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Abstract - The Cebu South Bus Terminal

(CSBT) has continuously developed over the years.

Recently,

The terminal had put up a conducive waiting and

ticketing area for the customers’ satisfaction. But

there is more to customer satisfaction. There are

several factors to be considered in meeting each

demand a customer wants. If the terminal has

succeeded in attracting customers, another factor that

needs consideration is the customers queuing time.

Waiting lines abound in all sorts of service systems

and they are non-value-added occurrences. For

customers, having to wait for service can range from

being acceptable, to being annoying, to being a

matter of life and death.

This study involves the analysis of the existing

ticketing system of Alcoy via Argao Ceres Bus Liner

of CSBT with which propositions are based. Assessed

in this research are the arrival of customers and thenumber of customers being served per unit time.

In the process of collecting factual data, the

inquiry made use of actual observation, interview and

tally method. Furthermore, the analysis made use of

goodness-of-fit test, hypothesis testing, queuing

theory and simulation.

With the foregoing findings, the company can

address the length of queue in the system through

adding the number of servers to be able to minimize

total system cost per unit time.

Keywords: queuing time, bus terminal,

ticketing system, waiting line, simulation

I. INTRODUCTION

Queuing theory is the study of queue or waiting lines.

Some of the analysis that can be derived using queuing

theory include the expected waiting time in the queue, the

average time in the system, the expected queue length, the

expected number of customers served at one time, the

probability of balking customers, as well as the

probability of the system to be in certain states, such as

empty or full.

Waiting lines are a common sight in bus terminals

especially during weekends and holidays. Hence, queuing

theory is suitable to be applied in a bus terminal setting

since it has an associated queue or waiting line where

customers who cannot be served immediately have to

queue (wait) for service. There are 11 servers working at

the same time. Based on personal interview and

observation, the Alcoy via Argao Ceres Bus Liner server

has the longest waiting line. This study uses queuing

theory to evaluate the said waiting line in CSBT at Cebu

City, Cebu. In addition, this study seeks to illustrate the

usefulness of applying queuing theory in a real case

situation, specifically, in finding the ideal number of

servers that would have the minimum total system cost at

maximum system capacity.

A. Objectives

1. To make a cost analysis of the system.2. To determine the ideal number of servers at

maximum system capacity.

B. Scope and Limitations of the Study

The study’s main subject is the queuing analysis

of the Alcoy via Argao Ceres Bus Liner ticketing

area. The focus of the study is not on redesigning the

process but rather on the ideal number of servers that

would minimize the total cost of the system. This

study focused only on the dense influx of passengers

in the ticketing area.

C. Statement of Assumptions

1. Salary of ticket officer per day is Php180.00.

2. The ticket officers work 8 hours a day.

3. Cost of customer waiting per hour is

Php20.00. This is for calculation purposes.

METHODOLOGY

Based on personal interview and actual observation,

the Alcoy via Argao Ceres Bus Liner server has the

Queuing Analysis of Ticketing System of Alcoy via Argao

Ceres Bus Liner at Cebu So=uth Bus Terminal

*Joahnna Jane C. Aratan, Jessabelle A. Caminero, Jaynamae N. Campo, Jessa

Rona C. Cepada, Estella Ching S. Dacutan, Ma. Gracelyn A. Demoral

Department of Industrial Engineering, Cebu Institute of Technology-University Cebu City,

Philippines, 6000

([email protected])



longest waiting line. After determining the longest

waiting line, tally method was used in getting the number

of arrivals and the customers being served per unit time.

II. RESULTS

A. Influx Rate of Passengers

The following are the influx rate of passengers for

each day per peak season. These indicate the number of

customers per minute who arrives and joins the queue.

Figure 1. Influx Rate of Passengers from Monday to

Friday (From 6:05 PM to 7:00 PM)

B. Calculations

GOODNESS-OF-FIT TEST OF ARRIVAL RATE OF

PASSENGERS

Chi-Square Goodness-of-Fit test is commonly used to

test association of variables in two-way tables, where the

assumed model of independence is evaluated against the

observed data. In general, the chi-square test statistic is

of the form

The Poisson distribution is used to model the number of events occurring within a given time interval.

The formula for the Poisson probability mass

function is

Lambda

(λ) is the shape parameter which indicates the average

number of events in the given time interval.

The following is the plot of the Poisson probability

density function for four values of λ.

Figure 2. Plot of the Poisson Probability Density

Function for Four Value of λ

Waiting lines are a direct result of arrival and service

variability. They occur because random, highly variable

arrival and service patterns cause systems to be

temporarily overloaded. In many instances, the

variabilities can be described by theoretical distributions.

In fact, the most commonly used models assume that the

customer arrival rate can be described by a Poisson

distribution and that the service time can be described bya negative exponential distribution. Figure 8 illustrate

these distributions.

0

0.1

0.2

0.3

0 1 2 3 4 5 6 7 8 9 10 11 12

Customersper timeunit

R e l a t i v e f r e q u e n c y

Figure 3. Poisson Distribution (rate)

The following are the summary of results:

Day

Ave. no.

of

arrivals

per min

χ c2 χ t

2Interpretatio

n

Mon 1.727 7.237 9.488Poisson

Distributed

Tue 1.636 7.928 9.488Poisson

Distributed

Wed 3.364 12.384 15.507Poisson

DistributedThu 1.873 8.008 12.592

Poisson

Distributed

Fri 2.091 10.219 15.507Poisson

Distributed

Ave 2.138 9.1552 12.516Poisson

Distributed

Table 1. Summary of Arrivals’ Results Using

Goodness-of-Fit Test (From Monday to

Friday)

The following are sample calculations:

x f o f ox P(x) f e (f o - f e)2/



f e

0 13 00.177

89.7773 1.062257

1 17 170.307

1

16.888

00.000743

2 8 16

0.265

2

14.585

1 2.973142

3 8 240.152

78.3975 0.018814

4 7 280.065

93.6262 3.139006

5 2 100.031

41.7270 0.043155

Σf o=

55

Σf ox

=

95

ΣP(x)

=

1.000

0

Σf e =

55.001

1

Xc2 =

7.2371

λ = 1.727

Table 2. Monday Arrivals’ Results Using Goodness-of-

Fit Test

*x is the number of customer arrival

*f o is the observed frequency of x

*λ is the customer arrival rate

* P(x) is the probability of x

*f e is the expected frequency of x

Six-Step Hypothesis Testing:

Step 1. State the null and alternative hypotheses:

Ho: The arrival of customers is Poisson Distributed.

Ha: The arrival of customers is not PoissonDistributed.

Step 2. Choose the level of significance: α , the

probability of making a Type I Error if H0 is true.

α = 0.05

Step 3. Determine the critical values for the level of significance α ,

d f = k-p-1 = 6-1-1 = 4

Xt2 = 9.488

Step 4. Decision Rule

|χ c2|≥|χ t

2|: Reject Ho

|χ c2|<|χ t

2|: Do not Reject Ho

Ste p 5. Calculate the test statistic

Xc2 = 7.2371

Step 6. Conclusion

Since χ c2<χ t

2: Do not Reject Ho

Therefore, the arrival of customers is Poisson Distributed.

λ = Σf ox/Σf oλ = 95/55

λ = 1.727

Figure 4. Graph of Poisson Distribution (Rate)

from Monday to Friday

There are numerous queuing models from which

analysts can choose. Naturally, much of the success of the

analysis will depend on choosing an appropriate model.

Model choice is affected by the characteristics of the

system under investigation. The main characteristics are

population source, number of servers (channels), arrival

and service patterns and queue discipline (order of

service). The approach to use in analyzing a queuing problem depends on whether the potential number of

customers is limited. There are two possibilities: infinite-

source and finite-source populations. In the case of this

study, the possibility is infinite-source.

The following is a list of symbols used for infinite-

source models.

Symbol Represents

λ Customer arrival rate

μ Service rate per server

Lq The average number of customers

waiting for service

L s The average number of customers inthe system (waiting and/or being

served)

r The average number of customers

being served

ρ The system utilization

DAYλ

(cpm)

µ

(cpm)

Monday 1.727 1.450

Tuesday 1.636 2.150

Wednesda

y 3.364 3.160



Thursday 1.873 1.800

Friday 2.091 2.850

Average2.138

2.282

Table 3. Summary of Results from ….Monday to

Friday

*cpm, customers per minute

No. of

servers1 2 3 4

(Lq) 13.91 0.41 0.14 0.07

(Ls) 14.85 0.88 0.45 0.31

(Wq) 6.51 0.19 0.07 0.03

(Ws) 6.94 0.41 0.21 0.14

(Pw) 0.94 0.47 0.31 0.23

Table 4. Effect of No. of Servers on the System

COST ANALYSIS

No. of

servers 1 2 3 4

Custome

r waiting

cost per

minute

4.94 0.29 0.15 0.10

Server

cost per

minute

0.38 0.75 1.13 1.50

Total

cost per

minute

5.32 1.04 1.28 1.60

Table 5. Total System Cost per minute

Sample computations:

Lq = λ 2 / [μ(μ-λ)]

= (2.138)2 / [2.282(2.282-2.138)]

= 13.91

Ls = λ / (μ-λ)

= 2.138 / (2.282-2.138)

= 14.85

Wq = λ / [μ(μ-λ)]

= 2.138 / [2.282(2.282-2.138)]

= 6.51 minutes/customer Ws = 1 / (μ-λ)

= 1 / (2.282-2.138)

= 6.94

Pw = 2.138 / 2.282

= 0.94

Each ticket officer is paid Php180 per day at

minimum. Therefore, the server cost per minute is

=(Php180/day)(1day/8hours)(1hour/60minutes)

= Php0.375/minute

Customer waiting cost per minute is L s x Php20/hour

=(14.85)(Php20/hour)(1hour/60minutes)

= Php4.94/minute

Total cost per minute is customer waiting cost per

minute plus server cost per minute. In calculating, we get,

= Php0.375/minute + Php4.94/minute

= Php5.32/minute

The following is the simulation layout of the existingsystem of Alcoy via Argao Ceres bus liner:

Figure 5. Simulation Layout of CSBT Alcoy via

Argao Ticketing Area

III. DISCUSSION

More customers queue at the Alcoy via Argao

ticketing area as 7:00 P.M. approaches. This is the time

where the Ceres bus liner has its last trip. This is also the

time where workers from different companies and

students flood in the terminal.

Since all the arrivals were Poisson Distributed,queuing theory was applicable. The effect of number of

servers on ticketing operation was computed and cost

analysis made possible. One of the requirements of any

practical system is that λ < μ, which means ρ < 1, failing

which an unstable system results. If the arrivals are faster

than the time in which they can be processed, the waiting

line and the waiting time will increase continuously, and

no steady state can be achieved.

Based on the results of the cost analysis, it was found

out that two (2) servers will minimize the total cost of the

system. Because the total cost will continue to increase

once the minimum has been reached.

Using simulation to aid in the analysis, it turned outthat the same number of servers is needed to lessen the

length of the queue.

IV. CONCLUSION

Based on the results, it was found out that the server of

Alcoy via Argao Ceres bus liner ticketing area is not

sufficient. Thus, there is a need to calculate for the ideal

number of servers for the system. By doing a cost and

simulation analysis of the system, the ideal number of

servers was determined. Based on the results, the bus liner

should have two (2) servers in order to minimize the total



cost per minute of the system. By doing so, the company

could save an amount of Php5.32/minute –

Php1.04/minute = Php4.28/minute. Therefore, a total

annual savings of

=(Php4.28/minute)(60minutes/hour)(8hours/day)

(350days/year)

= Php719,040/year

V. RECOMMENDATION

Primary Recommendation

The researchers recommend that the Alcoy via

Argao Ceres bus liner ticketing area should have two

(2) servers in their ticketing area to minimize total

cost in the system.

Secondary Recommendation

Further research must be conducted in the CSBT

regarding the ticketing process, the layout of the

ticketing area, the capacity of the bus and other

operations in the bus terminal that needs to be

evaluated for further improvements.

REFERENCES

[1] http://ascelibrary.org/proceedings/resource/2/asc

ecp/387/41139/478_1?isAuthorized=no

[2] http://www.clancor.net/ticket-system.html

[3] http://www.daniweb.com/web-development/php/threads/227665

[4] http://www.lockmedia.com/solutions/bus_ticketi

ng_system_demo.asp

[5] http://www.stat.yale.edu/Courses/1997-

98/101/chigf.htm

[6] Stevenson, William J. Operations

Management. 9th Ed. Philippines: MacGraw-

Hill, 2007, ch. 14, pp. 720-722

[7] Levin, Rubin, Stinson and Gardner Quantitative

Approaches to Management, 6th Ed. Singapore:

McGraw-Hill Companies, Inc., 2001, ch. 18, pp.

813-830

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