For my project on other operations research techniques I have decided to research waiting lines and queuing models. 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.

Queuing models 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 models that can be used to help decision makers.

Queuing theory was born in the early 1900s with the work of A. K. Erlang of the Copenhagen Telephone Company, who derived several important formulas for tele-traffic engineering that today bear his name. The range of applications has grown to include not only telecommunications and computer science, but also manufacturing, air traffic control, military logistics, design of theme parks, and many other areas that involve service systems whose demands are random. Queuing theory is considered to be one of the standard methodologies (together with linear programming, simulation, etc.) of operations...

...REVISED
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CHAPTER 14
WAITINGLINE
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 waitingline 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, waitingline, 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....

...T E R
WaitingLine and Queuing Theory Models
14
TEACHING SUGGESTIONS
Teaching Suggestion 14.1: Topic of Queuing. Here is a chapter that all students can relate to. Ask about student experiences in lines. Stress that queues are a part of our everyday lives and how things have changed at banks, post ofﬁces, and airports in just the past decade. (We now wait in a common line for the ﬁrst available server.) Teaching Suggestion 14.2: Cost of Waiting Time from an Organizational Perspective. Students should realize that different organizations place different values on customer waiting time. Ask students to consider different scenarios, from a drive-through restaurant to a doctor’s ofﬁce to a registration line in their college or motor vehicle ofﬁce. It becomes clear that organizations place different values on their customers’ time (with most colleges and DMVs unfortunately placing minimal cost on waiting time). Teaching Suggestion 14.3: Use of Poisson and Exponential Probability Distributions to Describe Arrival and Service Rates. These two distributions are very common in basic models, but students should not take their appropriateness for granted. As a project, ask students to visit a bank or drive-through restaurant and time arrivals to see if they indeed are Poisson distributed. Note that other...

...Ch 12. WaitingLineModels
Contents
1. Structure of WaitingLine System
2. Single-Channel WaitingLineModel with Poisson Arrivals and
Exponential Service Times
3. Multiple-Channel WaitingLineModel with Poisson Arrivals and
Exponential Service Times
4. Economic Analysis of WaitingLines
5. OtherWaitingLineModels
6. Single-Channel WaitingLineModel with Poisson Arrivals and
Arbitrary Service Times
7. Multiple-Channel Model with Poisson Arrivals, Arbitrary Service
Times and No WaitingLine
8. WaitingLineModel with Finite Calling Population
9. Estimations of Arrival Process and Service Time Distribution
1
권치명
WaitingLineModels
Waitingline or Queue
Model is developed to help manager make to better decision for
the operation of waitingline.
Erlang (a Danish Telephone engineer) began a study of
congestion and waiting times in the completion of telephone
calls.
Operating Characteristic (performance Measure) for a
waitingLine...

...Queues defined 243
Economics of the WaitingLine Problem
Cost-effectiveness balance The practical view of waitinglines
245
The Queuing System
Customer arrivals Distribution of arrivals The queuing system: factors Exit Queuing system defined Arrival rate defined Exponential distribution defined Poisson distribution defined Service rate defined
252 261 263 263
WaitingLineModels Approximating Customer Waiting Time Computer Simulation of WaitingLines Conclusion
technical note
TECHNICAL NOTE SIX
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WAITINGLINE MANAGEMENT
technical note
243
WE’ VE ALL HAD TO WAIT IN LINES AND KNOW THAT WHATEVER LINE WE CHOOSE, THE OTHER ONES WILL GO FASTER . HERE PEOPLE LINE UP FOR THE ENTRANCE TO THE LOUVRE IN PARIS, FRANCE.
Understanding waitinglines or queues and learning how to manage them is one of the most important areas in operations management. It is basic to creating schedules, job design, inventory levels, and so on. In our service economy we wait in line every day, from driving to work to checking out at the supermarket. We also encounter waitinglines at factories— jobs wait in lines to be...

...Management of WAITINGLINES
KEY IDEAS
1. Waitinglines are an important consideration in capacity planning. Waitinglines tie up additional resources (waiting space, time, etc.); they decrease the level of customer service: and they require additional capacity to reduce them.
2. Waitinglines occur whenever demand for service exceeds capacity (supply). Even in systems that are underloaded, waitinglines tend to form if arrival and service patterns are highly variable because the variability creates temporary imbalances of supply and demand.
3. All of the waitinglinemodels presented in the chapter (except the constant service time model) assume, or require, that the arrival rate can be described by a Poisson distribution and that the service time can be described by a negative exponential distribution. Equivalently, we can say that the arrival and service rates must be Poisson, and the interarrival time and the service time must be exponential. In practice, one would check for this using a statistical Chi Square test: for problems provided here and in the textbook, assume that these distributions hold. Note that if these assumptions are not met, alternate approaches (e.g., intuition, simulation, other models) should be considered.
4. Much...

...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 waitinglines 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...

...an absolute must not only to add to the bottom line of a firm, but even for its mere survival. OM is a highly dynamic and expanding field of management. In this course, we will study both manufacturing and service operations, emphasizing their differences as well as similarities. We will examine the role of operations management in the organization by exploring a number of concepts and techniques. The interaction of operations with other business areas and environmental factors, and how operations management can contribute to the achievement of organizational goals, also will be discussed.
•
Course Learning Outcomes
The objective of the course is to develop your understanding of the major concepts and trade-offs involved in making OM decisions. At the end of this course, you will: 1. Recognize the important role of operations in an organization’s success 2. Develop a comprehensive understanding of operational issues and decisions and how they relate to each other, and to other areas of the organization and its environment 3. Understand related operational and economical concepts and techniques 4. Apply these techniques At the end of the course, you will be able to: 1. Identify the fundamental managerial trade-off in an operations decision environment 2. Develop a decision model and formulate an appropriate objective 3. Evaluate alternative solutions and analyze the objective to optimize the decision 4. Utilize data, models,...

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