group assignement queuing model jan 28

7/30/2019 Group Assignement Queuing Model Jan 28

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Unity University

School of Graduate Studies

Department of Business Administration

MBA General-Regular

Title: The Application of Queuing Model: A Case of Dashen Bank Main

Area Branch

Type: Group Work

Submitted To: Mathiwos Enserumu (Phd)

Prepared by:

Selamawit Dechassa Cherenet Berhanu Semere Deribe Metkel Kebede Dawit Deribew Frewoyeni Getahun Netsanet Melaku

January 25, 2013

Addis Ababa, Ethiopia


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Table of Contents

Acknowledgement................................................................................................................................................................... ii

1 Introduction ..................................................................................................................................................................... 1

1.1 Background of the Study and the Company .............................................................................................. 1

1.2 Statement of the problem ................................................................................................................................. 2

1.3 Objective of the study ......................................................................................................................................... 3

1.4 Methodology ........................................................................................................................................................... 3

1.4.1 Design .............................................................................................................................................................. 3

1.4.2 Data source and data collection method ........................................................................................... 3

1.4.3 Data analysis method ................................................................................................................................ 3

1.5 Scope and Limitation of the study ................................................................................................................. 41.6 Significance of the study .................................................................................................................................... 4

2 Literature Review .......................................................................................................................................................... 5

2.1 Definitions: .............................................................................................................................................................. 5

2.2 Queuing Theory .................................................................................................................................................... 6

2.3 Queuing analysis ................................................................................................................................................... 7

2.4 Elements of a queue ............................................................................................................................................ 7

2.5 Components of Queuing System: ................................................................................................................... 8

2.6 Types of queuing system ................................................................................................................................. 10

2.6.1 The Single-Server Waiting Line System .......................................................................................... 10

2.6.2 The Multiple-Server Waiting Line ..................................................................................................... 13

3 Data analysis .................................................................................................................................................................. 15

4 Concluding statement and Recommendation .................................................................................................. 20

4.1 Concluding Statement ...................................................................................................................................... 20

4.2 Recommendations ............................................................................................................................................. 20

5 Reference ......................................................................................................................................................................... 21


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Acknowledgement

First of all we would like to express gratitude to our Instructor Matiwos Ensermu (PhD.) for

his lecture and unlimited assistance anytime and anywhere. Further we appreciate the

Kadisco Hospital management for their support to get the required information by

observing the hospitals service process. We would also like to give thanks to our friend

Michael Addisu for his support in consulting us in the approach of analysis. Last but not

least Dashen bank main area branch accountant and the supportive team of tellers for their

willingness and readiness to provide us with significant data information and data.


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1 IntroductionQueuing theory is the mathematical study of waiting lines or queue. The theory enables

mathematical analysis of several related processes, including arriving at the queue, waiting

in the queue and being served by the server(s) at the front of the queue. This paper consists

of five parts the first part contains; the background of the study and the company,

statement of the problem, objective of the study, methodology, scope and limitation and

significance of the study. Whereas the second part consists of the literature review queuing

systems characteristics, analysis and types of queue systems most common in the queue

models. This is followed by our proposed or suitable queuing system model is shown that is

the multiple-queuing system for our case. Experimental results are shown, followed by

brief concluding statements and recommendations

1.1 Background of the Study and the CompanyCurrently banks are one of the most important units of the public in Ethiopia. It can also be

observed that the competitive banks try to get full advantage of any new technology to

increase customer satisfaction. Therefore our paper has focused on analyzing the queues to

optimize the operations and to reduce waiting time for customers of Dashen bank.

This paper focuses on the bank lines system and queuing processes that are used in banks

to serve the customers. Recently banks we see in the city or the country use standard

queuing models. To avoid standing in a queue for a long time or in a wrong line, most banks

use automatic queue system to give tickets to all customers. The customer can push a

specific button in tickets supplier device according to transaction needs. The new economic

policy introduced in November, 1991 caused the culmination of the command economic

heralding the establishment of a market oriented one. This policy change created an

opportunity and a conducive environment for the emergence of private financialinstitutions aimed at the bringing a meaningful economic role in the development efforts of

the country.

Dashen Bank was established as per the intent of the new policy and the Ethiopian

investment code. It came into existence on September 20, 1995 according to the


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commercial code of Ethiopia, 1960, and the licensing and supervision of banking business

proclamation No. 84/1994.

The first founding members were 11 businessmen and professional that agreed to combine

their financial resources and expertise to form this new private bank.

The rationale behind its name, "Dashen Bank" is related to "Ras Dashen" which is the

highest mountain of Ethiopia. It is also the habitat of rare wild animals; the Wali Ibex, the

Gelada Baboon, and the Lammergeyer - the beautiful bone breaker eagle. These unique

characteristics of the mountain coincided with the interest of the founders of the Bank and

prompted them to adopt this great name and epitomize their aspiration. Rightly, reaching

the top of banking business in dynamic and competitive business environment symbolized

the highest peak, while the unique and efficient services the bank caters for the public

through state -of-the-art computer technology and carefully selected and trained man-

power equated with the rare wild animals. Today, indeed, reliability, efficiency and

modernity are the hallmark and the bank's distinguishing features which make them

synonymous with Dashen Bank as much as the rare animals are synonymous with Ras-

Dashen Mountain.

The business purpose of the banks as enshrined in its basic documents is to render

commercial banking activities both at the domestic and international spheres.

Customers are presumed to be one of the most important stakeholders in any organization

because without them, organizations are not likely to succeed. Usually customers are

dissatisfied when there is high junk in the process of taking service. Thus many companies

try to apply the contemporary technology to satisfy customers in many situations. To

reduce queue, customers waiting time, Dashen bank implement modern technology like

queue machine which help the customer to order in first come first served way to take allservice in one window.

1.2 Statement of the problemService is a social act which takes place in direct contact between the customer and

representatives of the service company. The arrival rate of customer may change due to the


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time of day, the day of the week, or the season of the year. A system with congestion

discourages arrivals. A queue forms whenever current demand exceeds the existing

capacity to serve. How is the performance of Dashen bank main area branch with regard to

service rate in giving service and queue of customers in taking service?

1.3 Objective of the studyThis paper seeks to show the contribution and applications of queuing theory in the

banking area by applying the mathematical model to assess their performance with regard

to customer queue and service rate. Thus, this paper assesses a range of queuing theory

results in the following areas at Dashen main area branch:

- The average number of customers spends in queuing system (waiting and beingserved).

- The average number of customers in the queue.- The average time a customer spends in the queue (waiting to be served).- The probability that a customer arriving in the system must wait for service.

1.4 Methodology1.4.1 Design

In the course of conducting this study, the studiers use mainly quantitative data and

partially qualitative data.

1.4.2 Data source and data collection methodThe studiers use secondary data gathered from queuing machine record and accountant

record. Primary data is taken from personnel of the bank, simply by oral interviewing.

1.4.3 Data analysis methodThe row data gathered are analyzed by using different descriptive methods like table and

mathematical model.


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1.5 Scope and Limitation of the studyThis paper focus on the analysis of queuing results on only Dashen bank main area branch.

In doing this paper the major difficulties faced by the studiers are:

- Because of high banking competition, it is hard to get any relevant and confidentialinformation from the concerned body.

- The document what we get from the bank queuing machine(which is average) andwhat the model required(Actual observation data per hour) has some gap and will

proceed on some fluctuation of the result.

- Before taking the case of Dashen bank we took the case of Kadisco Hospital. After athree days observation the computation stated that the average arrival rate (lambda)

was greater than the average service time (). If the arrival rate is higher than theservice rate, the system will be blocked. Hence, we will only consider the analysis of

the system where the arrival rate is less than the service rate. This action/decision

resulted in time constraint as we changed the case; which also required an

application of a different type of queuing system due the differed transaction.

1.6 Significance of the studyThe study is important for the studiers to analyze the difference and relationship between

the theory and real practice of the queue model. The result would be used by the bank to

enhance its service by maintaining its good part and adjusting its drawbacks. When the

bank enhances its service the customer will be satisfied and in the long run they will be

loyal to the bank.


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2 Literature Review2.1 Definitions:

Service:Service is any activity or series of activities of more or less intangible nature that

normally, but not necessarily, take place in interactions between the customer and service

employees and/or systems of the service provider, which are provided as solutions to

customer problems.

Quality:Quality is a measure of the extent to which a thing or experience meets a need,

solves a Problem, or adds value for someone.

Customer Satisfaction:Customer satisfaction is the customers evaluation of a product or

service in terms of whether that product or service has met their needs and expectations.

Happy and satisfied customers behave in a positive manner. Customer satisfaction is

derived largely from the quality and reliability of products and services.

Customers often have to wait during the process of acquiring and consuming many

products and services. These waiting experiences are typically negative and have been

known to affect customers' overall satisfaction with the product or service. To better

manage these waiting experiences, many firms have instituted a variety of programs not

only to reduce the actual duration of the wait but also to improve customers' perceptions of

it.

Waiting lines form because people or things arrive at the servicing function, or server,

faster than they can be served.

Waiting in queues waiting lines is one of the most common occurrences in everyone's life.

Anyone who has gone shopping or to a movie (esp. Ambassador Cinema) has experienced

the inconvenience of waiting in line to make purchases or buy a ticket. Not only do peoplespend a significant portion of their time waiting in lines, but products queue up in

production plants, machinery waits in line to be serviced, planes wait to take off and land,

and so on.


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The improvement of service with respect to waiting time has also become more important

in recent years because of the increased emphasis on quality, especially in service-related

operations. When customers go into a bank to take out a loan, cash a check, or make a

deposit; take their car into a dealer for service or repair; or shop at the grocery store, they

increasingly equate quality service with rapid service. Aware of this, more and more

companies are focusing on reducing waiting time as an important component of quality

improvement.

Arrival time:the time that the customer arrives at the queue.

Departure time: the time that the customer gets out of the system after successfully

completing the service. Departure time can be measured in two way; departure time from

the queue and departure time from the system.

Waiting time: is the time that the customer waits in the queue before getting served by

any server. It may also be called time in the queue.

Service time:the time it takes to serve a customer.

Time in the system: the total time that the customer has spent from joining the queue and

getting out of the system after getting required service.

Queue length:maximum number of customers that is in the queue waiting to be served.

Balking:is when any customer who is not joining the queue upon arrival and leaving the

system without being served. The more the balking rate is the less the system efficiency is.

2.2 Queuing TheoryA queue is the line of people or things waiting to be served. A queue is formed whenever a

customer arrives at a service, finds the server is already busy, and waits to be served.

Queuing theory is a mathematical approach to the analysis of systems that involve waitingin line or queues. The origin of queuing theory is found in telephone network congestion

problems and the work of A. K. Erlang. Erlang, a Danish mathematician, was scientific

adviser for the Copenhagen Telephone Company. In 1917 he published a paper outlining

the development of telephone traffic theory in which he was able to determine the

probability of the different numbers of calls waiting and of the waiting time when the


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system was in equilibrium. He assumed Poisson inputs (arrivals) from unlimited sources

and exponential holding times. Erlang's work provided the stimulus and formed the basis

for the subsequent development of queuing theory.

Queuing theory is the mathematical theory of waiting lines. More generally, queuing theory

is concerned with the mathematical modeling and analysis of systems that provide service

to random demands. A queuing model is an abstract description of such a system. Typically,

a queuing model represents (1) the system's physical configuration, by specifying the

number and arrangement of the servers, which provide service to the customers, and (2)

the stochastic (that is, probabilistic or statistical) nature of the demands, by specifying the

variability in the arrival process and in the service process.

2.3 Queuing analysisQueuing analysis is a probabilistic form of analysis, not a deterministic technique. Thus, the

results of queuing analysis, referred to as operating characteristics, are probabilistic. These

operating statistics (such as the average time a person must wait in line to be served) are

used by the manager of the operation containing the queue to make decisions.

Most businesses and organizations have sufficient serving capacity available to handle their

customers in the long run. Waiting lines result because customers do not arrive at a

constant, evenly spaced rate, nor are they all served in an equal amount of time. Customers

arrive at random times, and the time required to serve them individually is not the same.

Thus, a waiting line is continually increasing and decreasing in length (and is sometimes

empty), and it approaches an average rate of customer arrivals and an average time to

serve the customer in the long run.

2.4 Elements of a queueThere are three basic elements of a queue.

- The customer- The server and- The queue


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The customer (not mandatory to be a person) will continue to come over but the main

Consideration here is how the customer is coming, the flow of the customer. Customer

behavior like how they arrive is key factor in a queue system.

The server is that what provides service to the customer whether there is a queue or not.

The service mechanism of a server is our main consideration in a queuing system. The

efficiency of a server can help reduce the queue length in several ways. A group of

customers that have requested/waiting for service but havent yet received any service

forms a queue.

2.5 Components of Queuing System:A queuing system is characterized by three components:

- Arrival process - Service mechanism - Queue discipline -

Arrival Process

To describe a queuing system, an input process and an output process must be specified.

The input process is usually called the arrival process. Arrivals are called customers.

Arrivals may originate from one or several sources referred to as the calling population.

The calling population can be limited or 'unlimited'. An example of a limited calling

population may be that of a fixed number of machines that fail randomly. The arrival

process consists of describing how customers arrive to the system. If Aiis the inter-arrival

time between the arrivals of the (i-1)th and ith customers, we shall denote the mean (or

expected) inter-arrival time by E(A) and call it ();= 1/(E(A) the arrival frequency.

To describe the output process (often called the service process) of a queuing system, we

usually specify a probability distributionthe service time distributionwhich governs a

customers service time. In most cases, we assume that the service time distribution is

independent of the number of customers present. This implies, for example, that the server

does not work faster when more customers are present.

There are two common situations in which the arrival process may depend on the number

of customers present. The first occurs when arrivals are drawn from a small population.


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Suppose that there are only four ships in a naval shipyard. If all four ships are being

repaired, then no ship can break down in the near future. On the other hand, if all four ships

are at sea, a breakdown has a relatively high probability of occurring in the near future.

Models in which arrivals are drawn from a small population are called finitesource models.

Another situation in which the arrival process depends on the number of customers

present occurs when the rate at which customers arrive at the facility decreases when the

facility becomes too crowded.

For example, if you see that the bank parking lot is full, you might pass by and come

another day. If a customer arrives but fails to enterthe system, we say that the customer

has balked. The phenomenon of balking was described by Yogi Berra when he said,

Nobody goes to that restaurant anymore; its too crowded. If the arrival process is

unaffected by the number of customers present, we usually describe it by specifying a

probability distribution that governs the time between successive arrivals.

Service Mechanism

The service mechanism of a queuing system is specified by the number of servers (denoted

by c), each server having its own queue or a common queue and the probability.

Queue Discipline

To describe a queuing system completely, we must also describe the queue discipline and

the manner in which customers join lines.

The queue discipline describes the method used to determine the order in which

customers are served. The common queue disciplines are:

FCFS discipline; (first come, first served), in which customers are served in the order of

their arrival.

LCFS discipline; (last come, first served), the most recent arrivals are the first to enter

service. If we consider exiting from an elevator to be service, then a crowded elevator

illustrates an LCFS discipline. Sometimes the order in which customers arrive has no effect

on the order in which they are served. This would be the case if the next customer to enter

service is randomly chosen from those customers waiting for service. Such a situation is


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referred to as the SIRO discipline(service in random order). When callers to an airline are

put on hold, the luck of the draw often determines the next caller serviced by an operator.

Finally, we consider priority queuing disciplines.A priority discipline classifies each arrival

into one of several categories. Each category is then given a priority level, and within eachpriority level, customers enter service on an FCFS basis. Priority disciplines are often used

in emergency rooms to determine the order in which customers receive treatment, and in

copying and computer time-sharing facilities, where priority is usually given to jobs with

shorter processing times.

2.6 Types of queuing systemAt any situation there can be three types of queuing system. But the element of the queuing

system is pre determined. The system efficiency depends on this elements behavior. A

queuing system can be more effective and efficient if the elements of the system are

organized and it is known to everyone how the system will behave at a particular time

period of the day. Depending on the queue behavior and service pattern a system will work

sound.

There can be three types of queuing system (in this paper we will discuss only the two);

- The Single-Server Waiting Line System- The multiple-Server waiting line System2.6.1 The Single-Server Waiting Line System

A single server with a single waiting line is the simplest form of queuing system. As such, it

will be used to demonstrate the fundamentals of a queuing system. In practice Single

Server Single Queue system is not that much efficient and effective for a busy and bigger

organization .It can create too much balking of customers depending on the arrival rate of

the customer making the system much more cost effective.

The central element of the system is a server, which provides some service to items. Items

from some population of items arrive at the system to be served. If the server is idle, an

item is served immediately. Otherwise, an arriving item joins a waiting line. When the

server has completed serving an item, the item departs. If there are items waiting in the


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queue, one is immediately dispatched to the server. The server in this model can represent

anything that performs some function or service for a collection of items.

The most important factors to consider in analyzing a queuing system are the following:

1. The queue discipline (in what order customers are served)2. The nature of the calling population (where customers come from)3. The arrival rate (how often customers arrive at the queue)4. The service rate (how fast customers are served)

2.6.1.1 The Arrival RateThe arrival rate is the rate at which customers arrive at the service facility during a

specified period of time. This rate can be estimated from empirical data derived from

studying the system or a similar system, or it can be an average of these empirical data.

2.6.1.2 The Service RateThe service rate is the average number of customers who can be served during a specified

period of time.

The assumption is that the following conditions exist in this type of system:

1. Arrivals are served on a first-in, first-out (FIFO) basis, and every arrival waits to beserved, regardless of the length of the line or queue.

2. Arrivals are independent of preceding arrivals. Arrivals at a service facility conform tosome probability distribution. Although arrivals could be described by any distribution,

it has been determined (through years of research and the practical experience of

people in the field of queuing) that the number of arrivals per unit of time at a service

facility can frequently be defined by a Poisson probability distribution and come from

an infinite (or very, very large) population.3. Service times vary from one customer to the next and are independent of one another.

Like arrival rate, service time is assumed to be defined by a probability distribution. It

has been determined by group in the field of queuing that service times can frequently

be defined by a negative exponential probability distribution. However, to analyze a


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queuing system, both arrivals and service must be in compatible units of measure. Thus,

service time must be expressed as a service rate to correspond with an arrival rate.

4. The service rate is faster than the arrival rate.These assumptions have been used to develop a model of a single-server queuing system.

Given that

= the arrival rate (average number of arrivals per time period)

= the service rate (average number served per time period)

And that< (customers are served at a faster rate than they arrive), we can state the

following formulas for the operating characteristics of a single-server model.

Customers must be served faster than they arrive, or an infinitely large queue will build up.

Operating characteristics here are,

The probability that n customers are in the queuing system is

The average number of customers in the queuing system

The average number of customers in the waiting line is

The average time a customer spends in the total queuing system

The average time a customer spends in the total queuing system


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The probability that the server is busy

The probability that the server is idle

Sometimes it cannot be assumed that a waiting line system has an arrival rate that is

Poisson distributed or service times that are exponentially distributed. For example, many

manufacturing operations use automated equipment or robots that have constant service

times. Thus, the single-server model with Poisson arrivals and constant service times is a

queuing variation that is of particular interest to manufacturing operations.

The constant service time model is actually a special case of a more general variation of the

single-server model in which service times cannot be assumed to be exponentially

distributed. As such, service times are said to be general, or undefined.

For some waiting line systems, the length of the queue may be limited by the physical areain which the queue forms; space may permit only a limited number of customers to enter

the queue. Such a waiting line is referred to as a finite queue and results in another

variation of the single-phase, single-channel queuing model.

The basic single-server model must be modified to consider the finite queuing system. It

should be noted that for this case, the service rate does not have to exceed the arrival rate

( > ) in order to obtain steady-state conditions.

2.6.2 The Multiple-Server Waiting LineIn multiple-server models, two or more independent servers in parallel serve a single

waiting line. If an item arrives and at least one server is available, then the item is


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immediately dispatched to that server. It is assumed that all servers are identical; thus, if

more than one server is available, it makes no difference which server is chosen for the

item. If all servers are busy, a queue begins to form. As soon as one server becomes free, an

item is dispatched from the queue using the dispatching discipline in force.

The key characteristics typically chosen for the multi-server queue correspond to those for

the single-server queue. That is, we assume an infinite population and an infinite queue

size, with a single infinite queue shared among all servers. Unless otherwise stated, the

dispatching discipline is FIFO. For the multi-server case, if all servers are assumed

identical, the selection of a particular server for a waiting item has no effect on service time.

The queuing formulas for a multiple-server queuing system will be discussed in detail in

the analysis part. These formulas, like single-server model formulas, have been developed

on the assumption of a first-come, first-served queue discipline, Poisson arrivals,

exponential service times, and an infinite calling population. The parameters of the

multiple-server model are as follows:

= the arrival rate (average number of arrivals per time period)

= the service rate (average number served per time period) per server (channel)

c = the number of servers

c = the mean effective service rate for the system, which must exceed the arrival rate

The formulas for the operating characteristics of the multiple-server model are as follows.

c > : the total number of servers must be able to serve customers faster than they arrive.


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3 Data analysisAs stated above the queuing system on the Main branch of Dashen Bank is taken with a goal

of making a decision analysis, whether to continue using all counters/tellers from the

branch, to add new counters in regards of the customer arrival pattern or decrease the

service time per customer.

We have a total eight counters/servers/tellers that are used to serve the customer. The

pattern of service is FCFS (First Come First Served) as queue discipline method. As the

arrival rates vary by time of a day and day of week, we restricted our analysis to a narrow

time interval for which the system is relatively stable (i.e. rush hour: 9 am to 10 am for

one week).

Below is the data the Dashen Bank provided us from their automated queuing machine

10-Jan-13

Transactions Service Time 9 a.m. - 10 a.m. Average Service time

Current Account 00:06:19 12

5.69

Money Transfer 00:05:31 6

Other 00:07:17 8

Payment Card 00:03:47 5

Saving Account 00:06:31 16

28.45 47

11-Jan-13

Transactions Service Time 9 a.m. - 10 a.m.


5.51


Other 00:04:57 8



27.57 49

12-Jan-13


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6.24


Other 00:05:49 10



31.20 43

14-Jan-13



6.64


Other 00:06:38 7



33.18 64

15-Jan-13



6.69


Other 00:07:17 4



33.43 51

Average service time= 6.15 mins

Arrival Rate () = 51 Customers per hour

Service rate () = 10 Customers per hour

Server (C) = 8 Tellers


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By taking into consideration the average of average of the waiting time that was rounded

up twice, the average customer in the service department was rounded up to 6.


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These operating characteristics suggest that the Dashen Bank eight-server operation would

handle the volume of customers extremely well. However, it still shows that the probability

that a customer must wait in the service as 18.2% with an average time in service

department of 7.06 mins per customer. It would not be relevant to add a counter on the

already existing ones. However, we believe the service rate can still improve which will in

turn affect the service time per customer.

Thus, we recomputed this system with specifically, note that the average time in the system

is an average of only 5.11 minutes per customer, which is excellent. The Probability that a

customer must wait for a service is 7.9%, which is acceptable, especially in light of the shortaverage waiting time.

Service rate () = 12 Customers per hour.

Arrival Rate () = 51 Customers per hour

Service rate () = 12 Customers per hour


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Server (C) = 8.0 Tellers

Po = 1.41% Probability that no customers are in the system

Pw = 7.9% Probability that a customer must wait for a service

Average number in the system (L) = 4 customers, on average, in the system

Average number in the queue (Lq) = 0 customers, on average, waiting to be served

Average time in the system (W) = 5.11 average time (mins) in the system per customer

Average time in the queue (Wq) = 0.11 average time (mins) waiting in line per customer


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4 Concluding statement and Recommendation4.1 Concluding Statement

The application of queuing theory in the banking system conducted a survey and analysis,

from a technical point of view of what Dashen bank should take measures to make their

customers the shortest waiting time; and from an economical point of view to optimize the

system with minimal cost, the bank to maximize efficiency. For the bank manager to

reasonably optimized system, improve efficiency; provide a scientific basis and practical

approach.

4.2 RecommendationsIn order to achieve the attributes stated above and realize the international standards of

waiting time, Dashen bank will have to consider minimizing the service time from 7.06

mins to 5.11 mins by either omitting some levels the processes per transaction or highly

automating the count of bulk money etc.

The details about how queuing model cannot be applied to certain types of services

(Kadisco Hospital case) will be explained on the group presentation.


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5 Reference Bernard W. Taylor, 2006, Introduction to Management Science, Ninth Edition,

Prentice Hall, USA

Cooper, R., 1981, Introduction to Queuing Theory, second edition, New York:North-Holland

David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm,KippMartin, 2012,An Introduction To Quantitative Approaches To Decision Making,

revised thirteenth edition, south western change learning, USA

Donald Waters, 2011, Quantitative methods for Business, fifth edition,PrenticeHall, USA

group assignement queuing model jan 28

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