1:34 780 50
1 2 84 10:19 1058 62 2 1 115 1:36 670 30
1 2 85 10:20 1056 67 2 1 116 1:37 700 171
1 2 86 10:23
929 68 2 1 117
1:40 709 85
1 2 87 10:26
801 196 2 1 118
1:40 744 100
1 2 88 10:29
845 60 2 1 119
1:41 769 44
1 2 89 10:31
785 39 2 1 120
1:41 780 53
1 2 90 10:35
600 51 2 1 121
1:42 773 105
1 2 91 10:37
489 69 2 1 122
1:42 900 42
1 2 92 10:37
600 105 2 1 123
1:43 858 54
1 2 93 10:40
555 159 2 1 124
1:43 924 358
1 2 94 10:41 696 242 2 1 125 1:44 1226 227
1 2 95 10:42 874 303 2 1 126 1:48 1239 50
1 2 96 10:44 1051 119 2 1 127 1:49 1249 29
1 2 97 10:46 1052 42 2 1 128 2:00 571 31
1 2 98 10:49
950 75 2 1 129
2:00 649 49
1 2 99 10:51
845 35 2 1 130
2:01 600 47
1 2 100
10:53
780 30 2 1 131
2:02 553 506
1 2 101 10:55 690 150 2 1 132 2:03 1067 47
1 2 102
10:57
720 80 2 1 133
2:05 960 76
1 2 103 10:58 760 138 2 1 134 2:05 1064 317
1 2 104 10:59 802 55 2 1 135 2:06 1287 193
1 2 105
11:00
801 61 2 1 136
2:14 974 349
1 2 106 11:02 746 67 2 1 137 2:18 1105 66
1 2 107
11:05
619 171 2 1 138
2:21 979 58
1 2 108 11:07 622 82 2 1 139 2:22 1020 76
1 2 109
11:12
420 84 2 1 140
2:29 704 89
1 2 110
11:14
396 58 2 1 141
2:30 720 457
1 2 111 11:14 458 75 2 1 142 2:32 1043 101
1 2 112 11:16 383 53 2 1 143 2:35 1020 118
1 2 113 11:18 300 30 2 1 144 2:37 1020 79
1 2 114
11:19
300 20 2 1 145
2:44 691 41
1 2 115
11:20
240 40 2 1 146
2:45 619 63
1 2 116
11:20
300 106 2 1 147
2:45 676 114
1 2 117
11:22
314 119 2 1 148
2:45 802 34
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

44

1 2 118
11:22
435 97 2 1 149
2:46 828 56
1 2 119
11:24
458 60 2 1 150
2:48 772 104
1 2 120
11:27
300 38 2 1 151
2:48 788 23
1 2 121
11:29
240 116 2 1 152
2:49 825 64
1 2 122
11:30
304 104 2 1 153
2:51 761 61
1 2 123
11:31
380 69 2 1 154
2:52 760 152
1 2 124
11:31
431 71 2 1 155
2:53 788 253
1 2 125 11:33 420 94 2 1 156 2:54 1075 66
1 2 126 11:34 446 67 2 1 157 2:57 1020 53
1 2 127 11:35 439 48 2 1 158 2:57 1027 144
1 2 128
11:37
391 36 2 2 1 8:30 120 259
1 2 129
11:37
475 75 2 2 2 8:30 401 132
1 2 130
11:37
520 190 2 2 3 8:30 509 68
1 2 131
11:39
600 235 2 2 4 8:35 261 62
1 2 132
11:39
785 20 2 2 5 8:35 319 54
1 2 133
11:42
660 45 2 2 6 8:36 325 36
1 2 134
11:43
600 127 2 2 7 8:37 600 60
1 2 135
11:45
673 133 2 2 8 8:39 540 45
1 2 136
11:47
720 36 2 2 9 8:39 555 390
1 2 137
11:49
624 61 2 2 10 8:41 845 61
1 2 138
11:50
623 111 2 2 11 8:42 884 140
1 2 139
11:51
692 118 2 2 12 8:42 984 54
1 2 140
11:53
694 196 2 2 13 8:44 900 23
1 2 141
11:54
798 219 2 2 14 8:47 727 107
1 2 142
11:55
999 39 2 2 15 8:47 860 119
1 2 143
11:59
780 51 2 2 16 8:48 921 50
1 2 144
11:59
789 45 2 2 17 8:49 931 172
1 2 145
12:00
324 34 2 2 18 8:52 939 298
1 2 146 12:02 885 132 2 2 19 8:53 1500 87
1 2 147 12:04 873 38 2 2 20 8:53 1593 171
1 2 148 12:05 840 50 2 2 21 8:54 1722 71
1 2 149 12:06 785 85 2 2 22 8:56 1651 346
1 2 150 12:06 940 60 2 2 23 8:56 1980 45
1 2 151 12:10 760 50 2 2 24 8:59 1860 161
1 2 152 12:14 540 47 2 2 25 9:00 1939 185
1 2 153 12:15 540 99 2 2 26 9:03 1934 74
1 2 154 12:17 501 168 2 2 27 9:03 2640 194
1 2 155 12:19 573 113 2 2 28 9:04 3300 103
1 2 156 12:20 640 75 2 2 29 9:09 2760 135
1 2 157 12:22 565 72 2 2 30 9:11 4020 84
1 2 158 12:22 613 52 2 2 31 9:15 4020 104
1 2 159 12:24 561 26 2 2 32 9:17 3978 113
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

45

1 2 160 12:30 295 229 2 2 33 9:19 3983 41
1 2 161 12:31 366 92 2 2 34 9:21 3942 151
1 2 162 12:33 394 66 2 2 35 9:25 3791 462
1 2 163 12:36 240 28 2 2 36 9:27 4169 486
1 2 164 12:36 300 82 2 2 37 9:28 4583 51
1 2 165 12:41 98 38 2 2 38 9:30 4532 43
1 2 166 12:41 120 42 2 2 39 9:33 4429 333
1 2 167 1:13 540 125 2 2 40 9:37 4456 253
1 2 168 1:22 120 50 2 2 41 9:38 4623 57
1 2 169 1:22 125 41 2 2 42 9:40 4566 38
1 2 170 1:23 144 111 2 2 43 9:46 4288 347
1 2 171 1:23 273 41 2 2 44 9:54 4181 90
1 2 172 1:24 292 67 2 2 45 10:00 3851 242
1 2 173 1:27 120 43 2 2 46 10:07 3720 73
1 2 174 1:28 62 57 2 2 47 10:42 1727 62
1 2 175 1:30 0
30 2 2 48 10:44 1665 145
1 2 176 1:35 0
91 2 2 49 10:51 980 98
1 2 177 1:38 0
60 2 2 50 10:52 1384 27
1 2 178 1:42 0
96 2 2 51 10:54 1357 67
1 2 179 1:42 84 65 2 2 52 10:57 1230 110
1 2 180 1:42 139 62 2 2 53 10:57 1360 420
1 2 181 1:42 197 77 2 2 54 10:59 1660 58
1 2 182 1:47 0
112 2 2 55 11:00 1662 92
1 2 183 1:47 68 68 2 2 56 11:14 850 93
1 2 184
1:48 120 30 2 2 57 11:16
840 1557
1 2 185 1:54 0
96 2 2 58 11:24 1867 75
1 2 186 1:54 84 84 2 2 59 11:27 1860 75
1 2 187 1:56 60 180 2 2 60 11:33 1605 65
1 2 188 1:58 120 60 2 2 61 11:44 1000 43
1 2 189
2:02 180 88 2 2 62 11:50
717 87
1 2 190
2:03 212 74 2 2 63 11:53
570 151
1 2 191
2:04 198 56 2 2 64 11:59
419 77
1 2 192
2:05 202 351 2 2 65 11:59
462 82
1 2 193
2:07 391 145 2 2 66 12:00
660 297
1 2 194
2:09 366 57 2 2 67 12:00
960 72
1 2 195 2:13 189 91 2 2 68 12:02 1020 40
1 2 196
2:15 218 428 2 2 69 12:05
728 199
1 2 197
2:15 630 194 2 2 70 12:06
949 61
1 2 198
2:18 612 106 2 2 71 12:16
408 116
1 2 199
2:18 720 30 2 2 72 12:18
412 347
1 2 200
2:22 540 79 2 2 73 12:20
600 185
1 2 201
2:28 244 91 2 2 74 12:24
595 286
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

46

1 2 202
2:29 300 33 2 2 75 12:25
780 63
1 2 203
2:31 240 56 2 2 76 12:27
773 58
1 2 204
2:32 184 54 2 2 77 12:30
655 113
1 2 205
2:32 250 51 2 2 78 12:34
480 62
1 2 206
2:32 309 91 2 2 79 12:35
538 100
1 2 207
2:36 216 98 2 2 80 12:35
558 38
1 2 208
2:37 300 95 2 2 81 12:36
580 62
1 2 209
2:37 385 67 2 2 82 12:36
638 96
1 2 210
2:38 378 56 2 2 83 12:38
542 71
1 2 211 2:44 82 67 2 2 84 12:39 660 177
1 2 212
2:44 135 75 2 2 85 12:41
663 36
1 2 213
2:46 120 60 2 2 86 12:42
687 50
1 2 214
2:43 120 69 2 2 87 12:47
540 60
1 2 215
2:47 180 31 2 2 88 12:48
540 84
1 2 216 2:50 0
53 2 2 89 12:49 576 38
1 2 217 2:51 0
774 2 2 90 12:49 600 58
1 2 218
2:51 180 107 2 2 91 12:50
600 115
1 2 219
2:52 133 307 2 2 92 12:54
365 55
1 2 220
2:52 426 210 2 2 93 12:55
430 186
1 2 221
2:53 636 279 2 2 94 12:56
600 83
1 2 222 2:53 957 78 2 2 95 12:58 57 100
1 3 1 8:30 539 119 2 2 96 1:00 597 114
1 3 2 8:30 600 60 2 2 97 1:00 660 50
1 3 3 8:30 720 44 2 2 98 1:01 610 63
1 3 4 8:30 736 76 2 2 99 1:04 487 133
1 3 5 8:30 840 116 2 2 100
1:07 534 61
1 3 6 8:30 904 64 2 2 101
1:08 533 76
1 3 7 8:30 1020 24 2 2 102 1:09 517 112
1 3 8 8:30 1056 96 2 2 103 1:13 405 121
1 3 9 8:30 1140 55 2 2 104 1:21 0
364
1 3 10 8:30 1145 65 2 2 105 1:38 0
116
1 3 11 8:30 1260 159 2 2 106 1:41 0
91
1 3 12 8:30 1401 81 2 2 107 2:22 900 417
1 3 13 8:30 1680 60 2 2 108 2:26 1080 165
1 3 14 8:30 1740 50 2 2 109 2:31 960 106
1 3 15 8:30 1750 48 2 2 110 2:36 734 234
1 3 16 8:30 1822 49 2 2 111 2:37 1020 66
1 3 17 8:30 1860 30 2 2 112 2:44 720 85
1 3 18 8:30 1863 23 2 2 113 2:47 635 393
1 3 19 8:30 1920 34 2 2 114 2:53 660 396
1 3 20 8:30 1926 83 2 3 1 8:30 480 79
1 3 21 8:30 2083 49 2 3 2 8:30 581 117
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

47

1 3 22 8:30 2100 49 2 3 3 8:30 660 36
1 3 23 8:30 2105 41 2 3 4 8:34 428 84
1 3 24 8:30 2184 47 2 3 5 8:36 600 46
1 3 25 8:31 2197 42 2 3 6 8:36 780 141
1 3 26 8:33 2100 52 2 3 7 8:37 279 50
1 3 27 8:33 2103 46 2 3 8 8:45 420 91
1 3 28 8:33 2177 22 2 3 9 8:49 360 46
1 3 29 8:33 2220 53 2 3 10 8:50 314 112
1 3 30 8:33 2222 37 2 3 11 8:50 480 192
1 3 31 8:34 2245 34 2 3 12 8:53 1140 77
1 3 32 8:34 2280 48 2 3 13 8:53 1243 74
1 3 33 8:34 2283 24 2 3 14 8:57 1049 110
1 3 34 8:34 2340 35 2 3 15 8:58 1119 157
1 3 35 8:35 2284 244 2 3 16 8:58 1208 214
1 3 36 8:35 2520 151 2 3 17 8:59 1440 258
1 3 37 8:36 2609 75 2 3 18 8:59 1860 177
1 3 38 8:36 2654 64 2 3 19 8:59 2040 147
1 3 39 8:36 2710 49 2 3 20 8:59 2193 749
1 3 40 8:36 2781 58 2 3 21 9:00 2880 235
1 3 41 8:37 2963 143 2 3 22 9:00 3065 94
1 3 42 8:37 3120 81 2 3 23 9:01 3271 67
1 3 43 8:39 3099 73 2 3 24 9:01 3780 100
1 3 44 8:39 3146 131 2 3 25 9:02 3800 90
1 3 45 8:39 3255 107 2 3 26 9:02 3950 70
1 3 46 8:40 3328 81 2 3 27 9:06 4480 55
1 3 47 8:40 3367 97 2 3 28 9:06 3825 110
1 3 48 8:40 3510 192 2 3 29 9:13 3535 77
1 3 49 8:42 3558 138 2 3 30 9:13 3578 562
1 3 50 8:42 3720 40 2 3 31 9:13 4091 50
1 3 51 8:42 3740 44 2 3 32 9:14 4101 41
1 3 52 8:43 3756 46 2 3 33 9:14 4180 448
1 3 53 8:43 3830 71 2 3 34 9:18 4332 57
1 3 54 8:44 3819 41 2 3 35 9:19 4335 102
1 3 55 8:44 3898 92 2 3 36 9:21 4353 78
1 3 56 8:44 3926 124 2 3 37 9:21 4440 107
1 3 57 8:45 3982 52 2 3 38 9:23 4393 122
1 3 58 8:46 3990 68 2 3 39 9:24 4451 86
1 3 59 8:46 4042 1159 2 3 40 9:25 4545 334
1 3 60 8:47 5103 88 2 3 41 9:26 4751 66
1 3 61 8:48 5195 123 2 3 42 9:27 4745 112
1 3 62 8:50 5192 34 2 3 43 9:28 4813 115
1 3 63 8:51 5213 353 2 3 44 9:28 4932 621
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

48

1 3 64 8:58 5100 159 2 3 45 9:29 5631 81
1 3 65 8:59 5181 36 2 3 46 9:30 5610 78
1 3 66 8:59 5265 60 2 3 47 9:31 5592 32
1 3 67 9:03 5085 255 2 3 48 9:31 5680 250
1 3 68 9:04 5250 116 2 3 49 9:31 5910 110
1 3 69 9:04 5340 34 2 3 50 9:31 6040 55
1 3 70 9:05 5366 136 2 3 51 9:32 6045 93
1 3 71 9:05 5470 130 2 3 52 9:32 6072 75
1 3 72 9:07 5520 47 2 3 53 9:32 6180 42
1 3 73 9:07 5533 73 2 3 54 9:35 6015 312
1 3 74 9:08 5580 49 2 3 55 9:37 6183 248
1 3 75 9:08 5591 45 2 3 56 9:37 6595 75
1 3 76 9:09 5606 52 2 3 57 9:38 6580 65
1 3 77 9:10 5614 36 2 3 58 9:38 6635 64
1 3 78 9:10 5698 107 2 3 59 9:39 7111 40
1 3 79 9:11 5651 191 2 3 60 9:40 6651 94
1 3 80 9:11 5880 105 2 3 61 9:42 6557 302
1 3 81 9:15 5715 102 2 3 62 9:44 6735 333
1 3 82 9:15 5853 75 2 3 63 9:44 7122 42
1 3 83 9:16 5838 52 2 3 64 9:48 6900 50
1 3 84 9:16 5906 49 2 3 65 9:48 7020 234
1 3 85 9:17 5880 37 2 3 66 9:48 7260 65
1 3 86 9:17 5943 48 2 3 67 9:49 7260 48
1 3 87 9:20 5772 132 2 3 68 9:51 7147 105
1 3 88 9:20 5940 492 2 3 69 9:52 7222 72
1 3 89 9:28 5688 102 2 3 70 9:53 7210 55
1 3 90 9:28 5706 42 2 3 71 9:57 7025 50
1 3 91 9:28 5784 72 2 3 72 9:58 7035 65
1 3 92 9:30 5709 129 2 3 73 9:58 7090 312
1 3 93 9:33 5700 191 2 3 74 9:59 7438 63
1 3 94 9:33 5880 49 2 3 75 10:00 7435 781
1 3 95 9:34 5880 51 2 3 76 10:00 8214 74
1 3 96 9:34 5889 263 2 3 77 10:01 8200 157
1 3 97 9:36 6060 46 2 3 78 10:06 8040 418
1 3 98 9:38 5954 134 2 3 79 10:06 8460 70
1 3 99 9:40 6000 314 2 3 80 10:06 8570 169
1 3 100 9:42 6226 78 2 3 81 10:08 8580 107
1 3 101 9:45 6088 65 2 3 82 10:08 8653 63
1 3 102 9:45 6143 113 2 3 83 10:09 8690 247
1 3 103 9:46 6180 30 2 3 84 10:10 8880 176
1 3 104 9:47 6180 264 2 3 85 10:11 8944 122
1 3 105 9:47 6456 93 2 3 86 10:12 9060 168
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

49

1 3 106 9:54 6063 44 2 3 87 10:14 9120 69
1 3 107 9:55 6079 103 2 3 88 10:28 8391 109
1 3 108 9:56 6156 65 2 3 89 10:32 8220 64
1 3 109 9:56 6211 64 2 3 90 10:34 8220 100
1 3 110 10:02 5907 32 2 3 91 10:40 7980 115
1 3 111 10:03 5935 58 2 3 92 10:44 7860 55
1 3 112 10:04 5933 61 2 3 93 10:54 7265 123
1 3 113 10:04 5940 52 2 3 94 10:56 7320 105
1 3 114 10:05 5940 53 2 3 95 11:02 7080 47
1 3 115 10:07 5827 67 2 3 96 11:04 6913 72
1 3 116 10:13 5880 38 2 3 97 11:08 6900 105
1 3 117 10:18 5302 33 2 3 98 11:10 6855 170
1 3 118 10:21 5209 79 2 3 99 11:16 6685 100
1 3 119 10:25 5010 130 2 3 100 11:29 6045 185
1 3 120 10:26 5060 108 2 3 101 11:35 5860 145
1 3 121 10:26 5192 57 2 3 102 11:43 5475 60
1 3 122 10:29 5075 210 2 3 103 11:44 5475 65
1 3 123 10:29 5225 65 2 3 104 11:46 5470 165
1 3 124 10:29 5314 141 2 3 105 12:03 4405 54
1 3 125 10:30 5439 48 2 3 106 12:07 4471 51
1 3 126 10:31 5451 77 2 3 107 12:20 3760 50
1 3 127 10:35 5254 34 2 3 108 12:27 3410 75
1 3 128 10:36 5252 411 2 3 109 12:28 3395 170
1 3 129 10:36 5671 91 2 3 110 12:40 2865 75
1 3 130 10:39 5580 30 2 3 111 12:49 2370 79
1 3 131 10:42 5400 30 2 3 112 12:51 2340 190
1 3 132 10:47 5160 90 2 3 113 12:59 2100 49
1 3 133 10:47 5250 45 2 3 114 1:04 1801 177
1 3 134 10:49 5205 73 2 3 115 1:09 1684 77
1 3 135 10:58 4712 86 2 3 116 1:09 1847 104
1 3 136 10:58 4746 38 2 3 117 1:23 1023 446
1 3 137 11:00 4080 69 2 3 118 2:11 900 56
1 3 138 11:06 4399 52 2 3 119 2:13 844 58
1 3 139 11:18 3746 71 2 3 120 2:13 906 51
1 3 140 11:27 3256 72 2 3 121 2:14 915 72
1 3 141 11:34 2884 64 2 3 122 2:15 903 62
1 3 142 11:38 2760 86 2 3 123 2:16 960 60
1 3 143 11:47 2280 26 2 3 124 2:18 900 55
1 3 144 11:49 2168 41 2 3 125 2:20 840 59
1 3 145 11:51 2127 47 2 3 126 2:29 360 127
1 3 146 11:59 1720 126 2 3 127 2:30 660 175
1 3 147 12:03 1594 206 2 3 128 2:33 605 173
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

50

1 3 148 12:07 1508 95 2 3 129 2:35 672 118
1 3 149 12:09 1533 39 2 3 130 2:36 734 193
1 3 150 12:11 1494 97 2 3 131 2:36 960 363
1 3 151 12:20 977 22 2 3 132 2:37 1317 57
1 3 152 12:27 655 86 2 3 133 2:39 1200 121
1 3 153 12:28 629 310 2 3 134 2:40 1319 404
1 3 154 12:40 199 279 2 3 135 2:41 1860 45
1 3 155 12:47 100 100 2 3 136 2:43 2160 299
1 3 156 1:35 0
60 2 3 137 2:45 2340 345
1 3 157 1:35 60 41 2 3 138 2:48 2520 210
1 3 158 1:36 0
59 2 3 139 2:50 2610 144
1 3 159 1:36 620 680 2 3 140 2:50 2706 112
1 3 160 1:38 660 60 2 3 141 2:55 2580 119
1 3 161 1:39 660 89 2 3 142 2:28 2520 280
1 3 162
1:41 631 249 2 4 1 8:30 300 260
1 3 163
1:42 802 202 2 4 2 8:30 580 45
1 3 164 1:42 1020 120 2 4 3 8:30 655 85
1 3 165 1:43 1080 281 2 4 4 8:30 720 65
1 3 166 1:45 1159 294 2 4 5 8:30 835 65
1 3 167 1:47 1345 116 2 4 6 8:30 890 229
1 3 168 1:48 1409 269 2 4 7 8:30 1080 176
1 3 169 1:50 1560 60 2 4 8 8:34 1020 73
1 3 170 1:50 1620 63 2 4 9 8:34 1440 407
1 3 171 1:50 1737 52 2 4 10 8:44 1213 63
1 3 172 1:51 1625 99 2 4 11 8:44 1270 30
1 3 173 1:51 1766 116 2 4 12 8:44 1360 110
1 3 174 1:52 1770 33 2 4 13 8:44 1500 287
1 3 175 1:52 1800 57 2 4 14 8:47 1573 29
1 3 176 1:55 1680 89 2 4 15 8:49 1544 400
1 3 177 1:56 1711 116 2 4 16 8:49 1864 352
1 3 178 1:59 1655 87 2 4 17 8:49 2232 149
1 3 179 2:01 1568 68 2 4 18 8:51 1963 184
1 3 180 2:02 1620 45 2 4 19 8:57 2139 97
1 3 181 2:02 1635 315 2 4 20 8:58 2102 38
1 3 182 2:02 1980 34 2 4 21 9:02 1944 62
1 3 183 2:02 2006 77 2 4 22 9:04 1882 131
1 3 184 2:03 1989 150 2 4 23 9:05 1931 127
1 3 185 2:04 2139 91 2 4 24 9:06 2100 173
1 3 186 2:05 2108 23 2 4 25 9:06 2227 120
1 3 187 2:09 1965 125 2 4 26 9:09 2167 707
1 3 188 2:11 1960 70 2 4 27 9:09 3840 66
1 3 189 2:13 1890 90 2 4 28 9:10 3894 74
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

51

1 3 190 2:13 1980 117 2 4 29 9:13 3720 96
1 3 191 2:14 1983 153 2 4 30 9:14 3744 104
1 3 192 2:15 2100 30 2 4 31 9:14 3880 263
1 3 193 2:16 2100 45 2 4 32 9:14 4140 417
1 3 194 2:18 1995 52 2 4 33 9:15 4443 110
1 3 195 2:20 1943 71 2 4 34 9:16 4513 80
1 3 196 2:29 1452 72 2 4 35 9:16 4620 50
1 3 197 2:35 1200 51 2 4 36 9:18 4503 100
1 3 198 2:36 1149 249 2 4 37 9:18 4643 69
1 3 199 2:37 1380 109 2 4 38 9:21 4694 349
1 3 200 2:39 1331 42 2 4 39 9:21 4765 133
1 3 201 2:40 1349 45 2 4 40 9:24 4812 56
1 3 202 2:41 1364 164 2 4 41 9:24 4876 52
1 3 203 2:48 1980 89 2 4 42 9:25 4884 131
1 3 204 2:50 1951 190 2 4 43 9:25 4993 159
1 3 205 2:50 2181 38 2 4 44 9:33 4714 67
1 3 206 2:50 2263 148 2 4 45 9:34 4707 40
1 3 207 2:51 2295 117 2 4 46 9:34 4787 93
1 3 208 2:54 2238 57 2 4 47 9:34 4814 35
1 3 209 2:55 2241 116 2 4 48 9:37 4719 98
1 3 210 2:56 2305 85 2 4 49 9:37 4800 176
1 3 211 2:57 2340 207 2 4 50 9:37 5100 221
1 3 212 2:58 2460 273 2 4 51 9:38 5280 62
1 4 1 8:30 1020 60 2 4 52 9:38 5342 58
1 4 2 8:30 1080 229 2 4 53 9:38 5580 95
1 4 3 8:30 1331 110 2 4 54 9:38 5665 71
1 4 4 8:30 1466 132 2 4 55 9:42 5474 55
1 4 5 8:30 1574 38 2 4 56 9:42 5539 45
1 4 6 8:30 1656 241 2 4 57 9:47 5340 107
1 4 7 8:30 1895 80 2 4 58 9:49 5520 76
1 4 8 8:30 1935 88 2 4 59 9:49 5624 60
1 4 9 8:30 2040 45 2 4 60 9:53 5400 239
1 4 10 8:30 2042 49 2 4 61 9:53 5640 86
1 4 11 8:30 2130 204 2 4 62 9:55 5614 51
1 4 12 8:30 2389 76 2 4 63 9:56 5623 49
1 4 13 8:30 2400 33 2 4 64 9:57 5634 65
1 4 14 8:30 2460 31 2 4 65 10:01 4249 72
1 4 15 8:30 2489 35 2 4 66 10:01 5460 88
1 4 16 8:30 2520 162 2 4 67 10:05 5312 173
1 4 17 8:30 2652 42 2 4 68 10:12 5079 54
1 4 18 8:30 2700 30 2 4 69 10:13 5085 258
1 4 19 8:30 2760 84 2 4 70 10:13 5307 51
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

52

1 4 20 8:30 2856 84 2 4 71 10:13 5376 78
1 4 21 8:30 5892 79 2 4 72 10:17 5178 135
1 4 22 8:30 3000 50 2 4 73 10:17 5340 89
1 4 23 8:30 3003 50 2 4 74 10:17 5431 80
1 4 24 8:33 2893 47 2 4 75 10:20 5291 109
1 4 25 8:33 2966 45 2 4 76 10:23 5242 46
1 4 26 8:33 3031 47 2 4 77 10:24 5254 92
1 4 27 8:33 3104 55 2 4 78 10:24 5282 118
1 4 28 8:33 3120 45 2 4 79 10:26 5284 119
1 4 29 8:33 3124 116 2 4 80 10:26 5405 512
1 4 30 8:35 3128 55 2 4 81 10:29 6000 221
1 4 31 8:35 3193 115 2 4 82 10:29 6720 109
1 4 32 8:35 3318 24 2 4 83 10:31 7200 76
1 4 33 8:35 3360 54 2 4 84 10:36 3404 92
1 4 34 8:40 3120 53 2 4 85 10:36 7032 49
1 4 35 8:40 3127 86 2 4 86 10:39 7523 84
1 4 36 8:40 3281 41 2 4 87 10:42 6840 59
1 4 37 8:40 3300 42 2 4 88 10:46 6660 97
1 4 38 8:40 3318 47 2 4 89 10:53 6323 52
1 4 39 8:40 3391 35 2 4 90 10:54 6360 458
1 4 40 8:43 3296 221 2 4 91 10:57 6960 238
1 4 41 8:43 3435 39 2 4 92 12:57 0
345
1 4 42 8:43 3480 36 2 4 93 1:02 0
49
1 4 43 8:43 3540 37 2 4 94 10:03 0
332
1 4 44 8:43 3563 103 2 4 95 1:04 344 200
1 4 45 8:43 3700 236 2 4 96 1:05 300 107
1 4 46 8:43 3944 44 2 4 97 1:07 253 72
1 4 47 8:43 3960 75 2 4 98 1:09 240 85
1 4 48 8:43 4065 87 2 4 99 1:10 275 132
1 4 49 8:44 4038 178 2 4 100 1:11 323 39
1 4 50 8:45 4160 122 2 4 101 1:12 480 205
1 4 51 8:46 4278 44 2 4 102 1:15 515 47
1 4 52 8:47 4774 41 2 4 103 1:17 468 95
1 4 53 8:47 4800 62 2 4 104 1:20 360 103
1 4 54 8:48 4800 51 2 4 105 1:23 257 839
1 4 55 8:48 4860 77 2 4 106 1:23 1080 57
1 4 56 9:11 7183 46 2 4 107 1:23 1200 440
1 4 57 9:11 7200 43 2 4 108 1:24 1600 338
1 4 58 9:11 7214 49 2 4 109 1:44 2760 77
1 4 59 9:11 7285 36 2 4 110 1:55 2640 64
1 4 60 9:11 7369 62 2 4 111 1:56 2199 135
1 4 61 9:11 7380 46 2 4 112 1:59 2124 433
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

53

1 4 62 9:11 7383 42 2 4 113 2:00 2471 68
1 4 63 9:15 7221 46 2 4 114 2:10 1980 59
1 4 64 9:15 7295 40 2 4 115 2:14 1800 167
1 4 65 9:15 7320 55 2 4 116 2:18 2160 156
1 4 66 9:26 6720 60 2 4 117 2:32 1620 166
1 4 67 9:26 6840 60 2 4 118 2:46 914 67
1 4 68 9:26 6900 92 2 4 119 2:46 967 34
1 4 69 9:26 6988 28 2 4 120 2:47 993 55
1 4 70 9:26 7020 37 2 4 121 2:48 1020 107
1 4 71 9:27 6973 83 2 4 122 2:49 1080 60
1 4 72 9:27 7070 225 2 4 123 2:50 1080 63
1 4 73 9:27 7205 217 2 4 124 2:52 1077 104
1 4 74 9:27 7468 51 2 4 125 2:56 900 173
1 4 75 9:35 7057 97 2 4 126 3:00 87 153
1 4 76 9:35 7140 165 2 4 127 3:00 1380 116
1 4 77 9:35 7275 167 2 5 1 8:30 780 195
1 4 78 9:35 7468 65 2 5 2 8:30 1005 191
1 4 79 9:35 7523 171 2 5 3 8:30 1174 69
1 4 80 9:36 7652 47 2 5 4 8:32 1105 60
1 4 81 9:36 7680 35 2 5 5 8:38 840 147
1 4 82 9:36 7740 43 2 5 6 8:40 873 69
1 4 83 9:36 7757 44 2 5 7 8:42 840 107
1 4 84 9:36 7833 55 2 5 8 8:50 540 177
1 4 85 9:39 7718 150 2 5 9 8:52 660 106
1 4 86 9:39 7808 60 2 5 10 8:54 614 1210
1 4 87 9:59 6668 42 2 5 11 10:00 360 510
1 4 88 9:59 6746 154 2 5 12 10:05 570 1277
1 4 89 9:59 6952 482 2 5 13 10:07 2460 122
1 4 90 9:59 7430 188 2 5 14 10:10 2280 58
1 4 91 9:59 7602 42 2 5 15 10:12 2220 99
1 4 92 9:59 7620 89 2 5 16 10:14 2181 67
1 4 93 10:14 3211 36 2 5 17 10:15 2340 90
1 4 94 10:14 3240 47 2 5 18 10:20 2130 73
1 4 95 10:14 3248 48 2 5 19 10:21 2127 78
1 4 96 10:14 3320 107 2 5 20 10:23 2049 235
1 4 97 10:14 3420 33 2 5 21 10:30 1874 190
1 4 98 10:14 3480 148 2 5 22 10:36 1686 119
1 4 99 10:24 3032 38 2 5 23 10:42 1447 288
1 4 100 10:24 3060 37 2 5 24 10:46 1519 176
1 4 101 10:28 2835 40 2 5 25 10:49 1523 129
1 4 102 10:28 2915 45 2 5 26 10:50 1560 96
1 4 103 10:35 2520 37 2 5 27 10:55 1380 79
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

54

1 4 104 10:38 2353 42 2 5 28 11:02 1061 367
1 4 105 10:38 2431 91 2 5 29 11:05 1234 153
1 4 106 10:44 2160 83 2 5 30 11:06 1320 116
1 4 107 10:44 2257 118 2 5 31 11:07 1324 130
1 4 108 10:44 2439 120 2 5 32 11:10 1320 47
1 4 109 10:44 2559 54 2 5 33 11:13 1147 153
1 4 110 10:44 2625 90 2 5 34 11:18 1054 80
1 4 111 10:45 2595 29 2 5 35 11:18 1140 216
1 4 112 10:45 2691 231 2 5 36 11:21 1560 286
1 4 113 10:47 2760 75 2 5 37 11:25 1740 161
1 4 114 10:47 2865 97 2 5 38 11:28 1699 49
1 4 115 10:47 2888 94 2 5 39 11:29 1800 156
1 4 116 10:49 2914 51 2 5 40 11:32 1764 381
1 4 117 10:49 2940 43 2 5 41 11:33 2100 336
1 4 118 11:06 1980 60 2 5 42 11:34 2364 38
1 4 119 11:06 2040 36 2 5 43 11:36 2280 46
1 4 120 11:10 1824 59 2 5 44 11:38 2220 216
1 4 121 11:10 1885 85 2 5 45 11:40 2364 181
1 4 122 11:13 1800 95 2 5 46 11:58 1463 39
1 4 123 11:16 1705 107 2 5 47 12:01 1364 85
1 4 124 11:16 1838 38 2 5 48 12:03 1279 115
1 4 125 11:20 1620 51 2 5 49 12:05 1284 65
1 4 126 11:20 1629 72 2 5 50 12:08 1159 85
1 4 127 11:20 1800 50 2 5 51 12:09 1254 99
1 4 128 11:22 1687 123 2 5 52 12:11 1155 101
1 4 129 11:22 1804 124 2 5 53 12:13 1174 75
1 4 130 11:30 1500 83 2 5 54 12:16 1039 55
1 4 131 11:30 1597 65 2 5 55 12:16 1140 60
1 4 132 11:44 812 152 2 5 56 12:19 1080 224
1 4 133 11:44 960 160 2 5 57 12:21 1156 195
1 4 134 11:50 740 80 2 5 58 12:24 1200 780
1 4 135 11:54 540 125 2 5 59 12:29 1380 297
1 4 136 11:56 540 45 2 5 60 12:37 1143 167
1 4 137 11:56 550 248 2 5 61 12:39 1216 155
1 4 138 11:58 662 82 2 5 62 12:40 1361 170
1 4 139 11:58 820 44 2 5 63 12:40 1551 105
1 4 140 12:00 776 71 2 5 64 12:42 1446 63
1 4 141 12:01 765 93 2 5 65 12:50 1023 159
1 4 142
12:01
792 50 2 5 66 12:57
804 127
1 4 143
12:04
682 22 2 5 67 1:06 377 113
1 4 144
12:04
720 175 2 5 68 1:10 300 149
1 4 145
12:05
705 298 2 5 69 1:12 331 172
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

55

1 4 146
12:08
907 400 2 5 70 1:16 279 94
1 4 147
12:13
987 144 2 5 71 1:16 305 206
1 4 148
12:17
903 28 2 5 72 1:19 399 95
1 4 149
12:21
780 56 2 5 73 1:19 424 25
1 4 150
12:21
784 49 2 5 74 1:22 339 50
1 4 151
12:23
735 39 2 5 75 1:23 349 64
1 4 152
12:27
540 32 2 5 76 1:23 405 386
1 4 153
12:30
420 51 2 5 77 1:24 360 412
1 4 154
12:32
309 45 2 5 78 1:25 668 109
1 4 155
12:36
144 89 2 5 79 1:26 739 546
1 4 156
12:36
295 98 2 5 80 2:02 780 76
1 4 157
12:37
257 55 2 5 81 2:05 660 50
1 4 158
12:38
262 72 2 5 82 2:05 720 287
1 4 159
12:39
250 55 2 5 83 2:07 853 49
1 4 160
12:39
315 31 2 5 84 2:09 804 68
1 4 161
12:40
884 115 2 5 85 2:11 736 132
1 4 162
12:41
380 49 2 5 86 2:13 724 106
1 4 163
12:42
371 38 2 5 87 2:16 378 84
1 4 164
12:43
180 28 2 5 88 2:17 720 54
1 4 165
12:44
245 20 2 5 89 2:20 600 110
1 4 166 12:44 0
171 2 5 90 2:20 670 37
1 4 167
12:45
420 54 2 5 91 2:21 693 51
1 4 168
12:46
420 51 2 5 92 2:22 702 81
1 4 169
12:47
369 61 2 5 93 2:23 681 228
1 4 170
12:51
188 55 2 5 94 2:24 873 66
1 4 171
12:51
253 53 2 5 95 2:26 807 146
1 4 172
12:53
200 200 2 5 96 2:29 780 87
1 4 173 1:23 1020 46 2 5 97 2:31 753 124
1 4 174 1:23 1034 46 2 5 98 2:31 869 282
1 4 175 1:25 988 118 2 5 99 2:32 1247 89
1 4 176 1:26 1050 67 2 5 100 2:32 1260 1007
1 4 177 1:26 1103 93 2 5 101 2:34 2113 159
1 4 178 1:28 1080 38 2 5 102 2:37 2074 240
1 4 179 1:30 972 120 2 5 103 2:38 2280 156
1 4 180 1:30 1092 50 2 5 104 2:38 2424 234
1 4 181 1:30 1154 134 2 5 105 2:51 1890 103
1 4 182 1:35 1020 115 2 5 106 2:53 1860 56
1 4 183 1:39 845 104 2 5 107 2:53 2760 84
1 4 184 1:42 801 27 2 5 108 2:54 2796 133
1 4 185 1:44 774 83 2 5 109 3:00 2543 100
1 4 186 1:54 180 31 2 5 110 3:03 2503 146
1 4 187 1:54 240 80 2 5 111 3:03 2597 45
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

56

1 4 188 1:56 220 181 2 5 112 3:04 2612 74
1 4 189
1:56 399 76 2 6 1 8:30 300 56
1 4 190
1:57 383 113 2 6 2 8:30 380 31
1 4 191
1:58 450 76 2 6 3 8:30 389 88
1 4 192
1:59 434 93 2 6 4 8:30 480 156
1 4 193
2:00 521 50 2 6 5 8:36 264 110
1 4 194
2:01 471 87 2 6 6 8:36 394 72
1 4 195
2:07 204 52 2 6 7 8:36 142 128
1 4 196
2:09 152 61 2 6 8 8:40 314 239
1 4 197
2:10 151 72 2 6 9 8:41 495 91
1 4 198
2:10 199 66 2 6 10 8:41 600 46
1 4 199
2:12 133 125 2 6 11 8:48 300 114
1 4 200
2:14 128 188 2 6 12 8:48 420 102
1 4 201
2:14 360 50 2 6 13 8:52 258 54
1 4 202
2:15 310 171 2 6 14 8:52 324 22
1 4 203
2:17 439 79 2 6 15 8:54 254 79
1 4 204
2:18 480 37 2 6 16 0:00 295 114
1 4 205
2:19 443 47 2 6 17 8:58 240 228
1 4 206
2:20 516 129 2 6 18 8:58 432 307
1 4 207
2:21 540 27 2 6 19 8:59 665 56
1 4 208
2:22 540 85 2 6 20 9:00 669 125
1 4 209 2:24 3395 35 2 6 21 9:00 784 210
1 4 210
2:45 480 33 2 6 22 9:01 994 47
1 4 211 2:32 87 200 2 6 23 9:01 1067 47
1 4 212 2:33 180 110 2 6 24 9:01 1026 156
1 4 213
2:35 130 70 2 6 25 9:06 924 132
1 4 214
2:36 180 35 2 6 26 9:07 972 62
1 4 215 2:37 145 68 2 6 27 9:07 1030 50
1 4 216 2:38 137 39 2 6 28 9:08 1260 90
1 4 217 2:38 218 38 2 6 29 9:09 1290 109
1 4 218 2:39 180 60 2 6 30 9:10 1361 48
1 4 219 2:39 240 60 2 6 31 9:13 1200 53
1 4 220 2:40 240 60 2 6 32 9:13 1260 55
1 4 221 2:40 300 51 2 6 33 9:14 1260 87
1 4 222 2:40 309 54 2 6 34 9:15 1293 134
1 4 223 2:40 375 43 2 6 35 9:15 1399 57
1 4 224 2:40 452 85 2 6 36 9:15 1462 63
1 4 225 2:40 487 35 2 6 37 9:15 1459 220
1 4 226 2:42 452 598 2 6 38 9:17 1659 75
1 4 227 2:42 994 94 2 6 39 9:17 2400 58
1 4 228 2:46 1260 111 2 6 40 9:20 2280 294
1 4 229 2:49 1149 129 2 6 41 9:24 2340 97
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

57

1 4 230 2:49 1320 146 2 6 42 9:28 2183 38
1 4 231 2:49 1474 75 2 6 43 9:30 2145 83
1 4 232 2:50 1459 90 2 6 44 9:30 2182 112
1 4 233 2:52 1487 103 2 6 45 9:35 2160 57
1 4 234 2:53 1446 63 2 6 46 9:35 2163 46
1 4 235 2:54 1447 87 2 6 47 9:36 2177 227
1 4 236 2:55 1500 40 2 6 48 9:37 2370 70
1 4 237 2:57 1440 90 2 6 49 9:38 2400 146
1 4 238 2:57 1530 66 2 6 50 9:43 2254 99
1 4 239 2:58 1524 35 2 6 51 9:43 2340 47
1 4 240 2:58 1560 49 2 6 52 9:43 2348 105
1 4 241 2:59 1560 210 2 6 53 9:45 2363 50
1 4 242 3:00 1710 145 2 6 54 9:45 2433 151
1 4 243 3:04 1565 215 2 6 55 9:48 2400 108
1 5 1 8:30 120 120 2 6 56 9:54 2112 135
1 5 2 8:30 240 22 2 6 57 9:57 2100 57
1 5 3 8:30 338 96 2 6 58 9:59 2040 110
1 5 4 8:30 362 153 2 6 59 10:05 1750 98
1 5 5 8:30 569 32 2 6 60 10:06 1832 108
1 5 6 8:30 840 120 2 6 61 10:10 1724 130
1 5 7 8:30 960 120 2 6 62 10:14 1594 65
1 5 8 8:32 720 30 2 6 63 10:15 1589 387
1 5 9 8:36 750 115 2 6 64 10:19 1682 176
1 5 10 8:38 755 95 2 6 65 10:21 1800 58
1 5 11 8:38 840 48 2 6 66 10:21 1802 353
1 5 12 8:40 732 59 2 6 67 10:24 2040 50
1 5 13 8:42 673 54 2 6 68 10:24 2050 85
1 5 14 8:43 679 43 2 6 69 10:29 1905 111
1 5 15 8:44 696 96 2 6 70 10:32 1800 44
1 5 16 8:47 600 167 2 6 71 10:32 1808 62
1 5 17 8:53 480 76 2 6 72 10:35 1686 835
1 5 18 8:54 524 132 2 6 73 10:37 2411 108
1 5 19 8:57 452 70 2 6 74 10:37 2063 100
1 5 20 9:03 180 66 2 6 75 10:39 2563 579
1 5 21 9:05 774 82 2 6 76 10:43 2824 550
1 5 22 9:06 752 55 2 6 77 10:44 3360 44
1 5 23 9:07 720 37 2 6 78 10:45 3310 46
1 5 24 9:09 660 157 2 6 79 10:47 3264 123
1 5 25 9:10 743 248 2 6 80 10:48 3321 100
1 5 26 9:11 915 116 2 6 81 10:48 3461 42
1 5 27 9:13 919 24 2 6 82 10:50 3360 58
1 5 28 9:14 955 112 2 6 83 10:54 3160 117
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

58

1 5 29 9:15 903 42 2 6 84 10:54 3243 62
1 5 30 9:16 921 67 2 6 85 10:54 3360 88
1 5 31 9:19 794 66 2 6 86 10:55 3392 79
1 5 32 9:20 788 62 2 6 87 10:56 3373 227
1 5 33 9:23 666 109 2 6 88 10:57 3566 68
1 5 34 9:24 737 57 2 6 89 10:58 3438 114
1 5 35 9:24 800 124 2 6 90 11:03 3084 476
1 5 36 9:26 796 65 2 6 91 11:03 3568 94
1 5 37 9:27 791 62 2 6 92 11:04 3600 44
1 5 38 9:28 840 101 2 6 93 11:06 3490 48
1 5 39 9:28 979 79 2 6 94 11:06 3562 158
1 5 40 9:37 540 105 2 6 95 11:09 3584 245
1 5 41 9:40 435 162 2 6 96 11:17 3339 140
1 5 42 9:48 153 213 2 6 97 11:19 3319 80
1 5 43 9:57 660 92 2 6 98 11:21 3300 58
1 5 44 10:00 568 126 2 6 99 11:22 3241 37
1 5 45 10:01 622 394 2 6 100 11:25 3142 130
1 5 46 10:02 900 48 2 6 101 11:29 3012 69
1 5 47 10:03 900 80 2 6 102 11:29 3063 94
1 5 48 10:06 780 40 2 6 103 11:30 3149 72
1 5 49 10:07 780 99 2 6 104 11:30 3197 68
1 5 50 10:08 801 58 2 6 105 11:32 3129 46
1 5 51 10:09 803 55 2 6 106 11:51 2063 176
1 5 52 10:11 748 69 2 6 107 12:06 3420 93
1 5 53 10:12 739 139 2 6 108 12:09 3327 330
1 5 54 10:14 780 79 2 6 109 12:10 3657 204
1 5 55 10:15 821 101 2 6 110 12:11 3753 256
1 5 56 10:20 540 43 2 6 111 12:13 3857 74
1 5 57 10:20 557 64 2 6 112 12:14 3843 83
1 5 58 10:21 553 122 2 6 113 12:15 3940 144
1 5 59 10:23 551 20 2 6 114 12:15 4036 37
1 5 60 10:24 591 140 2 6 115 12:15 4119 196
1 5 61 10:26 571 79 2 6 116 12:15 4380 67
1 5 62 10:26 612 45 2 6 117 12:16 4433 94
1 5 63 10:30 447 134 2 6 118 12:19 4279 105
1 5 64 10:31 493 99 2 6 119 12:21 4294 71
1 5 65 10:33 514 189 2 6 120 12:21 4343 141
1 5 66 10:36 480 60 2 6 121 12:21 4560 91
1 5 67 10:42 180 60 2 6 122 12:24 4049 129
1 5 68 10:43 130 54 2 6 123 12:25 4400 62
1 5 69 10:44 136 38 2 6 124 12:27 4338 39
1 5 70 10:45 180 70 2 6 125 12:29 4299 157
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

59

1 5 71 10:46 230 96 2 6 126 12:31 4262 43
1 5 72 10:46 254 128 2 6 127 12:34 4159 106
1 5 73 10:49 186 241 2 6 128 12:36 4173 96
1 5 74 10:50 365 169 2 6 129 12:40 4020 54
1 5 75 10:55 272 244 2 6 130 12:40 4023 96
1 5 76 10:57 372 62 2 6 131 12:41 5427 276
1 5 77 10:59 310 111 2 6 132 12:41 4440 60
1 5 78 11:00 379 101 2 6 133 12:41 4500 588
1 5 79 11:02 398 183 2 6 134 12:47 4692 583
1 5 80 11:05 395 185 2 6 135 1:16 3840 94
1 5 81 11:06 510 30 2 6 136 1:18 3806 97
1 5 82 11:07 480 37 2 6 137 1:25 3529 75
1 5 83 11:10 313 28 2 6 138 1:36 3000 336
1 5 84 11:11 345 525 2 6 139 1:36 3324 40
1 5 85 11:13 720 84 2 6 140 1:39 3224 130
1 5 86 11:18 516 46 2 6 141 1:40 3274 125
1 5 87 11:18 590 101 2 6 142 1:55 2489 49
1 5 88 11:21 429 62 2 6 143 2:01 2160 38
1 5 89 11:25 247 109 2 6 144 2:06 1862 83
1 5 90 11:28 198 103 2 6 145 2:10 1779 75
1 5 91 11:29 245 20 2 6 146 2:16 1464 75
1 5 92 11:30 195 49 2 6 147 2:18 1389 30
1 5 93 11:31 206 146 2 6 148 2:22 1239 93
1 5 94 11:32 300 210 2 6 149 2:23 2040 59
1 5 95 11:33 450 64 2 6 150 2:25 1980 60
1 5 96 11:34 446 113 2 6 151 2:41 1440 96
1 5 97 11:35 480 30 2 6 152 2:46 1224 193
1 5 98 11:37 423 21 2 6 153 2:47 1331 69
1 5 99 11:41 282 131 2 6 154 2:48 1322 88
1 5 100 11:43 271 112 2 6 155 2:52 1234 143
1 5 101 11:45 279 52 2 6 156 2:54 1211 167
1 5 102 11:46 287 147 2 6 157 2:58 1164 40
1 5 103
11:48
260 80 2 7 1 8:30 420 196
1 5 104
11:50
240 103 2 7 2 8:30 644 135
1 5 105
11:52
187 50 2 7 3 8:30 780 105
1 5 106
11:53
193 55 2 7 4 8:30 855 172
1 5 107
11:55
138 54 2 7 5 8:37 780 97
1 5 108
11:55
204 84 2 7 6 8:39 743 238
1 5 109
11:56
240 60 2 7 7 8:40 925 118
1 5 110
11:58
180 70 2 7 8 8:45 747 58
1 5 111
11:59
230 141 2 7 9 8:47 689 59
1 5 112
11:59
329 64 2 7 10 8:49 630 77
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

60

1 5 113
12:00
325 56 2 7 11 8:50 613 130
1 5 114
12:01
329 29 2 7 12 8:51 663 229
1 5 115
12:03
360 143 2 7 13 8:54 734 35
1 5 116
12:05
397 37 2 7 14 8:54 819 69
1 5 117
12:08
263 83 2 7 15 8:56 750 38
1 5 118
12:09
300 39 2 7 16 8:59 652 80
1 5 119
12:10
240 92 2 7 17 9:02 512 138
1 5 120
12:11
268 69 2 7 18 9:04 494 100
1 5 121
12:12
259 116 2 7 19 9:04 634 369
1 5 122
12:14
263 63 2 7 20 9:05 925 41
1 5 123 12:15 260 67 2 7 21 9:05 1004 90
1 5 124
12:16
253 87 2 7 22 9:08 854 44
1 5 125
12:16
406 56 2 7 23 9:09 870 56
1 5 126
12:19
290 65 2 7 24 9:11 814 194
1 5 127
12:21
285 154 2 7 25 9:11 980 54
1 5 128 12:23 251 96 2 7 26 9:11 1046 128
1 5 129 12:24 335 40 2 7 27 9:11 1158 41
1 5 130 12:29 120 60 2 7 28 9:13 1117 62
1 5 131 12:30 120 145 2 7 29 9:13 1200 100
1 5 132 12:30 275 86 2 7 30 9:15 1160 116
1 5 133 12:30 1740 180 2 7 31 9:17 1164 52
1 5 134 1:06 1380 171 2 7 32 9:18 1172 76
1 5 135 1:10 1269 148 2 7 33 9:19 976 307
1 5 136 1:12 1361 71 2 7 34 9:20 2460 150
1 5 137 1:16 1170 98 2 7 35 9:20 2610 91
1 5 138 1:18 1192 97 2 7 36 9:20 2700 59
1 5 139 1:19 1155 65 2 7 37 9:24 2520 60
1 5 140 1:21 1090 45 2 7 38 9:24 2580 46
1 5 141 1:23 1045 110 2 7 39 9:27 2414 108
1 5 142 1:25 1055 46 2 7 40 9:28 2486 42
1 5 143 1:26 469 131 2 7 41 9:29 2504 70
1 5 144 1:28 1020 89 2 7 42 9:31 2434 431
1 5 145 1:30 969 32 2 7 43 9:32 2783 39
1 5 146 1:32 937 136 2 7 44 9:32 2864 68
1 5 147 1:32 1041 41 2 7 45 9:32 2676 167
1 5 148 1:37 880 53 2 7 46 9:36 3109 148
1 5 149 1:40 720 30 2 7 47 9:36 2961 45
1 5 150 1:40 737 51 2 7 48 9:36 3036 48
1 5 151 1:42 686 35 2 7 49 9:38 3060 97
1 5 152 1:42 771 146 2 7 50 9:39 3083 231
1 5 153 1:49 445 176 2 7 51 9:41 3212 91
1 5 154 1:49 629 44 2 7 52 9:42 3240 73
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

61

1 5 155 1:49 705 91 2 7 53 9:42 3347 220
1 5 156 1:50 674 74 2 7 54 9:43 3427 321
1 5 157 1:51 720 60 2 7 55 9:43 3826 57
1 5 158 1:51 780 60 2 7 56 9:45 3769 102
1 5 159 1:53 720 114 2 7 57 9:46 3727 372
1 5 160 1:55 606 54 2 7 58 9:46 3840 55
1 5 161 1:55 672 132 2 7 59 9:46 4020 119
1 5 162 1:57 720 163 2 7 60 9:47 3960 271
1 5 163 1:59 737 27 2 7 61 9:47 4229 65
1 5 164 2:00 770 141 2 7 62 9:49 4164 94
1 5 165 2:02 744 209 2 7 63 9:50 4250 67
1 5 166 2:05 1260 420 2 7 64 9:50 4313 119
1 5 167 2:05 1800 147 2 7 65 9:56 4020 54
1 5 168 2:05 1953 313 2 7 66 9:58 3960 50
1 5 169 2:07 2120 97 2 7 67 10:01 3790 100
1 5 170 2:07 2263 91 2 7 68 10:02 3870 171
1 5 171 2:09 2172 59 2 7 69 10:05 3879 76
1 5 172 2:11 2113 104 2 7 70 10:08 3743 66
1 5 173 2:13 2129 109 2 7 71 10:11 3617 43
1 5 174 2:13 2260 43 2 7 72 10:13 3574 47
1 5 175 2:16 2154 62 2 7 73 10:14 3587 53
1 5 176 2:17 2100 55 2 7 74 10:14 3600 54
1 5 177 2:23 1800 70 2 7 75 10:14 3660 73
1 5 178 2:24 1800 50 2 7 76 10:15 3707 94
1 5 179 2:26 1740 91 2 7 77 10:17 3613 81
1 5 180 2:26 1829 137 2 7 78 10:23 3412 77
1 5 181 2:29 1752 235 2 7 79 10:23 3455 42
1 5 182 2:31 1877 30 2 7 80 10:32 2940 53
1 5 183 2:31 1967 154 2 7 81 10:36 2760 80
1 5 184 2:32 1993 43 2 7 82 10:36 2860 81
1 5 185 2:34 1950 364 2 7 83 10:38 2779 63
1 5 186 2:37 2100 159 2 7 84 10:38 2836 56
1 5 187 2:38 2181 56 2 7 85 10:39 2810 77
1 5 188 2:38 1045 196 2 7 86 10:41 2763 58
1 5 189 2:44 2049 88 2 7 87 10:45 2585 286
1 5 190 2:44 2160 49 2 7 88 10:46 2839 250
1 5 191 2:44 2220 51 2 7 89 10:47 3009 107
1 5 192 2:47 2049 47 2 7 90 10:48 3082 53
1 5 193 2:47 2122 71 2 7 91 10:49 3089 50
1 5 194 2:48 2111 171 2 7 92 10:50 3099 129
1 5 195 2:48 2300 40 2 7 93 10:50 3210 76
1 5 196 2:50 2260 280 2 7 94 10:52 3134 117
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

62

1 5 197 2:51 2460 120 2 7 95 10:53 3197 114
1 5 198 2:53 2460 97 2 7 96 11:01 2843 114
1 5 199 2:53 2543 120 2 7 97 11:03 2849 57
1 5 200 2:54 2723 121 2 7 98 11:03 2672 118
1 5 201 2:54 2842 82 2 7 99 11:10 2614 57
1 5 202 2:54 2940 60 2 7 100 11:10 2677 107
1 5 203 2:56 2880 110 2 7 101 11:16 2450 5
1 5 204 3:00 2710 47 2 7 102 11:17 2400 90
1 5 205 3:00 2783 113 2 7 103 11:17 2781 30
1 5 206 3:03 2730 165 2 7 104 11:26 2280 66
1 5 207 3:04 2865 66 2 7 105 11:26 2394 153
1 5 208 3:04 2919 74 2 7 106 11:28 3000 60
1 6 1 8:30 420 267 2 7 107 11:30 2940 157
1 6 2 8:30 693 523 2 7 108 11:32 2963 99
1 6 3 8:30 910 173 2 7 109 11:35 2924 92
1 6 4 8:30 1037 165 2 7 110 11:39 2712 265
1 6 5 8:30 1172 81 2 7 111 11:46 2627 83
1 6 6 8:30 1211 251 2 7 112 11:57 2374 110
1 6 7 8:30 1465 249 2 7 113 12:00 4380 86
1 6 8 8:30 1636 240 2 7 114 12:04 4414 72
1 6 9 8:30 1816 185 2 7 115 1:05 622 63
1 6 10 8:30 1931 182 2 7 116 1:07 559 162
1 6 11 8:30 2049 480 2 7 117 1:07 757 319
1 6 12 8:30 2469 232 2 7 118 1:11 798 212
1 6 13 8:30 2657 197 2 7 119 1:17 706 65
1 6 14 8:30 3025 64 2 7 120 1:21 521 26
1 6 15 8:30 3081 309 2 7 121 1:22 525 151
1 6 16 8:35 3012 60 2 7 122 1:24 494 350
1 6 17 8:35 3072 285 2 7 123 1:24 864 75
1 6 18 8:35 3327 207 2 7 124 1:24 909 55
1 6 19 8:35 3667 67 2 7 125 1:30 614 40
1 6 20 8:40 3974 284 2 7 126 1:30 694 127
1 6 21 8:41 4170 364 2 7 127 1:30 1020 111
1 6 22 8:42 4406 199 2 7 128 1:30 1089 102
1 6 23 8:44 4387 148 2 7 129 1:31 1167 223
1 6 24 8:45 4479 90 2 7 130 1:32 1364 85
1 6 25 8:59 3669 153 2 7 131 1:36 1860 77
1 6 26 8:59 3756 186 2 7 132 1:40 1680 43
1 6 27 8:59 3930 65 2 7 133 1:44 2100 76
1 6 28 9:00 3925 166 2 7 134 1:52 1724 194
1 6 29 9:00 4059 190 2 7 135 1:52 1890 103
1 6 30 9:02 4049 34 2 7 136 1:54 1980 76
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

63

1 6 31 9:05 3955 265 2 7 137 1:58 1920 151
1 6 32 9:10 3780 30 2 7 138 2:02 1829 100
1 6 33 9:10 3840 44 2 7 139 2:04 1849 75
1 6 34 9:10 3916 48 2 7 140 2:10 1920 99
1 6 35 9:15 3688 193 2 7 141 2:13 1860 96
1 6 36 9:15 3795 55 2 7 142 2:15 1824 75
1 6 37 9:17 3740 35 2 7 143 2:17 1860 112
1 6 38 9:18 3765 176 2 7 144 2:19 1860 147
1 6 39 9:27 3324 231 2 7 145 2:19 2013 43
1 6 40 9:29 3360 30 2 7 146 2:20 2030 52
1 6 41 9:29 3390 40 2 7 147 2:29 1500 58
1 6 42 9:29 3470 271 2 7 148 2:35 1200 122
1 6 43 9:33 3371 54 2 7 149 2:37 1200 58
1 6 44 9:33 3437 167 2 7 150 2:38 1200 125
1 6 45 9:35 3450 202 2 7 151 2:40 1255 252
1 6 46 9:35 3548 353 2 7 152 2:46 1123 291
1 6 47 9:36 3795 63 2 7 153 2:50 1320 193
1 6 48 9:40 3612 63 2 7 154 2:50 1560 81
1 6 49 9:42 3549 64 2 7 155 2:56 1299 84
1 6 50 9:44 3540 313 2 7 156 2:58 1210 68
1 6 51 9:44 3869 313 2 7 157 3:00 1200 83
1 6 52 9:46 3976 356 2 7 158 3:01 1237 55
1 6 53 9:47 4220 25 2 8 1 8:30 120 36
1 6 54 9:53 3900 55 2 8 2 8:30 180 101
1 6 55 9:54 3900 156 2 8 3 8:30 259 40
1 6 56 9:55 3984 65 2 8 4 8:30 339 48
1 6 57 9:56 3979 144 2 8 5 8:30 411 61
1 6 58 9:57 4020 49 2 8 6 8:30 420 44
1 6 59 9:58 3966 186 2 8 7 8:30 426 32
1 6 60 10:04 3840 124 2 8 8 8:30 514 85
1 6 61 10:07 3834 86 2 8 9 8:30 549 145
1 6 62 10:07 3868 40 2 8 10 8:30 764 91
1 6 63 10:08 3853 199 2 8 11 8:32 673 49
1 6 64 10:08 4074 103 2 8 12 8:36 504 215
1 6 65 10:12 3851 44 2 8 13 8:36 769 65
1 6 66 10:15 3747 315 2 8 14 8:36 780 34
1 6 67 10:21 3612 432 2 8 15 8:41 490 86
1 6 68 10:27 3840 90 2 8 16 8:44 464 130
1 6 69 10:28 3870 312 2 8 17 8:45 514 131
1 6 70 10:31 3908 56 2 8 18 8:54 83 134
1 6 71 10:34 3792 132 2 8 19 8:55 129 806
1 6 72 10:36 3830 215 2 8 20 8:56 943 211
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

64

1 6 73 10:42 3555 243 2 8 21 8:59 912 47
1 6 74 10:42 3732 66 2 8 22 9:00 925 237
1 6 75 10:52 3186 66 2 8 23 9:01 1108 185
1 6 76 10:53 3240 53 2 8 24 9:01 1283 39
1 6 77 10:54 3187 156 2 8 25 9:01 1320 44
1 6 78 11:03 2791 353 2 8 26 9:02 1320 256
1 6 79 11:07 2858 278 2 8 27 9:14 884 95
1 6 80 11:08 3120 60 2 8 28 9:14 909 56
1 6 81 11:11 3060 60 2 8 29 9:15 913 39
1 6 82 11:11 3371 348 2 8 30 9:15 994 91
1 6 83 11:18 3263 359 2 8 31 9:19 900 81
1 6 84 11:33 2664 264 2 8 32 9:22 819 68
1 6 85 11:34 2880 240 2 8 33 9:24 1440 91
1 6 86 11:39 2880 60 2 8 34 9:25 2040 339
1 6 87 11:43 2700 41 2 8 35 9:34 1821 62
1 6 88 11:44 2659 79 2 8 36 9:35 1819 48
1 6 89 11:44 2760 42 2 8 37 9:38 1711 41
1 6 90 11:47 2658 198 2 8 38 9:40 1620 49
1 6 91 11:48 2820 238 2 8 39 9:44 1381 178
1 6 92 11:48 3122 273 2 8 40 9:45 1503 140
1 6 93 11:49 3329 136 2 8 41 9:46 1663 160
1 6 94 11:54 3073 88 2 8 42 9:46 1743 97
1 6 95 11:54 3165 231 2 8 43 9:46 1886 129
1 6 96 11:55 3294 112 2 8 44 9:51 1740 69
1 6 97 11:58 3122 182 2 8 45 9:52 1791 227
1 6 98 11:58 3360 49 2 8 46 10:03 1264 51
1 6 99 12:04 3011 54 2 8 47 10:03 1333 23
1 6 100 12:04 3072 72 2 8 48 10:05 1310 270
1 6 101 12:05 3060 600 2 8 49 10:06 1500 143
1 6 102 12:05 3900 47 2 8 50 10:08 1537 143
1 6 103 12:06 3900 300 2 8 51 10:12 1440 86
1 6 104 12:16 4440 300 2 8 52 10:16 1294 125
1 6 105 12:36 5220 225 2 8 53 10:20 1169 130
1 6 106 12:40 5115 25 2 8 54 10:20 1279 97
1 6 107 12:41 5100 50 2 8 55 10:22 1302 53
1 6 108 12:41 5160 74 2 8 56 10:24 1249 78
1 6 109 12:47 4906 54 2 8 57 10:24 1291 63
1 6 110 12:48 4912 58 2 8 58 10:27 1168 107
1 6 111 12:48 4974 238 2 8 59 10:28 1241 48
1 6 112 12:50 5036 947 2 8 60 10:35 893 150
1 6 113 12:51 5002 202 2 8 61 10:36 923 42
1 6 114 12:58 4800 102 2 8 62 10:38 960 119
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

65

1 6 115 12:59 4818 18 2 8 63 10:39 1020 101
1 6 116 1:00 4800 60 2 8 64 10:46 679 119
1 6 117 1:04 4620 75 2 8 65 10:49 620 321
1 6 118 1:16 3405 165 2 8 66 10:53 720 59
1 6 119 1:26 3480 174 2 8 67 10:53 780 423
1 6 120 1:37 2966 56 2 8 68 10:55 1137 300
1 6 121 1:40 2850 90 2 8 69 10:57 1260 46
1 6 122 1:49 2400 300 2 8 70 11:03 911 125
1 6 123 1:59 2400 49 2 8 71 11:03 1026 47
1 6 124 2:10 1751 71 2 8 72 11:04 1039 93
1 6 125 2:16 1500 49 2 8 73 11:05 1126 51
1 6 126 2:17 1451 210 2 8 74 11:08 1015 267
1 6 127 2:20 1481 161 2 8 75 11:09 1288 146
1 6 128 2:20 1620 98 2 8 76 11:17 782 35
1 6 129 2:28 1222 77 2 8 77 11:21 627 224
1 6 130 2:29 1205 344 2 8 78 11:21 840 182
1 6 131 2:29 1521 286 2 8 79 11:21 1020 58
1 6 132 2:30 1715 88 2 8 80 11:28 660 92
1 6 133 2:31 1687 119 2 8 81 11:31 568 170
1 6 134 2:32 1688 171 2 8 82 11:36 458 61
1 6 135 2:34 1697 77 2 8 83 11:36 517 70
1 6 136 2:35 1740 99 2 8 84 11:38 447 92
1 6 137 2:41 1440 12 2 8 85 11:38 595 202
1 6 138 2:42 1440 60 2 8 86 11:38 753 51
1 6 139 2:44 1380 120 2 8 87 11:52 0
235
1 6 140 2:45 1500 43 2 8 88 11:55 0
36
1 6 141 2:51 1157 317 2 8 89 11:57 0
64
1 6 142 2:54 1320 60 2 8 90 12:00 180 107
1 7 1 8:30 130 205 2 8 91 12:01
193 139
1 7 2 8:30 635 507 2 8 92 12:04
234 115
1 7 3 8:30 1028 178 2 8 93 12:05 299 152
1 7 4 8:30 1150 217 2 8 94 12:06 327 103
1 7 5 8:30 1353 46 2 8 95 12:08 344 201
1 7 6 8:30 1427 201 2 8 96 12:12 263 336
1 7 7 8:30 1526 73 2 8 97 12:16 407 194
1 7 8 8:30 1573 143 2 8 98 12:25 0
82
1 7 9 8:30 1680 42 2 8 99 12:27 0
113
1 7 10 8:30 1688 140 2 8 100 12:27 120 153
1 7 11 8:30 1848 95 2 8 101 12:29 147 786
1 7 12 8:30 1873 193 2 8 102 12:30 861 92
1 7 13 8:30 2044 151 2 8 103 12:37 589 70
1 7 14 8:30 2193 253 2 8 104 12:39 519 68
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

66

1 7 15 8:30 2360 155 2 8 105 12:42 391 109
1 7 16 8:30 2505 55 2 8 106 1:37 0
321
1 7 17 8:30 2570 60 2 8 107 1:37 339 139
1 7 18 8:30 2595 305 2 8 108 1:43 71 29
1 7 19 8:30 2830 59 2 8 109 1:45 60 133
1 7 20 8:30 2891 356 2 8 110 1:47 120 551
1 7 21 8:30 3195 225 2 9 1 8:30 0
71
1 7 22 8:30 3390 45 2 9 2 8:30 109 91
1 7 23 8:30 3465 92 2 9 3 8:30 198 39
1 7 24 8:30 3493 61 2 9 4 8:30 201 158
1 7 25 8:30 3552 56 2 9 5 8:36 240 97
1 7 26 8:30 3616 146 2 9 6 8:39 143 40
1 7 27 8:30 3729 59 2 9 7 8:41 240 272
1 7 28 8:45 2890 54 2 9 8 8:42 448 424
1 7 29 8:45 2956 51 2 9 9 8:47 564 71
1 7 30 8:45 3025 75 2 9 10 8:50 433 49
1 7 31 8:48 2890 170 2 9 11 8:51 444 35
1 7 32 8:48 3020 65 2 9 12 8:55 240 49
1 7 33 8:49 3015 555 2 9 13 8:58 120 57
1 7 34 8:51 3720 60 2 9 14 8:58 123 104
1 7 35 8:52 3900 180 2 9 15 8:59 619 99
1 7 36 8:53 4080 60 2 9 16 9:00 700 59
1 7 37 8:56 3993 38 2 9 17 9:01 701 126
1 7 38 8:56 4020 55 2 9 18 9:03 1560 60
1 7 39 8:58 3905 175 2 9 19 9:04 1520 119
1 7 40 8:58 4030 160 2 9 20 9:05 1581 39
1 7 41 9:00 4050 150 2 9 21 9:06 1602 53
1 7 42 9:01 4200 57 2 9 22 9:06 1669 126
1 7 43 9:02 4143 46 2 9 23 9:08 1663 138
1 7 44 9:02 4337 57 2 9 24 9:08 1765 40
1 7 45 9:04 4280 190 2 9 25 9:09 1785 71
1 7 46 9:05 4330 55 2 9 26 9:10 1774 35
1 7 47 9:11 4035 70 2 9 27 9:16 1499 78
1 7 48 9:13 3965 141 2 9 28 9:19 1361 98
1 7 49 9:20 3660 44 2 9 29 9:20 1323 34
1 7 50 9:21 3660 20 2 9 30 9:25 1109 210
1 7 51 9:21 3700 250 2 9 31 9:29 1080 59
1 7 52 9:21 3870 40 2 9 32 9:31 1020 60
1 7 53 9:22 4020 490 2 9 33 9:32 1020 100
1 7 54 9:22 4520 49 2 9 34 9:35 920 118
1 7 55 9:22 4591 42 2 9 35 9:36 982 62
1 7 56 9:23 4609 79 2 9 36 9:45 1260 65
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

67

1 7 57 9:25 4530 469 2 9 37 9:50 1075 176
1 7 58 9:27 4661 388 2 9 38 9:53 1079 135
1 7 59 9:30 4933 43 2 9 39 9:53 1184 73
1 7 60 9:33 4830 155 2 9 40 9:53 1231 131
1 7 61 9:34 4920 45 2 9 41 9:53 1339 66
1 7 62 9:36 4870 55 2 9 42 9:54 1333 149
1 7 63 9:46 4215 280 2 9 43 9:58 1304 122
1 7 64 9:46 4475 245 2 9 44 10:02 1182 184
1 7 65 9:48 4530 210 2 9 45 10:04 1238 74
1 7 66 9:48 4860 90 2 9 46 10:08 1044 45
1 7 67 9:56 4470 50 2 9 47 10:14 759 72
1 7 68 9:57 4480 50 2 9 48 10:15 747 68
1 7 69 9:58 4440 60 2 9 49 10:17 679 55
1 7 70 10:01 4320 214 2 9 50 10:23 384 71
1 7 71 10:02 4466 86 2 9 51 10:24 373 102
1 7 72 10:03 4740 80 2 9 52 10:24 511 242
1 7 73 10:05 4720 320 2 9 53 10:25 720 385
1 7 74 10:05 4940 170 2 9 54 10:27 1620 87
1 7 75 10:06 5010 90 2 9 55 10:31 1473 55
1 7 76 10:06 5100 280 2 9 56 10:33 1380 38
1 7 77 10:06 5360 239 2 9 57 10:34 1380 56
1 7 78 10:07 5481 62 2 9 58 10:44 784 572
1 7 79 10:13 5179 79 2 9 59 10:53 872 179
1 7 80 10:16 5100 101 2 9 60 10:55 933 349
1 7 81 10:16 5179 53 2 9 61 10:55 1260 44
1 7 82 10:19 5066 68 2 9 62 10:56 1260 81
1 7 83 10:33 4278 61 2 9 63 10:57 1299 58
1 7 84 10:40 3917 317 2 9 64 11:09 621 44
1 7 85 10:49 3720 289 2 9 65 11:13 457 292
1 7 86 10:49 2831 181 2 9 66 11:15 645 65
1 7 87 11:08 2830 231 2 9 67 11:22 240 40
1 7 88 11:10 3079 167 2 9 68 11:22 300 43
1 7 89 11:10 2792 515 2 9 69 11:26 77 379
1 7 90 11:17 2729 68 2 9 70 11:32 120 58
1 7 91 11:26 2781 67 2 9 71 11:33 120 131
1 7 92 11:27 2774 237 2 9 72 11:33 289 75
1 7 93 11:30 2777 123 2 9 73 11:34 274 45
1 7 94 11:39 2354 260 2 9 74 11:36 180 49
1 7 95 11:46 2220 54 2 9 75 11:37 180 167
1 7 96 11:47 2220 155 2 9 76 11:38 253 68
1 7 97 11:51 2115 234 2 9 77 11:39 245 66
1 7 98 11:55 2121 31 2 9 78 11:39 360 59
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

68

1 7 99 12:05 1560 30 2 9 79 11:41 300 36
1 7 100 12:08 1400 66 2 9 80 11:42 264 41
1 7 101 12:08 1444 210 2 9 81 11:45 163 86
1 7 102 12:08 1714 41 2 9 82 11:48 0
181
1 7 103 12:27 653 87 2 9 83 11:50 76 232
1 7 104
12:29
566 42 2 9 84 11:51
264 50
1 7 105
12:33
404 251 2 9 85 11:52
274 45
1 7 106 12:34 573 33 2 9 86 10:53*
3889 126
1 7 107 12:38 327 173 2 9 87 10:53*
4003 49
1 7 108 12:40 310 113 2 9 88 12:00 54 197
1 7 109 12:41 377 97 2 9 89 10:36*
5160 44
1 7 110 12:42 460 100 2 9 90 10:37*
5160 133
1 7 111
12:44
420 207 2 9 91 12:04
107 75
1 7 112
12:46
513 333 2 9 92 12:04
180 99
1 7 113
12:48
720 120 2 9 93 12:05
201 50
1 7 114
12:52
660 222 2 9 94 12:05
271 88
1 7 115
12:53
780 198 2 9 95 12:07
360 158
1 7 116
12:54
900 109 2 9 96 12:013
144 68
1 7 117 12:55 900 156 2 9 97 12:16 0
50
1 7 118 12:57 900 30 2 9 98 12:17 0
65
1 7 119 12:57 910 130 2 9 99 12:18 0
116
1 7 120 12:58 1020 103 2 9 100 12:21 0
177
1 7 121 1:00 337 257 2 9 101 12:22 63 35
1 7 122
1:44 360 112 2 9 102
12:22
148 62
1 7 123
1:44 428 161 2 9 103
12:22
206 116
1 7 124
1:44 567 65 2 9 104
12:22
330 43
1 7 125
1:45 562 33 2 9 105
12:22
407 155
1 7 126 1:47 529 226 2 9 106 12:29 72 108
1 7 127 1:47 603 363 2 9 107 12:31 84 92
1 7 128
1:48 960 328 2 9 108
12:32
180 216
1 7 129 1:52 1052 212 2 9 109 12:33 324 280
1 7 130 1:52 1260 60 2 9 110 12:35 480 44
1 7 131 1:55 1200 97 2 9 111 12:36 540 244
1 7 132
2:00 983 383 2 9 112
12:36
780 56
1 7 133 2:01 1620 120 2 9 113 12:46 182 38
1 7 134 2:01 1920 136 2 9 114 12:49 84 84
1 7 135 2:04 1844 266 2 9 115 12:49 180 54
1 7 136 2:08 1758 160 2 9 116 12:52 0
62
1 7 137 2:09 1838 948 2 9 117 1:25 300 60
1 7 138 2:14 3050 76 2 9 118 1:31 0
80
1 7 139 2:25 2434 74 2 9 119 1:32 40 40
1 7 140 2:28 2300 231 2 9 120 1:33 0
87
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

69

1 7 141 2:32 2249 155 2 9 121 1:35 0
94
1 7 142 2:39 1974 39 2 9 122 1:35 60 73
1 7 143 2:41 1821 28 2 9 123 1:38 0
100
1 7 144 2:45 1673 20 2 9 124 1:38 120 99
1 7 145 2:49 1400 890 2 9 125 1:39 141 41
1 7 146 2:50 1470 163 2 9 126 1:44 40 78
1 7 147 2:56 1547 78 2 9 127 1:45 22 147
1 7 148 3:02 1229 80 2 9 128 1:48 0
55
1 8 1 8:30 305 122 2 9 129 1:50 0
51
1 8 2 8:30 423 123 2 9 130 1:50 0
55
1 8 3 8:30 600 93 2 9 131 1:51 0
70
1 8 4 8:30 87 178 2 9 132 1:52 1080 552
1 8 5 8:30 809 44 2 9 133 1:54 1548 164
1 8 6 8:30 885 202 2 9 134 1:54 1624 170
1 8 7 8:30 983 174 2 9 135 1:57 1620 46
1 8 8 8:30 1109 49 2 9 136 2:08 968 37
1 8 9 8:30 1180 128 2 9 137 2:09 985 55
1 8 10 8:30 1292 142 2 9 138 2:11 934 47
1 8 11 8:30 1390 151 2 9 139 2:12 947 90
1 8 12 8:30 1599 68 2 9 140 2:12 977 40
1 8 13 8:30 1651 151 2 9 141 2:14 937 56
1 8 14 8:30 1815 111 2 9 142 2:15 941 82
1 8 15 8:30 1980 80 2 9 143 2:16 919 65
1 8 16 8:30 2100 40 2 9 144 2:16 960 136
1 8 17 8:30 2160 111 2 9 145 2:18 1020 60
1 8 18 8:30 2229 189 2 9 146 2:19 1080 83
1 8 19 8:30 2460 156 2 9 147 2:22 960 150
1 8 20 8:30 2604 314 2 9 148 2:26 840 78
1 8 21 8:30 4870 85 2 9 149 2:26 960 87
1 8 22 8:30 3045 101 2 9 150 2:28 933 68
1 8 23 8:30 3064 244 2 9 151 2:29 925 131
1 8 24 8:30 3600 47 2 9 152 2:31 914 87
1 8 25 8:35 3406 344 2 9 153 2:35 827 96
1 8 26 8:40 3362 62 2 9 154 2:35 851 378
1 8 27 8:42 3360 115 2 9 155 2:36 900 46
1 8 28 8:44 3365 125 2 9 156 2:45 367 88
1 8 29 8:44 3480 97 2 9 157 2:48 339 135
1 8 30 8:45 3503 95 2 9 158 2:50 360 89
1 8 31 8:45 3767 107 2 9 159 2:57 120 261
1 8 32 8:48 4030 61 2 9 160 3:01 159 58
1 8 33 8:48 4089 89 2 9 161 3:02 151 468
1 8 34 8:48 4250 139 2 10 1 8:30 780 157
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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70

1 8 35 8:50 4231 132 2 10 2 8:30 983 25
1 8 36 8:55 4039 319 2 10 3 8:30 1020 32
1 8 37 8:59 4140 360 2 10 4 8:30 1036 33
1 8 38 9:04 4260 213 2 10 5 8:30 1123 64
1 8 39 9:05 4467 70 2 10 6 8:30 1179 75
1 8 40 9:05 4517 73 2 10 7 8:30 1224 39
1 8 41 9:06 4504 79 2 10 8 8:30 1260 50
1 8 42 9:08 4500 45 2 10 9 8:30 1270 73
1 8 43 9:09 4500 106 2 10 10 8:30 1437 148
1 8 44 9:10 4514 94 2 10 11 8:30 1560 87
1 8 45 9:11 4600 220 2 10 12 8:30 1653 124
1 8 46 9:12 4740 103 2 10 13 8:38 1320 616
1 8 47 9:12 4877 117 2 10 14 8:38 2024 95
1 8 48 9:13 4880 53 2 10 15 8:41 1839 115
1 8 49 9:16 4767 48 2 10 16 8:43 1874 95
1 8 50 9:16 4839 110 2 10 17 8:44 1959 56
1 8 51 9:16 4969 80 2 10 18 8:45 1963 49
1 8 52 9:17 4949 107 2 10 19 8:49 1740 51
1 8 53 9:23 4680 31 2 10 20 8:52 1563 82
1 8 54 9:25 4570 212 2 10 21 8:53 1620 107
1 8 55 9:25 4838 50 2 10 22 8:55 1573 94
1 8 56 9:25 4908 53 2 10 23 8:56 1659 72
1 8 57 9:26 4915 133 2 10 24 8:57 1647 38
1 8 58 9:27 4962 42 2 10 25 8:58 1669 620
1 8 59 9:27 4980 60 2 10 26 9:01 2069 59
1 8 60 9:30 4920 96 2 10 27 9:04 2040 209
1 8 61 9:38 4524 283 2 10 28 9:08 1980 63
1 8 62 9:38 4841 401 2 10 29 9:09 1980 130
1 8 63 9:43 4920 104 2 10 30 9:10 2058 120
1 8 64 9:45 4876 231 2 10 31 9:14 3000 98
1 8 65 9:45 5125 290 2 10 32 9:14 3082 63
1 8 66 9:48 5255 283 2 10 33 9:16 3019 68
1 8 67 9:55 5152 73 2 10 34 9:16 3180 157
1 8 68 9:55 5199 409 2 10 35 9:16 3323 69
1 8 69 9:58 5450 59 2 10 36 9:19 3194 165
1 8 70 10:01 5331 165 2 10 37 9:21 3269 236
1 8 71 10:02 5406 121 2 10 38 9:21 3513 62
1 8 72 10:02 5465 154 2 10 39 9:26 3480 100
1 8 73 10:05 5671 238 2 10 40 9:31 3300 200
1 8 74 10:06 5733 61 2 10 41 9:31 3520 94
1 8 75 10:16 5129 176 2 10 42 9:33 3420 179
1 8 76 10:16 5313 358 2 10 43 9:44 3840 199
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

---

71

1 8 77 10:25 5675 376 2 10 44 9:47 3881 62
1 8 78 10:26 5479 139 2 10 45 9:49 3780 155
1 8 79 10:34 5580 228 2 10 46 9:51 3900 155
1 8 80 10:37 5292 192 2 10 47 9:53 3925 71
1 8 81 10:40 5340 108 2 10 48 9:58 3674 84
1 8 82 10:52 5232 42 2 10 49 9:59 3770 107
1 8 83 10:57 4590 368 2 10 50 9:59 3783 50
1 8 84 11:03 4642 142 2 10 51 10:00 3793 42
1 8 85 11:06 4440 86 2 10 52 10:04 3840 163
1 8 86 12:12 4354 79 2 10 53 10:04 3977 98
1 8 87 12:45 535 195 2 10 54 10:06 3999 93
1 8 88 12:49 240 141 2 10 55 10:06 4086 37
1 8 89 12:49 159 77 2 10 56 10:09 3929 64
1 8 90 12:51 82 63 2 10 57 10:10 3925 48
1 8 91 12:51 139 79 2 10 58 10:10 3997 76
1 8 92 12:57 240 75 2 10 59 10:13 3861 58
1 8 93 12:58 240 30 2 10 60 10:13 3923 44
1 8 94 12:58 445 45 2 10 61 10:14 3939 55
1 8 95 1:00 200 74 2 10 62 10:14 4020 130
1 8 96 1:03 66 66 2 10 63 10:15 4130 50
1 8 97 1:04 180 140 2 10 64 10:57 1620 150
1 8 98 1:06 160 50 2 10 65 10:57 1770 296
1 8 99 1:06 230 141 2 10 66 10:58 2014 129
1 8 100 1:07 209 132 2 10 67 10:59 2065 85
1 8 101 1:07 257 58 2 10 68 10:59 2160 321
1 8 102 1:08 259 126 2 10 69 10:59 2499 110
1 8 103 1:09 307 57 2 10 70 11:00 2569 135
1 8 104 1:12 190 40 2 10 71 11:01 2580 30
1 8 105 1:13 252 89 2 10 72 11:01 2584 45
1 8 106 1:17 120 31 2 10 73 11:02 2600 56
1 8 107 1:17 132 55 2 10 74 11:06 2424 73
1 8 108 1:19 77 36 2 10 75 11:10 2220 120
1 8 109 1:21 60 79 2 10 76 11:13 2160 157
1 8 110 1:22 101 136 2 10 77 11:14 2340 86
1 8 111 1:23 145 127 2 10 78 11:18 2160 135
1 8 112 1:24 198 78 2 10 79 11:22 2040 71
1 8 113 1:29 0
88 2 10 80 11:25 1920 76
1 8 114 1:30 92 191 2 10 81 11:26 1920 44
1 8 115 1:32 741 81 2 10 82 11:26 1980 58
1 8 116 1:37 0
60 2 10 83 11:32 1680 326
1 8 117 1:37 1440 540 2 10 84 11:34 1860 141
1 9 1 8:30 502 125 2 10 85 11:42 1539 84
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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72

1 9 2 8:30 617 110 2 10 86 11:46 1335 55
1 9 3 8:30 747 202 2 10 87 11:47 1340 49
1 9 4 8:30 905 114 2 10 88 11:49 1291 57
1 9 5 8:30 1031 131 2 10 89 11:50 1294 76
1 9 6 8:30 1200 48 2 10 90 11:54 1098 33
1 9 7 8:30 1212 132 2 10 91 11:56 1020 40
1 9 8 8:30 1380 111 2 10 92 12:10 185 154
1 9 9 8:30 1449 154 2 10 93 12:13 211 104
1 9 10 8:30 1655 83 2 10 94 12:14 780 150
1 9 11 8:30 1692 77 2 10 95 1:05 420 83
1 9 12 8:30 1855 125 2 10 96 1:06 457 71
1 9 13 8:30 1970 59 2 10 97 1:11 201 184
1 9 14 8:30 2013 63 2 10 98 1:24 197 148
1 9 15 8:30 2088 288 2 10 99 1:24 409 85
1 9 16 8:30 2325 136 2 10 100
1:24 564 41
1 9 17 8:30 2429 39 2 10 101
1:26 403 64
1 9 18 8:32 2520 346 2 10 102
1:28 339 72
1 9 19 8:33 2714 108 2 10 103
1:32 147 257
1 9 20 8:36 2666 62 2 10 104
1:32 370 127
1 9 21 8:39 2544 136 2 10 105
1:35 303 56
1 9 22 8:40 2588 210 2 10 106
1:35 367 138
1 9 23 8:43 2678 53 2 10 107
1:36 480 43
1 9 24 8:43 2745 255 2 10 108
1:38 366 83
1 9 25 8:43 2970 330 2 10 109
1:38 523 70
1 9 26 8:43 3300 190 2 10 110
1:40 453 134
1 9 27 8:45 3420 360 2 10 111
1:42 439 287
1 9 28 8:45 4566 186 2 10 112
1:55 300 70
1 9 29 8:47 4746 206 2 10 113
1:59 170 50
1 9 30 8:48 4960 204 2 10 114
1:59 180 50
1 9 31 8:48 5116 41 2 10 115
2:00 130 83
1 9 32 8:52 4955 126 2 10 116
2:00 287 200
1 9 33 8:53 5009 255 2 10 117
2:08 0
121
1 9 34 8:53 5234 53 2 10 118
2:08 173 53
1 9 35 8:54 5241 58 2 10 119
2:08 126 125
1 9 36 8:55 5246 168 2 10 120
2:10 180 57
1 9 37 8:55 5435 175 2 10 121
2:11 123 94
1 9 38 8:56 5624 88 2 10 122
2:12 209 380
1 9 39 8:57 5596 160 2 10 123
2:24 0
165
1 9 40 8:58 5736 138 2 10 124
2:27 0
223
1 9 41 9:03 5898 41 2 10 125
2:30 120 76
1 9 42 9:03 5977 192 2 10 126
2:31 120 40
1 9 43 9:04 6205 78 2 10 127
2:31 184 31
Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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73

1 9 44 9:05 6707 56 2 10 128
2:35 33 65
1 9 45 9:05 6371 238 2 10 129
2:39 0
216
1 9 46 9:09 6853 238 2 10 130
2:41 84 100
1 9 47 9:13 7091 62 2 10 131
2:43 104 61
1 9 48 9:14 5775 236 2 10 132
2:46 0
141
1 9 49 9:14 6095 270 2 10 133
2:47 99 89
1 9 50 9:17 6059 116 2 10 134
2:48 120 86
1 9 51 9:18 6094 125 2 10 135
2:51 34 50
1 9 52 9:21 5943 91 2 10 136
2:53 0
151
1 9 53 9:21 6166 137 2 10 137
2:55 29 149

Legend:
C1 = Teller Number
C2 = Day Number
C3 = Customer Number
C4 = Arrival Time
C5 = Waiting Time in Seconds
C6 = Service Time in Seconds
























Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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74


D. Arrival Time and Service Time

Probability
Arrival Time Probability
22 2.71828 36 0.9974

22 2.71828 37 0.9985
λ e x
P(X
≤ x)
22 2.71828 38 0.9992

22 2.71828 39 0.9996
22 2.71828 0 2.1571E10
22 2.71828 40 0.9998
22 2.71828 1 5.0167E09
22 2.71828 41 0.9999
22 2.71828 2 5.8445E08
22 2.71828 42 0.9999
22 2.71828 3 4.5483E07
22 2.71828 43 1.0000
22 2.71828 4 2.6604E06
22 2.71828 44 1.0000
22 2.71828 5 1.2479E05
22 2.71828 45 1.0000
22 2.71828 6 4.8899E05
22 2.71828 46 1.0000
22 2.71828 7 1.6470E04
22 2.71828 47 1.0000
22 2.71828 8 4.8688E04
22 2.71828 48 1.0000
22 2.71828 9 1.2836E03
22 2.71828 49 1.0000
22 2.71828 10 3.0569E02
22 2.71828 50 1.0000
22 2.71828 11 0.0066

22 2.71828 12 0.0133
λ = mean arrival rate
22 2.71828 13 0.0247
x = number of arrivals
22 2.71828 14 0.0428

22 2.71828 15 0.0697
Service Time Probability
22 2.71828 16 0.1071

22 2.71828 17 0.1560
μ e
x p(st ≤ x)
22 2.71828 18 0.2166
22 2.71828 19 0.2875
14 2.71828
0.1
0.7534
22 2.71828 20 0.3664
14 2.71828
0.2
0.9392
22 2.71828 21 0.4500
14 2.71828
0.3
0.9850
22 2.71828 22 0.5346
14 2.71828
0.4
0.9963
22 2.71828 23 0.6165
14 2.71828
0.5
0.9991
22 2.71828 24 0.6924
14 2.71828
0.6
0.9998
22 2.71828 25 0.7600
22 2.71828 26 0.8179
14 2.71828
0.7
0.9999
22 2.71828 27 0.8656
14 2.71828
0.8 0.999986
22 2.71828 28 0.9035
14 2.71828
0.9 0.999997
22 2.71828 29 0.9326
14 2.71828
1 0.999999
22 2.71828 30 0.9542

22 2.71828 31 0.9697
µ = mean service rate
22 2.71828 32 0.9805
22 2.71828 33 0.9877
x = service time
22 2.71828 34 0.9925

22 2.71828 35 0.9955

Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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E. Multiple-Server Operating Characteristics of Customers Serviced at Landbank-
La Trinidad, Benguet

Queueing Analysis: Multiservers (2) Single-Queue

Inputs
Time unit hour
Arrival rate (λ) 22.2571
Service rate (μ) 14.4286
Number of servers (k) 2

Performance measure
Utilization rate 0.79
Probability that the teller is idle (Po) 0.12
Average number of the customers in the system (L) 5
Average time a customer spends in the system, hours (W) 0.21
Average number of customers in the queue (Lq) 3
Average time a customer spends in the queue, hours (Wq) 0.14
Probability that an arriving customer has to wait for service (Pw) 0.69



Queueing Analysis: Multiservers (3) Single-Queue

Inputs
Time unit hour
Arrival rate (λ) 22.2571
Service rate (μ) 14.4286
Number of servers (k) 3

Performance measure
Utilization rate 0.52
Probability that the teller is idle (Po) 0.19
Average number of the customers in the system (L) 2
Average time a customer spends in the system, hours (W) 0.08
Average number of customers in the queue (Lq) 0.27
Average time a customer spends in the queue, hours (Wq) 0.01
Probability that an arriving customer has to wait for service (Pw) 0.26


Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet
/ Melanie B. Menzi & Rhea B. Ngoaban. 2008

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Document Outline

• Analysis of Queueing of Customers Serviced at Landbank-La Trinidad, Benguet.
  • BIBLIOGRAPHY
  • ABSTRACT
  • TABLE OF CONTENTS
  • INTRODUCTION
  • REVIEW OF LITERATURE
  • THEORETICAL FRAMEWORK
  • METHODOLOGY
  • RESULTS AND DISCUSSION
  • SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
  • LITERATURE CITED
  • APPENDIX

---