Queuing Theory

In: Business and Management

Submitted By tzaditz
Words 2526
Pages 11
Queuing Theory

Queuing Theory

• Queuing theory is the mathematics of waiting lines. • It is extremely useful in predicting and evaluating system performance. • Queuing theory has been used for operations research. Traditional queuing theory problems refer to customers visiting a store, analogous to requests arriving at a device.

Long Term Averages
• Queuing theory provides long term average values. • It does not predict when the next event will occur. • Input data should be measured over an extended period of time. • We assume arrival times and service times are random. • • • •

Assumptions
Independent arrivals Exponential distributions Customers do not leave or change queues. Large queues do not discourage customers. Many assumptions are not always true, but queuing theory gives good results anyway

Queuing Model
Q W λ Tw
Tq
S

Interesting Values
• Arrival rate (λ) — the average rate at which customers arrive. • Service time (s) — the average time required to service one customer. • Number waiting (W) — the average number of customers waiting. • Number in the system (Q) — the average total number of customers in the system.

More Interesting Values
• Time in the system (Tq) the average time each customer is in the system, both waiting and being serviced. Time waiting (Tw) the average time each customer waits in the queue. Tq = Tw + s

Arrival Rate
• The arrival rate, λ, is the average rate new customers arrive measured in arrivals per time period. Common units are access/second • The inter-arrival time, a, is the average time between customer arrivals. It is measured in time per customer. A common unit would be seconds/access.



a=1/λ

Random Values
• We assume that most of the events we are interested in occur randomly.
– Time of a request to a device – Time to service a request – Time user makes a request

Exponential…...

Similar Documents

Queiuing Theory

...Queuing Theory Most restaurants want to provide an ideal level of service wherein they could serve their customers at the least minimum time. However, as the restaurant established its name to the public, it makes a great queuing or waiting line that most of the customers do not want. Not all restaurants desire for queue since it could make confusions to them and because of their losses from the customers who go away and dissatisfied. For some time, adding chairs and tables are not enough to solve the queuing problem. In the case of Tamagoya Noodle House, they have this principle of serving the customer with their high quality ramen regardless of the number of customers. In short, they are more on the quality than the quantity; not on the profit side but rather on the quality side. But because they really want to serve more customers especially those ramen lovers who came from far places, they want to solve these queuing problems. Service time distribution Arrivals Customer 3 Customer 2 Customer 1 Service Facility Queue Fig. 1 Queuing System Configuration Assumptions of the model: Since Tamagoya Noodle House uses a Single-Channel, Single-Phase model in order to avoid confusion of customer’s order. The model we used assumes that seven conditions exist: 1. Arrivals are served on a First-in, First-out basis. Though some of customers who ordered less and or senior citizens were prioritized to be served first. 2. Every......

Words: 1117 - Pages: 5

System Theory

...Systems theory: a scientific/philosophical approach and set of concepts, rather than a theory, for the transdisciplinary study of complex phenomena. It was first proposed by the biologist Ludwig von Bertalanffy in the 1940's (anthology: "General Systems Theory", 1968), as a reaction against scientific reductionism*. Rather than reducing a phenomenon (say, the human body) to a collection of elements or parts (say, the organs or cells), systems theory focuses on the relations and interactions between the parts, which connect them into a whole (see holism*). The particular arrangement of elements and relations determines an emergent* organization, or system*. That organization is abstract, independent of the concrete substance of the elements, which may be atoms, molecules, cells, transistors, or people. This entails that the same principles of organization can be found in different domains: physics, chemistry, biology, psychology, sociology, technology... One of the aims of systems theory is to unify different scientific disciplines by uncovering these general principles (see unity of science*). Systems theory studies characteristics common to many or all complex systems.......

Words: 1755 - Pages: 8

Netw320 Wk 4 Lab Ipv4 Tos and Router Queuing

...documentation to obtain additional information needed to execute a step, solve a problem, or build the simulation. In other instances, you may need to do research within your textbook or other online resources to understand and answer a question. When you encounter the  symbol, a question is asked and must be answered in your lab report. Example:  3 => question number 3. Answer each and every question in the lab. Note: There may be additional questions at the end of the lab – don’t forget those. Create your report using the template starting on page 2 and submit it to the Week 4 Dropbox by the due date. Have fun while learning! Thanks NETW320, Lab #4, IPv4 TOS and Router Queuing Lab Report Required Lab Questions for NETW320, IPv4 TOS, and Router Queuing Policies (This section is worth 75% of your grade for this lab) 1) In the Results Browser, expand Email and select Download Response Time (sec). Change the view from As Is to Time Average and select the Show button. Copy and label this graph to your lab report. Then use this graph to answer the following questions (note in your estimations disregard the first 1/3 of the graph to allow for start-up oscillation time to stabilize).  1. For the FIFO run, estimate the Email Download Response Time. FIFO estimated e-mail download response time is 7.3 seconds.  2. For the PQ run, estimate the Email Download Response Time. PQ estimated e-mail download response time is 12.5 seconds. ......

Words: 1087 - Pages: 5

Queuing Theory

...Introduction Being in a queue (waiting line) is an inevitable fact of our daily life, such as waiting for checkout at a supermarket, or waiting to make a bank deposit. Queuing theory, started with research by Agner Krarup Erlang, is used to examine the impact of management decisions on these waiting lines (Anderson et.al, 2009). A basic Queuing Model structure consists of three main characteristics, namely behaviour of arrivals, queue discipline, and service mechanism (Hillier and Lieberman, 2001). In this assignment, New England Foundry’s queuing problem will be solved in Excel, and then, time and cost savings will be identified. First of all, current and new situation will be analysed in order to demonstrate the queuing model by using Kendall’s Notation (for the current queuing problem, queuing model is M/M/s). After that, arrival rate, queue size, and service rate will be defined, and added-in Excel file (Queuing models.xlsx). The results will be discussed at the end. Description New England Foundry (NEF) produces four different types of woodstoves for home use and additional products that are used with these four stoves. Due to the increase in energy prices, George Mathison president of the company wants to change the layout to increase the production of their bestselling type of Warmglo III. NEF has several operations in order to produce woodenstoves which are illustrated as a flow diagram in Figure 1. Current State Analysis Current layout offers one counter...

Words: 1225 - Pages: 5

Theory

...Theory “Adlerian Psychology focuses on people's efforts to compensate for their self-perceived inferiority to others. These feelings of inferiority may derive from one's position in the family constellation, particularly if early experiences of humiliation occurred; a specific physical condition or defect existed; or a general lack of social feeling for others was present (Adler, n.d.)”. These feelings in society guide the professional behavior that makes up the theory of criminal justice is a crucial part of criminal justice system, and the ethics that make up moral principles of right and wrong, administration that distributes burden and stresses common good in our legal system. We are, faced with ethical issues every day and must deal with components that make up our involved system in a professional manner. The administration of criminal justice, especially the policing of society and individual rights requires professional behavior in certain situations and may often for those on the outside looking in to find it difficult to handle. The criminal justice system has obligations of making moral judgments of what is right or wrong and must be done professionally and with the use of critical thinking. Because law enforcement its successes and failures are often judged by society vise right and wrong the system is under great scrutiny even from those that manage the system, and understand the stresses involved. The relationship between theories, and how they are......

Words: 1462 - Pages: 6

Queuing

...Queuing Theory Queuing Theory is generated from the service industries such as shops and retail dealers that need to pay much attention to the feeling of the customers and, at the mean time, to the cost with that the service was offered. As a retailer manager, one of the important things he or she might focus on is that the queue line length which could not be too long or too short. If the queue line is too long, the customer would be impatient and complain about the service quality the shop offers while if the shop gives too many counters to deal with the customers transaction further to reduce the length of the queue, it is definitely to increase the cost of the operation. Queue Theory is a kind of tool that could help the managers who need to analyze the queue line and estimate the cost of controlling it to understand the situation and make a decision on it. The prerequisite of Queue Theory is that the customers, services and other factors in the systems are discrete. In other words they are independent with each other since the rate of the customer coming and the rate of the service provided would not affect each other. Then these factors could meet the demand of Poisson Distribution. There are four models about Queuing Theory according to our textbook: MM1- Single-Server Queuing Model, MMS- Multiple-Server Queuing Model, MD1- Constant-Service-Time Model and Limited-Population Model. They are very useful in the different areas in the business. The first model......

Words: 1374 - Pages: 6

Operations Research- Queuing Model

...QUEUING THEORY HISTORY • Queuing theory had its beginning in the research work of a Danish engineer named A.K. Erlang. • In 1909, Erlang experimented with fluctuating demand in telephonic traffic. • 8 years later, he published a report addressing the delays in automatic dialing equipment. • At the end of World War II, Erlang’s early work was extended to more general problems and to business applications of waiting lines. M/M/1 SINGLE - CHANNEL WITH POISSON Azenith Cayetano THE M/M/1 NOTATION REPRESENTS: Arrival distribution Service time distribution M = Poisson M = Exponential No. of service channels open m = 1 QUEUING EQUATIONS: λ = mean number of arrivals per time period (for example, per hour) μ = mean number of people or items served per time period SAMPLE PROBLEM 1 Angie is the Branch Manager of Citibank Lagos and she wants to improve the service of the bank by reducing the average waiting time of the bank’s clients. She was able to determine the average arrival and the average number of clients serviced per hour.  How many clients are in the bank at any given time? How much time does a client spend in the bank? How many clients are waiting to be served? How much time does a client spend waiting?  What is the probability that the teller is busy? What is the probability that there are no clients? DATA TABLE Given Description Value m λ μ Number of tellers Arrivals per hour Serviced per hour 1 11 12 1. Compute......

Words: 2416 - Pages: 10

Queuing Theory

...Table of contents 1. Introduction 2. Arrival Pattern of customers 3. Service Patterns 4. System Capacity 5. Number of Service Channels 6. Queue Discipline 7. Queuing Cost 8. The Four Models 9. Model-1(Single Channel Queuing Model) 10. Model-2 (Multiple-Channel Queuing) 11. Model-3 (Constant-Service-Time) 12. Model-3 (Constant-Service-Time) 13. Simulation 14. Conclusion Abstract This report is about queuing theory, it’s application and analysis. Queuing theory has a vast number of applications starting from the simplest day to day life examples to complicated computer algorithms. To further explain the queuing theory analysis we have used simulation of an example from our case study. We have done an in depth analysis of the four queuing theory models and chosen one of them for the simulation. The results can be helpful in improving the overall performance of the manufacturing facility. Introduction According to U. Narayan Bhat waiting line are a phenomena through which businesses and facilities can be helped in an orderly manner. There are several ways to forma queue (waiting line), for instance when people wait to get a boarding pass from an airline counter, there can be 3 service stations (airline counters) and hence 3 waiting lines, or there can be one service station and hence one queue. These days we mostly see one counter for airline services as this benefit the passengers and airline best. This conclusion...

Words: 2220 - Pages: 9

Theory

...I. What is a concept? a. A building block of a theory, can be a few of them, b. abstract ideas that cannot be visualized. Such as pain or coping or social support. You can have an idea in your mind of what these are but you cant actually touch any of these. Can you touch social support? You can probably touch a part of your body that may feel some sense of pain but the actual concept itself cannot be touched. c. Tend to be universal which means they apply equally to everything related. d. Concepts tend to be the basic elements of propositions (or statements that result from reason). If you remember geometry they had the proposition they had the “if A equaled B and B equaled C.Does A equal C.” That is the idea of what propositions are and they take concepts and build on them to create these statements to help define whatever we are discussing such as theory, research study. e. Help to integrate unrelated phenomena into a hypothesis which creates research. Critical to have very defined concepts and the concepts needed to be created into hypothesis so that you had something to study. That is critical when we discuss concepts and research i. Phenomenon is any even that can be experiences via senses, it is observable and can be seen. ii. Proposition: closed sentence or statement 1. Like geometry: If A=B and B=C, then A=C 2. Tend to be true or false 3. Content of beliefs and or......

Words: 998 - Pages: 4

Queuing Theory Based Approach to the Analysis of Sales Checkout at Montagu Spar Supermarket

...Great Zimbabwe University Faculty of Agriculture and Natural Sciences Department of Mathematics and Computer Science Student: Sigwadhi Teddy M149125 Research Project (HSOR 460) Proposal Presentation in partial fulfilment of BSc. 4th Year Special Honours Degree in Operations Research and Statistics Supervisor: Mr. R. Mawonike Research Topic  Queuing theory based approach to the analysis of sales checkout at Montagu Spar supermarket  Location: Avenues Area, Harare, Zimbabwe Background of the study • Zimbabwe is an important emerging country among the developing countries. • The Spar Montagu has been chosen to be the research object primarily because of its clientele which have different buying behaviors. There are a mix of customers, low to high class customers and it has been seen to provide interesting results on the busy and non busy periods. • The main purpose of this project is to study the application of queuing theory and to evaluate the parameters involved in the service unit for the sales checkout operation in Spar Montagu supermarket Background of the study continued… • Queuing theory is the theory of waiting lines and service provision • A mathematical model is to be developed to analyse the performance of the checking out service unit • Two parameters need to be determined from the data collected in the supermarket through the mathematical model to the service point. • One parameter is the customer arrival rate to the service point per hour • The other is......

Words: 848 - Pages: 4

Queuing

...Methodology Theory chapter Empirical findings Analysis chapter Result chapter Conclusion Hand in paper Presentation w12 w13 w14 April w15 w16 w17 w18 May w19 w20 w21 ------ ---------------- ----------- ----------- ------ ----------- ------ ------ --------------------W22 Table 1.1- Time frame The preliminary work of the thesis started on week eleven (11) with literature survey on scientific journals, articles, text books etc. with respect to the area of study, followed by the Page 13  Linnaeus University School of Engineering Department of Terotechnology (Total Quality Maintenance) 4SE31E Degree Project Master Thesis commencement of the study paper, i.e. writing of the introduction chapter. The methodology chapter begins immediately, which was followed by the theoretical chapter, the empirical findings chapter and the analysis chapter. The result and conclusion chapter follows afterwards and finally handing in of the complete paper, 1.9. Thesis disposition This study is discerned in the parts of Introduction, Methodology, Theoretical framework, and the Empirical findings. This is followed by the Analysis, Results and Conclusions which is a normal in writing a thesis. Figure 1.1 below describes the disposition of this thesis. Chapter 1 Introduction -Background -Problem discussion, presentation and formulation. -Purpose -Relevance -Limitation -Timeframe -Disposition Chapter 2 Methodology Chapter 3 Theoretical framework - Relevant theories and......

Words: 17171 - Pages: 69

Theory

...ethics as an ethical framework (the greatest good for the greatest number) opposes the ethical principle of deontology (i.e., the rightness of an act itself determines what is right). Both of these impact the nursing profession. Modern social exchange theories are based on the principle of utility. Read the assumptions of social exchange theory and consider how these would affect the nurse-patient relationship, compared to how these impact the nurse within the health care environment. To what extent are all theories ethical? Is social exchange theory compatible with the values of the nursing profession? Theories from the sociologic sciences are integral to the discipline of nursing (McEwen &Wills, 2014). Social exchange theory deals with the many different types of interactions among patients and their nurses. The social exchange theory is defined as “a flow of emotional concern, instrumental aid, information, and or appraisal (information relevant to self-evaluation) between people” (Leahy-Warren, 2007, p. 370). The implication for using non-nursing theories to develop nursing knowledge is that borrowed theories are potentially useful for understanding the patient nurse interaction. The two categories of social exchange theories are individualistic and collectivist. In individualistic frame work “human beings are motivated by self-interest to act” (McEwen &Wills, 2014). In individulistic method the nurse will provide comprehensive nursing care with the intent of......

Words: 514 - Pages: 3

Queueing Theory

...Queuing Theory Queuing Theory Waiting in lines is a social phenomenon that people face on a daily basis. Queues of people form when checking in at the airport, purchasing items at a cash register, and getting on rides in amusement parks. Waiting in lines can have both economic costs and psychological costs when customers perceive it as a negative experience. Waiting too long in line can be extremely frustrating for customers and staff. Analyzing and understanding queuing systems for service businesses involves finding and managing the best level of service that will keep customers happy and costs under control. The problem for managers in most queuing situations is the trade-off decision between adding costs of providing more rapid service against the inherent cost of waiting. To analyze a queuing system one must look at arrival characteristics including the pattern in which customers arrive at the facility, customer behaviors once they are in line, and the size of the customer population. Service characteristics, such as, the configuration of the service system and the pattern of service times must also be considered in the mathematical model (Render, Stair, Hannah, & Hail, 2015). In this paper, I will discuss the advantages and disadvantages of queuing theory for an organization in the service industry and the benefits provided by the constant service time model Queuing Systems for Service Businesses Queuing systems are put in place to serve customers in an......

Words: 818 - Pages: 4

Theory

...foundational theories which helped to shed more light about leadership (Burns, 1978). Thus, it is impossible to analyze and evaluate leadership theories without going back to their origins (Field & Seters, 1990) There are several leadership theories that have been researched, developed and discussed by various researchers. They include; personality, influence, behavior, situational, transactional, anti-leadership, culture, transformational and contingency theories. The sole objective of this essay is to critically evaluate a group of contingency theories of leadership. The most notable contingency theories of leadership include Fried Fiedler’s, Path-Goal and Vroom-Jago (Field&Seters, 1990). This essay will start by evaluating Fiedler’s theory, followed by Path-Goal theory and the last three theories will be evaluated as a single group and it will discuss which of the said model is best suited to improve the work culture in Zambia. According to (Bryman, 2011), contingency theories are advanced on the platform that dictates that there is no single best method that can be used alone to make a decision or lead an organization. These theories seek to offer and explain the effectiveness of a given leadership style. Thus, the theories differ in the way they address and deal with a specific situation. Fred Fiedler’s contingency theory of leadership is basically about how certain leaders fit in certain situations as a result of their leadership styles. In addition, the......

Words: 3303 - Pages: 14

Theory of Theory

...Modern Times and Marxist Criticism Marxist Criticism revolves around the theories and ideologies of Karl Marx. While his work is still commonly studied and referenced, I have found some of his principles to be outdated. Marx lived from 1818 until 1883, so, his principles are based on what was going on during his lifetime. In nearly two hundred years, some ideologies of Marxist Criticism don’t fit the social norm as well as they did in his time. Ideologies such as religion, consumerism, and rugged individualism have grown with society and don’t have the same effect as they once did. In Marxist Criticism you will find one of Marx’s ideologies to be religion. Religion is an ideology that helps to keep the poor satisfied with their lot in life, or at least tolerant of it, as a tranquilizer might do. (Tyson, 59) With religion being a major part of many people’s life in the 1800’s his view on its role in society as the “opiate of the masses” is different now that it is the twenty-first century than it was during the nineteenth century. In centuries prior religion would include the conviction that the poor, if they remain nonviolent, will find their reward in heaven. (Tyson, 59) While that ideology was extremely relevant in Marx’s time, religion today isn’t a requirement, it isn’t expected thus making it outdated. While religion is still widespread, it has become common to not be religious at all. A growing number of people are identifying as Atheist or Agnostic, choosing......

Words: 1098 - Pages: 5

Stompin Tom - Boots To The Board. | 100 Steckkarten C6 NEU mit 4 Streifen und Folie (Kobra VF4/Lindner 869) | ウェディング 小物