Waiting Models.. 11

CONTENT:

1. INTRODUCTION.2. LOCATION.3. WORKING OF ATM.4. PROBLEM DEFINATION.(i) Problem statement.(ii) Problem significance.(iii) Problem objective.(iv) Problem constraints.5. ATM QUEUING.6. LITERATURE REIVIEW.7. INTRODUCTION TO SIMULATION AND

QUEUING.8. LITTLE’S LAW.9. OBJECTIVE OF THE STUDY.10. CONCLUSION.11. DATA INTERPRETATION.

INTRODUCTION:-

An automated teller machine or automatic teller machine (ATM), also known as

a Cashpoint (which is a trademark of Lloyds TSB), cash machine or sometimes a hole in the

wall in British English, is a computerised telecommunications device that provides the clients of

afinancial institution with access to financial transactions in a public space without the need for

a cashier, human clerk or bank teller. ATMs are known by various other names including ATM

machine, automated banking machine, and various regional variants derived

from trademarks on ATM systems held by particular banks.

Invented by John Shepherd-Barron, the first ATM was introduced in June 1967 at Barclays

Bank in Enfield, UK. On most modern ATMs, the customer is identified by inserting a

plastic ATM card with a magnetic stripe or a plastic smart card with a chip, that contains a

unique card number and some security information such as an expiration date or CVVC (CVV).

Authentication is provided by the customer entering a personal identification number (PIN).

Using an ATM, customers can access their bank accounts in order to

make cash withdrawals, credit card cash advances, and check their account balances as well as

purchase prepaid cell phone credit. If the currency being withdrawn from the ATM is different

from that which the bank account is denominated in (e.g.: Withdrawing Japanese Yen from a

bank account containing US Dollars), the money will be converted at a wholesale exchange rate.

Thus, ATMs often provide the best possible exchange rate for foreign travellers and are heavily

used for this purpose

LOCATION:-

ATMs are placed not only near or inside the premises of banks, but also in locations such as

shopping centers/malls, airports, grocery stores, petrol/gas stations, restaurants, or anywhere

frequented by large numbers of people. There are two types of ATM installations: on- and off-

premise. On-premise ATMs are typically more advanced, multi-function machines that

complement a bank branch's capabilities, and are thus more expensive. Off-premise machines

are deployed by financial institutions and Independent Sales Organizations (ISOs) where there is

a simple need for cash, so they are generally cheaper mono-function devices. In Canada, ABMs

not operated by a financial institution are known as "White Label ABMs"

Many ATMs have a sign above them, called a topper, indicating the name of the bank or

organization owning the ATM and possibly including the list of ATM networks to which that

machine is connected.

WORKING OF ATM :

The ATM machine gained Shepherd-Barron an ever-lasting recognition in the banking

world and paved the way for hi-tech banking techniques, online bank accounts and PIN

and chip security technology. The four-digit internationally accepted standard PIN was

also invented by him. Earlier, he had a six-digit Army serial number in his mind but later

his wife suggested for a shorter PIN as it would be easy to remember. Finally in 1967

that the first ATM that dispensed paper currency round the clock, was unveiled. The

ATM machine installed outside a Barclay’s bank in North London started dispensing

cash on a 24 hour basis.

As the plastic cards were still to have come into existence, this machine accepted and

generated money through cheques impregnated with certain chemicals. Majorly a mild

radioactive substance, Carbon 14 was used for detection by the machine. Once the PIN

was given, the machine gave out the cash. This radioactive substance had no ill effects

on the health of users and Shepherd-Barron claimed that a user would have to eat

about 136,000 cheques to suffer any kind of ill-effects. Reg Varney, a famous TV sitcom

popular became the first person to use the ATM in the year 1967 and withdrew about 10

dollars. The amount seems too less for us, but this money was enough for a complete

night out spent on the tiles in London, inclusive of dinner, drinks, a show and a taxi-ride

back to home, in short enough cash for a “Wild Weekend”.

While this prototype device originated by Shepherd-Barron had started functioning,

various parallel developments were happening in different parts of the world. An

American Engineer Donald Wetzel of Docutel engineered the Docuteller ATM which

was declared as the first modern magstripe machine. It recognized magnetically

encoded plastic (credit cards) and not the usual paper cheques.

And there have been a lot of efforts gone into final development of the ATM, the ones

we see today, the ones we use so frequently, and the ones which have made our lives

revolve around plastic money. The development of ATM ever since its baby steps in the

late 1930s and then gearing up for longer runs in the 1960s, and finally a matured and

stable stage that we see the ATMs in today. Undoubtedly, most of the ideas and patents

contributed for makeover of the ATM from time to time form the backbone of what was

initiated as “holes in the wall”.

Today, ATMs hold a strong foothold in the world, offering everyone a better access to

their money, be it in any corner of the world. Let’s put figures to assumptions, there are

about 1.8 million ATMs in use around the world with ATMs on cruise and navy ships,

airports, newsagents and petrol stations. ATMs too have been categorized as on and off

premise ATMs. On Premise ATMs are capable to connect the users to the bank with

multi-function capabilities. Off premise, ATM machines on the other hand are the "white

label ATMs" and are limited to cash dispense, no balance enquiries, no statement print-

out.

The developments have not stopped; the contactless technology is on its rise.

Shepherd-Barron continued to take inimitable and lively interest in technology well even

in his old age and had foreseen a future where plastic cards too would be numbered.

For his excellent and unforgettable contributions to financial technologies, he was also

offered the OBE in the year 2005. And in the year 2010, he took his last breath and left

behind his legacy of technological advancements which would refuses to end. Many

more inventions are in process and many will be successful too. The time is just right to

bring in the glorious inventions rolling in.

Application of Simulation Technique in Queuing Model for ATM

Facility:

ATM is an automatic teller machine which is used to save the cost and reach

ability of a bank by satisfying customer needs. Customers can withdraw and

deposit money without any paper work and it facilitates them to reduce time

and cost to go to bank in person. By

Considering the utility of ATM services of different banks at global, the

authors adopted simulation technique for identifying the pitfalls of existing 3

ATM services of 3 different banks at VIT

(Vellore Institute of Technology) and also planning to propose a new ATM

service from any one of these banks or other than the existing banks based

upon the service required from the customers. The authors formulated a

suitable simulation technique which will reduce idle time of servers and

waiting time of customers for any bank having ATM facility. This technique

will be helpful for any bank at global for improving their customer’s service

towards competitive advantage.

Keywords: Simulation, Queuing, ATM, Idle time, Services.

1. Problem Definition:

Automatic Teller Machines (ATM) indicates the development of Information

Technology in Banking sector two types of ATMs need to be addressed, one

of which is the branch ATM, the other being the out of branch ATM. The

branches will take care of the ATM located in their respective branches, while

the out of branch

ATMs such as those located in department store will be taken care by cash

centers. Each cash center has ATMs under its responsibility.

At VIT there are three ATMs out of which two are out of branch ATM(SBI and

CENTURION BANK) and one is branch ATM (INDIAN BANK). The major

problem faced by these ATMs are the long queue of customers at the peak

hours and then at the off peak hours the lack of customer entry. The number

of customer are so large that many a times customer waits for more than

half an hour to get his turn but at nights the ATMs remain idle that there are

no customers to serve . Depending on the current capacity of each ATM,

many alternative decisions can be made. Now the work process decision is

made by operators. Thus, the problem of ATM facility is significant.

In this study, methodology “Simulating ATMs” is proposed in order to

maximize efficiency of banks to improve their customer’s service and

increasing long term relationship with them and also to reduce the

congestion at the ATM centre at peak hours. The process will show how

much time a customer spends and give suggestion whether a new ATM is

required or with the same resources the performance can be improved. This

research will support the banks in terms of decision making for reducing the

waiting time of customers, by solving a simulation model with the help of

queuing theory.

The technique of simulation has long been used by the designers and

analysis in the physical sciences and it promises to become an important

tool for tackling the complicated problems of managerial decision making. It

is actually imitation of reality and when it is being put into mathematical

form it is called simulation. Generally, the main objective of simulation is to

minimize the managerial problem in terms of decision making and hence

helps in reaching solution with at most accuracy. Also it is comparatively free

from mathematical solution, hence can be easily understood by the

operating personal and nontechnical managers.

On the other hand queuing model is used to overcome the congestion of the

traffic; this traffic can be of any form. This model mainly used in situation

where customers are involved, hence when it is being coupled with

simulation it becomes very much conducive to get solution to solve the

problem related to customers. Therefore, these two models are used to

understand the situation related to ATM waiting line and to find some

alternative to overcome this problem by suggesting certain alternatives.

1.1 Problem Statement

In most of the ATMs the major problem is waiting of customers in the queue

for more duration. Mainly the objective of ATM for bank is to keep away the

customers from coming to bank and make the process easy for them to

avoid the basic procedure they do in bank. But as stated the problem which

most ATM face is the long queue in front, but then when the problem is only

for a short while as rest of the time the ATM remains idle means adding to

the operating cost. The problem is to determine whether only one machine is

required to fulfill the need or two more machines needed to be installed to

give comfort to customer which is really of short period of time.

1.2 Problem Significance

The cost of the installing an ATM machine accounts for a sizeable part of the

total operating cost of a company. Adding to it is cost of extra security guard

who is needed to be placed there. But the customer satisfaction point of it is

necessary to incur these expenses as retaining them is more important,

hence these cost are overshadowed by this fact. This research will provide a

robust problem solving technique for the real world; make a decision related

to reducing the ATM queuing problem to reduce operating cost.

1.2.1 Problem Objective

The overall objective of the research is to develop a model to reduce the

waiting time of customers and the total cost related to ATM installation.

1.3 Problem Constraints

In this research, the researcher has focused on the Problem of waiting of

customer in ATMs for long to undergo a simple transaction with the available

ATM machine, also to know whether another machine is required to reduce

the traffic at the centers by keeping in mind the cost incurred in installing.

2. ATM Queuing: Simulation model(SM)

The ATM queuing resembles the typical simulation model coupled with

queuing theory in ‘Operations Research’ literature. In order to solve the

queuing model with simulation the service facility must be manipulated so

that an optimum balance is obtained between the cost of waiting time and

the cost of idle time. The cost of waiting generally includes either the indirect

cost or loss of customers. By increasing the investment in labor and service

facility waiting time and the losses associated with it can be decreased. If we

consider Cw= expected waiting cost/unit/unit time, Ls= expected number of

units in the system/unit time and

Ce = cost of servicing one unit:

Then,

The expected waiting cost per unit time=Cw* Ls……….(1)

Expected service cost per unit time=Ce*A……………..(2)

Total cost=Cw*Ls+ Ce*A………………………………(3)

The model is designed to set m number of customer to use effectively use

the system to minimum total cost, each starting and ending of the process,

such that each period of time whether it is a busy or free period the total

cost occurred to bank must be less, and customer need not to stay for long

in queue and get the best out of the service. Depending on the nature of

each application, queuing and simulation may possess different

characteristics, which in turn decide the way the process must be carried

out.Characteristics of Queuing models shown in the following table.

Characteristics

1. Input or arrival distribution

2. Output or departure distribution

3. Service channels

4. Service discipline

5. Maximum number of customers allowed in the system

6. Calling source or population

Literature Review: Basic Simulation model and Algorithms

Simulation with queuing model for various applications other than the ATM

problem have been worked upon which is being shown below:

Pieter Tjerk de Boer (1983) in his article discussed that the estimation of

overflow probabilities in queuing networks has received considerable

attention in the importance sampling simulation literature. Most of the

literature has concentrated on heuristically derived changes of measure,

which perform well in many, but not all, models. Adaptive methods (i.e.,

methods which try to iteratively approach the optimal change of measure)

have only been applied to queuing problems in which a different adaptive

method is used than in the present work, and where only a few simple

models are considered.

S. S. Lavenberg (1989) in his article discussed that simulation was found to

be a viable tool for numerically studying a complex queuing model which is

not analytically tractable.

Moderate simulation durations (durations of 500 and 1000 tours were used

where the average computer time to simulate a tour was 0.03 second using

a large computer) were sufficient to obtain fairly accurate confidence interval

estimates. The model was first simulated under saturated conditions with

independent replications used to estimate a confidence interval for A, the

maximum input rate for which regenerative simulation is applicable. Savings

or insertion procedures, which build a solution in such a way that at each

step of the procedure a current configuration that is possibly infeasible. The

alternative configuration is one that yields the largest saving in terms of

some criterion function, such as total cost, or that inserts least expensively a

demand entity in the current configuration into the existing route or routes.

Examples of these procedures can be found in Clarke and Wright (1964) or in

Solomon (1987).

Improvement or exchange procedures, such as the well known branch

exchange heuristic which always maintain feasibility and strive towards

optimality. Other improvement procedures were described by Potvin and

Rousseau (1995), including Or opt exchange method in which one, two, three

consecutive nodes in a route will be removed and inserted at another

location within the same or another route; kinter change heuristic in which k

links in the current routes are exchanged for k new links; and 2 – opt

procedure which exchanges only two edges taken from two different routes.

Mathematical programming approaches, which include algorithms that are

directly based on a mathematical programming formulation of the underlying

queuing problem. An example of this procedure was given by Fisher and

Jaikumar (1981). Christofides et al (1981) discussed Lagrangean relaxation

procedures for the queuing of customer in front of ATM. Interactive

optimization, which is a general purpose approach in which a high degree of

human interaction is incorporated into the problem solving process. Some

adaptations of this approach to queuing are presented by Krolak et al (1970).

Heuristic approaches: E.g:- Simulation Model (SA). For example, Brame and

SimchiLevi

(1995) introduced the locationbased heuristic for general queuing problem,

which is based on formulating the queuing problem as a location problem –

commonly called the capacitated concentrator location problem. This

location problem was subsequently solved and the solution was transformed

back into a solution to the queuing problem. The method incorporates many

queuing features into the model.

Computation Burden

Important consideration in the formulation and solution of waiting time

problem is the computation burden associated with various solution

techniques for these problems. The nature of the growth of computation time

as a function of problem size is an issue of both theoretical and practical

interest. Most waiting time and idle time problems may be formulated on the

basis of Monte Carlo method which provide an approximate but a quite

workable solution to the problem. The technique has been used to tackle a

variety of problems involving stochastic situations and mathematical

problems, which cannot be solved with mathematical techniques and where

physical experimentation with the actual system is impracticable. Thus these

problem are of a waiting line situation. So, a Simulation technique in queuing

model is used for solving ATM waiting time problem.

2 Problem Methodology

Introduction to simulation and queuing

It is the imitation of reality like laboratories in which number of experiments

are performed on simulated models to determine the behavior of real system

in true environments.

The example cited above is of simulating the reality in the physical form, and

are referred to as analogue simulation. For the complex and intricate

problem of managerial decision making, the analogue simulation may not be

practicable, and actual experimentation with the system may not be

uneconomical. Under such circumstances, the complex system is formulated

into a mathematical model for which a computer programme is developed,

and the problem is solved by using high speed electronic computer, and

hence it is named as system simulation.

Queuing theory has been applied to a variety of business situations. All

situations are related to customer involvement. Generally, the customer

expects a certain level of service, whereas the firm provides service facility

and tries to keep the costs minimum while proving the required service. This

widely used in manufacturing units. Here it helps in reducing the overhead

charges and the overall cost of manufacturing. Also used to know is the unit

arrive, at regular or irregular intervals of time at a given point called the

service point.

3.2 Simulation and Queuing for ATM Waiting line

The proposed method here tells about how the three ATM centers of VIT are

performing.

What is the frequency at which each customer enters when the hour is busy

hour and same day the idle time of ATM at off peak hour? Then the routine in

weekends when there are no classes how the rate of customer entry is

fluctuating.

4.2 Discussions

This research has been done by the researcher through observing the

customers arrival time, waiting time in the queue, different behaviour of

customers in the queue like balking, reneging, jockeying and service time

with ATM machine. The researcher has observed those information for 2

months duration in all the three ATMs at VIT during weekdays busy, free

hours and week end busy and free hours. Generally, arrivals do not occur at

fixed regular intervals of times but tend to be clustered for a duration of a

week. The Poisson distribution involves the probability of occurrence of an

arrival are random and independent of all other operating conditions. The

inter arrival rate (i.e., the number of arrivals per unit of time) λ is calculated

by considering arrival time of the customers to that of the number of

customers.

Service time is the time required for completion of a service i.e., it is the time

interval between beginning of a service from ATM machine and its

completion. In this research the researcher has calculated mean service time

μ of customers by considering different service time for customers to that of

the number of customers.

Based upon the tabulation and taking one day as a standard, the researcher

inferred that during week days prime hours there is heavy crowd in Indian

bank and SBI ATMs, which implies that the utilization factor is 1. It is vivid

that the equipment ATM is 100% utilized by the customers. In the non busy

hours, utilization factor is 50% for INDIAN BANK and 55% for SBI. In weekend

period the utilization factor is 62% for INDIAN BANK and 64% for SBI.

The reason for the minimum utilization factor of Indian Bank and Centurion

Bank is that the customers will face “Out of Service Problem” frequently ( On

an average of 2 times in a week, this can be found by the researcher through

observation) than the SBI Bank. The researcher has observed for 2 months,

this kind of problem was not there with SBI ATM Service for a single time.

Hence most of the customers preferred SBI ATM Service. But SBI officials

would take more time to reload the currency in the ATM machine than the

Indian Bank. Only few customers have the ATM transaction with Centurion

Bank, the reason would be the dissatisfaction of customer service and it has

minimum number branches through out

India. This result was found by interviewing with the customers, those who

avail Centurion ATM bank facility. These are the existing pit falls of existing

ATM services of SBI, Indian bank and Centurion bank.

The comparison between waiting time in the queue and system by using

both simulation and queuing model shows more variation because the study

was undergone with the observation of minimum number of customers with

minimum duration. Due to limited time, the research had been conducted

with minimum sample size, this research can be extended with larger sample

size and more days of observation, it paves the way to give more accurate

results. The researcher found that the customers, who are availing different

ATM services at VIT preferred SBI ATM service. The reason would be number

of branches of SBI is more than

Indian bank throughout the country and it has direct impact with respect to

the composition of VIT students from various part of the country. This study

also reveals that the Minimum

Ws and Wq of customers of SBI ATM than the other two banks of Indian and

Centurion Bank ATMs. This proves that the customers are satisfied with the

service provided by SBI ATM than the other two banks.

5. Recommendation for Further Study

Several aspects of waiting problem for the ATM that remained unsolved in

this study will form interesting topics for further study. The following

recommendations are made for further studies:

It is observed that if a person is not well versed with ATM takes more time

which is not considered. Also many customers stand in the queue and leave

which can be put into the consideration.

· The time the workers take to feed the ATM with currency is not considered.

· Out of stock situation can be considered.

· On holidays mostly after exams the utility of ATM to be considered.

The main limitation of the research due to time constraint it is observed with

minimum sample, if sample size would have increased, the result obtained

by both in simulation and queuing will coincide.

This study would not consider waiting cost and service cost due to non

availability of original information. For future research, this study can be

extended by considering the cost factors to find out the best ATM facility.

Little's law:

The long-term average number of customers in a stable system L is equal

to the long-term average effective arrival rate, λ, multiplied by the

(Palm-)average time a customer spends in the system, W; or

expressed algebraically: L = λW.

It is a restatement of the Erlang formula, based on the work of Danish

mathematician Agner Krarup Erlang (1878 – 1929). Offered traffic E (in erlangs)

is related to the call arrival rate, λ, and the average call-holding time, h, by:

E = λh

Although it looks intuitively reasonable, it's a quite remarkable result, as it implies

that this behavior is entirely independent of any of theprobability

distributions involved, and hence requires no assumptions about the schedule

according to which customers arrive or are serviced.

The first proof was published in 1961 by John Little, then at Case Western

Reserve University. His result applies to any system, and particularly, it applies

to systems within systems. So in a bank, the customer line might be one

subsystem, and each of the tellers another subsystem, and Little's result could

be applied to each one, as well as the whole thing. The only requirements are

that the system is stable and non-preemptive; this rules out transition states such

as initial startup or shutdown.

In some cases it is possible to mathematically relate not only

the average number in the system to the average wait but relate the entire

probability distribution (and moments) of the number in the system to the wait.

Imagine a small store with a single counter and an area for browsing, where only one

person can be at the counter at a time, and no one leaves without buying something. So

the system is roughly:

Entrance → Browsing → Counter → Exit

This is a stable system, so the rate at which people enter the store is the rate

at which they arrive at the store, and the rate at which they exit as well. We

call this the arrival rate. By contrast, an arrival rate exceeding an exit rate

would represent an unstable system, where the number of waiting customers

in the store will gradually increase towards infinity.

Little's Law tells us that the average number of customers in the store, L, is

the effective arrival rate, λ, times the average time that a customer spends in

the store, W, or simply:

Assume customers arrive at the rate of 10 per hour and stay an average

of 0.5 hour. This means we should find the average number of customers

in the store at any time to be 5.

Now suppose the store is considering doing more advertising to raise

the arrival rate to 20 per hour. The store must either be prepared to

host an average of 10 occupants or must reduce the time each

customer spends in the store to 0.25 hour. The store might achieve

the latter by ringing up the bill faster or by adding more counters.

We can apply Little's Law to systems within the store. For example,

the counter and its queue. Assume we notice that there are on

average 2 customers in the queue and at the counter. We know the

arrival rate is 10 per hour, so customers must be spending 0.2 hours

on average checking out.

We can even apply Little's Law to the counter itself. The average

number of people at the counter would be in the range (0, 1) since

no more than one person can be at the counter at a time. In that

case, the average number of people at the counter is also known

as the utilisation of the counter.

It should be noted however, that because a store in reality

generally has a limited amount of space, it cannot become

unstable. Even if the arrival rate is much greater than the exit rate,

the store will eventually start to overflow, and thus any new

arriving customers will simply be rejected (and forced to go

somewhere else or try again later) until there is once again free

space available in the store. This is also the difference between

the arrival rate and the effective arrival rate, where the arrival rate

roughly corresponds to the rate of which customers arrive at the

store, whereas the effective arrival rate corresponds to the rate of

which customers enter the store. In a system with an infinite size

and no loss, the two are however equal.

Little’s Law

Given just a few properties of a queue, we can answer some questions about

waiting times without knowing anything other than the average line length

and the average customer arrival rate.

For example, If a customer joins the line just after a customer begins to be

served, then intuitively one would expect the newly arriving customer to

wait (Line Length) x (Cycle Time). Let’s use numbers to make this point

more concrete. Assume a Queue at Starbucks Coffee is:

(8 customers) x (1 min/customer) = 8 minutes

If the line length is doubled to 16 people, then the waiting time should be

(16 customers)(1 min/customer) = 16 minutes

Similarly, doubling the cycle time to 2 minutes should also raise the waiting

time to 16 minutes. This last point on Cycle Time is critical, because this

often becomes the most controllable variable available to the firm – in other

words, line length, demand fluctuations or arrival rate are often not

controlled by the firm, but the Cycle Time it takes to serve a customer is

controllable and so becomes a critical variable to focus on.

The above example all points us to Little’s Law, but before I show Little’s

Law, here are some definitions:

Lq: The average number of people in a line awaiting service.

Wq: The average length of time a customer waits before being served.

Throughput: Mean Outflow (average numbers of items leaving a system,

not entering it)

Little’s Law

Now, let’s generalize the example above and arrive at Little’s Law:

Wq = Lq / Throughput

Littles Law and can be applied in any system in which the mean waiting

time, mean line length (or inventory size), and mean throughput (outflow)

remain constant. To some extent this is an arbitrary decision, but in most

real-world situations, measuring the outflow of a queue is easier than

measuring its inflow.

Another interesting point is the generality of this formula. For one thing,

this relation will hold no matter what the distribution of inter-arrival times

or processing times is. Even more amazingly, Little’s law is not restricted to

simple systems with one line and a number of servers. It will hold no matter

what the internal structure of a system is.

Little’s Law Example: Patient Flow in Hospital

To illustrate the use of Little’s Law, let’s use an example of Queueing in

Healthcare. What if we wanted to know the following:

What the average time in the system for a patient at a hospital?

This includes all the multiple phases, disease states, surgery procedures,

etc.

Suppose we know the following:

Lq: The average number of patients is 102.5

Wq: [This is the unknown]

Throughput: Average discharge rate is 67.5 patients per day.

In other words,

W = L/Throughput => Average Time in Hospital = Average # of Patients /

Average Discharge Rate = 102.5 patients /67.2 patients per day = 1.53

Days

Knowing that a patient in this hospital can expect to stay an average of 1.53

days can help the hospital administrators plan for care, staffing, budgeting,

and other internal items that will help the hospital’s level of service.

Weaknesses of Little’s Law

While Little’s Law is convenient to use and gets us a decent approximation

to most queueing questions, it’s clearly not perfect. For example, process

utilization must be less than 100% or else the line will grow to infinity (this

is otherwise known as WIP Explosion).

Little’s Law Applications

Other ways in which Little’s Law can be used are the following:

Estimate Waiting Times: [W = Average Number of Customers /

Average Throughput] (as the patient flow example above)

Planned Inventory Time: Suppose a product is scheduled so that we

expect it to wait for 2 days in finished goods inventory before shipping to

the customer. This two days is called planned inventory time and is

sometimes used as protection against system variability to ensure high

delivery service. Using Little’s Law, the total amount of inventory in

finished goods can be computed as [FGI = Throughput x Planned

Inventory Time]

WIP Reduction: Reducing WIP in a process without making any other

changes will also reduce throughput. So, simply reducing inventory is

not enough to achieve a system. An integral part of any Lean

Manufacturing implementation is an effort to reduce variability (often

the domain of to enable a line to achieve the same (or greater)

throughput with less WIP.

OBJECTIVES OF THE STUDY :-

The Bank will open several new branch during the coming year.

Each new branch is designed to have one automated teller machine (ATM).

A concern is that during busy periods several customers may have to wait to use the

ATM.

This concern prompted the bank to undertake a study of the ATM waiting line system.

The bank established service guidelines for its ATM system stating that the average

customer waiting time for an ATM should be one minute or less

Inter arrival time:-

Arrival times are determined by randomly generating the

time between two successive arrivals, referred to as the

Inter arrival time.

Service Time

2 minutes and a standard

deviation of 0.5 minutes,

Excel function =NORMINV(RAND(),2,0.5)

.

Conclusion

The main purpose of this study is to develop an efficient procedure for ATM

queuing problem, which can be daily used by banks to reduce the waiting

time of customers in the system. The queuing characteristics of customers

were observed and the researcher compared the process of customer

behavior of different ATM services at VIT. It is concluded that the SBI ATM

service should introduce in men’s hostel (around ¾ th students strength stay

in hostel) will facilitate pulling more customers towards SBI ATM service. The

researcher suggested that the SBI can install a new ATM machine in Men’s

hostel in spite of high installation cost and there by reduce the customer cost

and service cost for attaining benefit in the long run. This will be helpful for

commercial bank to sustain more potential customers in high competitive

situations with other private banks