Name of authors: Vasumathi.A and Dhanavanthan P
Title of Article: Application of Simulation Technique in Queuing Model for ATM Facility
Journal Name: International Journal of Applied Engineering Research, Dindigul Volume 1, No 3
Date of publications: 2010
Pages of article: Pages 469-482 (14 pages)

JOURNAL SUMMARY
1.0 Issues/ Problem Statement:

Most of the ATMs have the problem of long queue of customers to undergo simple transaction at the peak hours and remain idle due to the lack of customer entry at the off peak hours.

2.0 Objectives:

1. To develop a simulation model to reduce the waiting time of customers and the total operation cost related to ATM installation.

2. To determine whether only one machine is required to fulfill the need or two more machines are needed to be installed to give comfort to customers who are really of short period of time.

3. To develop an efficient procedure for ATM queuing problem

3.0 Literature Review:

Apart from ATM problem, simulation with queuing model had been used for various applications too:

According to Pieter Tjerk de Boer (1983), substantial focus has been dedicated to the estimation of overflow probabilities in queuing networks. A different adaptive method has applied to queuing problems than in the present work with few simple models been considered.The article of S. S. Lavenberg(1989) has discussed that simulation is feasible for statistically studying a complex queuing model. Moderate simulation durations are found to be sufficient to obtain precise confidence interval estimates. As current configuration at each step of savings or insertion procedures is possibly infeasible, thus the alternative configuration is one that yields the largest savings in some criterion functions with these procedures can be found in Clarke and Wright (1964) or in Solomon (1987).

...
Case Study for Bank ATMQueuingModel
Bhavin Patel1 and Pravin Bhathawala2
1Assistant Professor, Humanities Department, Sankalchand Patel College of Engineering, Visnagar, Gujarat, India; 2 Professor & Head, Department of Mathematics, BIT, Baroda, Gujarat, India
Abstract:
Bank ATMs would avoid losing their
customers due to a long wait on the line. The bank initially provides one ATM. However, oneATM would not serve a purpose when customers withdraw to use ATM and try to use other bank ATM. Thus, to maintain the customers, the service time needs to be improved. This paper shows that the queuing theory may be used to solve this problem. We obtained the data from a bank ATM in a city. We used Little’s Theorem and M/M/1 queuingmodel. The arrival rate at a
bank ATM on Monday during banking time is
customer per minute (cpm) while the service rate
is ? ? cpm. The average number of customers
in the ATM is ? ?and the utilization period is
? ?. We discuss the benefits of applying
queuing theory to a busy ATM in conclusion.
Keywords: Bank ATM, Little’s Theorem, M/M/1
queuingmodel, Queue, Waiting lines
Here, ?is the average customer arrival rate and 𝑇 is the average...

...Waiting Lines & QueuingModels
American Military University
Business 312
For my project on other operations research techniques I have decided to research waiting lines and queuingmodels. My interest in this application stems from my personal dislike for standing in lines and waiting on hold while on the phone. This is virtually my only pet peeve; nothing aggravates me faster than standing in a line or waiting on hold. Like most people I go out of my way to avoid lines, using strategies such as arriving early or visiting during non-peak times. However, before investigating this topic, I had no idea there was a specific science behind the madness.
Queuingmodels are important applications for predicting congestion in a system. This can encompass everything from a waiting line at pharmacy to traffic flow at a busy intersection. This is important because it can impact businesses in unforeseen ways. Customers may begin to believe that they are wasting their time when they are forced to wait in line for service and continued delays may begin to negatively influence their shopping preferences.
Organizations design their waiting line systems by weighing the consequences of having a customer wait in line, versus the costs of providing more service capacity. Queuing theory provides a variety of analytical...

...REVISED
M14_REND6289_10_IM_C14.QXD 5/12/08 1:01 PM Page 218
218
CHAPTER 14
WAITING LINE
AND
QUEUING THEORY MODELS
Alternative Example 14.3: A new shopping mall is considering setting up an information desk manned by two employees. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. a. Find the proportion of the time that the employees are idle. b. Find the average number of people waiting in the system. c. Find the expected time a person spends waiting in the system. ANSWER: (servers). a. P 20/hour, 30/hour, M 2 open channels
SOLUTIONS TO DISCUSSION QUESTIONS AND PROBLEMS
14-1. The waiting line problem concerns the question of ﬁnding the ideal level of service that an organization should provide. The three components of a queuing system are arrivals, waiting line, and service facility. 14-2. The seven underlying assumptions are: 1. Arrivals are FIFO. 2. There is no balking or reneging. 3. Arrivals are independent. 4. Arrivals are Poisson. 5. Service times are independent. 6. Service times are negative exponential. 7. Average service rate exceeds average arrival rate. 14-3. The seven operating characteristics are: 1. Average number of customers in the system (L) 2....

...Study for Restaurant QueuingModel
Mathias Dharmawirya
School of Information Systems Binus International – Binus University Jakarta, Indonesia mdharmawirya@binus.edu
Erwin Adi
School of Computer Science Binus International – Binus University Jakarta, Indonesia eadi@binus.edu busy fast food restaurant [3], as well as to increase throughput and efficiency [5]. This paper uses queuing theory to study the waiting lines in Sushi Tei Restaurant at Senayan City, Jakarta. The restaurant provides 20 tables of 6 people. There are 8 to 9 waiters or waitresses working at any one time. On a daily basis, it serves over 400 customers during weekdays, and over 1000 customers during weekends. This paper seeks to illustrate the usefulness of applying queuing theory in a realcase situation. II. QUEUING THEORY In 1908, Copenhagen Telephone Company requested Agner K. Erlang to work on the holding times in a telephone switch. He identified that the number of telephone conversations and telephone holding time fit into Poisson distribution and exponentially distributed. This was the beginning of the study of queuing theory. In this section, we will discuss two common concepts in queuing theory. A. Little’s Theorem Little’s theorem [7] describes the relationship between throughput rate (i.e. arrival and service rate), cycle time and work in process (i.e. number of customers/jobs in the system)....

...servers Waiting Cost ִcustomer dissatisfaction ִloss of potential customers ִcapital tied up in WIP ִstorage facility cost
Balance …
4
5
Description of queues
server
Customer arrivals
queue
Customer departures
system
Priority rules: e.g., first-come-first-serve
6
Types of Queuing Systems
Single stage system
multiple stage system
parallel single stage system
multi-channel single stage system
7
Other Arrival Characteristics
Size of Arrival Units Degree of patience Balking Reneging Jockeying
Managerial Issues of Queuing Systems
System Design • how many servers • arrangement of queue • fast vs. slow server • size of waiting area
System Management/Operations • management of arrivals • customer perception of waiting times
9
Managerial Issues of Queuing Systems (cont’d) Performance Evaluations • Average number of customers in the queue: Nq • Average waiting time (time in the queue): Tq • Average number of customers in the system: N or Ns • Average time in the system: T or Ts • System capacity utilization: ρ • Probability of 0 customers in the system: P0 • Probability of k customers in the system: Pk • Probability of waiting time less than a specific amount
10
Performance Measures: How?
Analytic methods ִexist for less complicated systems ִalready established/easy to execute ִexact results Simulation ִpossible for any system...

...OKKO CASE STUDY
2012
Casey Adam, B00550 592
Couch John,
Croteau Elizabeth
Foster Travis
1/1/2012
Contents
Facilities Design Case Study 1
Executive Summary 1
Problem Statement 1
Group Layout 1
Machine Requirements 1
Cell Layouts 2
Dock Requirements 3
Office Layout 3
Material Handling Requirements 4
Manual Handling 4
Forklift Handling 4
Employee Requirements 5
Additional Facility Requirements 6
Cafeteria 6
Restrooms 6
Changing room 6
Parking Requirements 6
Costs 6
Land and Construction 6
Personnel Costs 7
Conclusion 7
Equipment 7
Processor 7
Facilities Design Case Study
Executive Summary
It is recommended that OKKO purchase xxx amount of land in Burnside for their new facility. This land will consist of xxx developed and the rest will be for green space and for a parking lot. The layout was decided to be a group layout for improved material flow throughout the workspace and more cohesiveness in the work place. The layout was developed using the following techniques:
* ROC
* Material Scrap Rate
* Machine Fraction Calculations
* CRAFT
* Material Handling Techniques
* Warehouse Operation Techniques
The diagram below highlights each of the required sections and the aisle spacing as requested.
This type of layout was possible...

...Problem: B&K groceries operates with three checkout counters. The manager uses the
following schedule to determine the number of counters in operation, depending on the number
of customers in line:
Number of customers in store Number of counters in operation
1 to 3 1
4 to 6 2
More than 6 3
Customers arrive in the counters area according to a Poisson distribution with a mean rate
of 10 customers per hour. The average checkout time per customer is exponential with mean
12 minutes. Determine the steady-state probability pn of n customers in the checkout area.
Solution:
λn = λ = 10 customers per hour, n = 0, 1, 2, . . .
µn =
60
12 = 5 customers per hour, n = 1, 2, 3
2 × 5 = 10 customers per hour, n = 4, 5, 6
3 × 5 = 15 customers per hour, n = 7, 8, . . .
Then:
p1 =
10
5
p0 = 2p0
p2 =
10 × 10
5 × 5
p0 = 4p0
p3 =
10 × 10 × 10
5 × 5 × 5
p0 = 8p0
p4 =
10 × 10 × 10 × 10
5 × 5 × 5 × 10
p0 = 8p0
p5 =
10 × 10 × 10 × 10 × 10
5 × 5 × 5 × 10 × 10
p0 = 8p0
p6 =
10 × 10 × 10 × 10 × 10 × 10
5 × 5 × 5 × 10 × 10 × 10
p0 = 8p0
pn≥7 =
10 × 10 × 10 × 10 × 10 × 10
5 × 5 × 5 × 10 × 10 × 10 10
15n−6
p0 = 8
2
3
n−6
p0
1
Example 1:
The weather in Amman can be cloudy (C), sunny (S), or rainy (R). Records over the past 16
days are
{CCRRSSCCCRCSSRCR}
Based on these records, use a Markov chain to determine the probability that a typical day in
Amman will be cloudy, sunny, or rainy?...

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