...Multiple-Server Waiting Line Model with Poisson Arrivals and Exponential Service Times Rechell Kaye B. Mosqueda, CPA Multiple-Server Waiting Line Model A multiple-server waiting line consists of two or more servers that are assumed to be identical in terms of service capability. For multipleserver systems, there are two typical queuing possibilities: (1) arriving customers wait in a single waiting line (called a “pooled” or “shared” queue) and then move to the first available server for processing, (2) each server has a “dedicated” queue and an arriving customer selects one of these lines to join (and typically is not allowed to switch lines). Multiple-Server Waiting Line Model The formulas for M/M/S are applicable if the following conditions exist: The arrivals follow a Poisson probability distribution. The service time for each server follows an exponential probability distribution. The service rate µ is the same for each server. The arrivals wait in a single waiting line and then move to the first open server for service. Multiple-Server Waiting Line Model Important Consideration The average service rate must always exceed the average arrival rate. µ> Otherwise, the queue will grow to infinity. Operating Characteristics k number of servers average arrival rate µ average service rate for each server Operating Characteristics The probability that no units are in the system: ...
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...There is more to life than money There is more to life than fame and There is more to life with Godiva’s chocolate Godiva Background Godiva Chocolatier, a Belgium chocolate manufacturer famous for its premium quality handcrafted chocolates, was founded in 1926 in Brussels by the master chocolatier Joseph Draps and it was purchased by the Campbell Soup Company which faciliatates the activities of brand aroun the World. In 2001 Godiva was purchased by the Turkish Yıldız Holding, owner of the Ülker Group. and on Februrary 1st 2013 the former owner of Godiva Chocolatier Yildiz Holding sold Godiva Chocolatier to the American food company The Kraft Foods Group. Godiva owns and operates more than 600 retail boutiques and shops in the United States, Canada, Europe, and Asia and is available via over 10,000 speciality retailers Global Marketing Strategy of Godiva Godiva is growing in the global market with accessing to new markets and new resources. The brand is very well known for its hand-made luxury chocolates and it is touching more people who have different cultures, economic environments with market development strategy(entering into new markets with existing products) and diversification strategy(entering into new markets with new products). Key Elements of Global Marketing Strategies of Godiva Customer Value: In fall 2009...
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...Juan Sanchez Dr. Bridgette McAden MAT 110/50 February 27, 2012 William A. Massey – Mathematician He was born in Jefferson City, Missouri, as the younger of two sons of Richard and Juliette Massey. He is a graduate of the public schools of St. Louis, Missouri and attended high school in University City, a suburb of St. Louis. After receiving a Harvard Book Award and a National Achievement Scholarship at University City High School, he entered Princeton University in 1973. There, he encountered his first real introduction to research mathematics in an honor calculus course taught by the late Ralph Fox. He wrote his undergraduate senior thesis, titled "Galois Connections on Local Fields,'' in algebraic number theory, under the direction of the late Bernard Dwork, and graduated from Princeton in 1977 with an A.B. in Mathematics (Magna Cum Laude, Phi Beta Kappa, and Sigma Xi). That same year he was awarded a Bell Labs Cooperative Research Fellowship for minorities to attend graduate school in the department of mathematics at Stanford University. In 1981, he received his Ph.D. degree from Stanford and his thesis, titled "Non-Stationary Queues,'' was directed by Joseph Keller. Dr. William Massey's parents, Juliette and Richard Massey Sr. were both educators; she was from Chattanooga, Tennessee and he was from Charlotte, North Carolina. They met at Lincoln University in Jefferson City, Missouri which became his birthplace. Professor Massey's initial fascination with numbers...
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...Co-requisites, and/or Other Restrictions A first course on probability theory. Course Description Overview of case studies. Brief review of probability theory. Queueing models and physical origin of random variables used in queueing models. Various important cases of the M/M/m/N queueing system. Little's law. The M/G/1 queueing system. Discrete time queueing systems. Simulation of queueing systems. Product form solutions of open and closed queueing networks. Convolution algorithms and Mean Value Analysis for closed queueing networks. Student Learning Objectives/Outcomes Ability to understand and apply M/M/1 queueing models Ability to understand and apply Little’s result for FIFO and non-FIFO queues Ability to understand and apply continuous parameter Markov chains and state dependent queueing models Ability to understand and apply M/G/1 queueing models Ability to understand and apply discrete parameter Markov chains and discrete-time queueing models Ability to understand and apply continuous-time open queueing network models Ability to understand and apply continuous-time closed queueing network models Application of the above concepts in computers and computer networks Required Textbooks and Materials Thomas G. Robertazzi, Computer Networks and Systems: Queueing Theory and Performance Evaluation, Third Edition, Springer-Verlag, 2000. Suggested Course Materials Trivedi, Probability & Statistics with Reliability, Queueing and Computer Science Applications,...
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...day company can hire one staff it cost €50000 so it means one staff can reduce 2 days , and 16 days reduce to 10 days company need only 3 staff , it means company can finish the work within 10 days and total cost 3x €50000. So its better to hire 3 engineers and we can reduce the number of working days with less cost. We consider a Level-2 IT service desk with two staff members. Each staff member can handle one service request in 4 working hours on average. Service times are exponentially distributed. Requests arrive at a mean rate of one request every 3 hours according to a Poisson process. What is the average time between the moment a service request arrives at this desk and the moment it is fulfilled? Queueing theory gives us the following formulas for calculating the above parameters for M/M/1 models: Lq—The average number of jobs (e.g. customers) in the queue. Wq—The average time one job spends in the queue. W—The average time one job...
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...PHILIPPINE WOMEN’S UNIVERSITY Waiting Line Theory A Narrative Report 2014 MBA PROGRAM Introduction Each organization has different illustrations of waiting lines or commonly called “queue”. No wonder why we also need to study waiting line because it is part of our everyday routine as well. It merely affects the performance and profit of the company. Waiting line or queue refers to a busy service facility or server so service is momentarily occupied or being used. One great example is during enrollment. At our very first step at the school gate, you will fall in line to have your bag checked by the security personnel. You will also need to fall in line at your college department to seek advise of what subjects needed to take. You might wait for your adviser attending to other students. At the time you have your subjects needed to enrol, you will need to fall in line at Registrar’s office for subjects encoding. Once you get your assessment form, you will be redirected to Accounting Office for payment and expect a new line again. Then, you will need to update your school ID card after payment, it means another line. Waiting line or queue is a repetitive scenario in our everyday lives. We can’t deny but we are also used in waiting. The organization itself also encounter waiting line or queue. One example is when an airplane has to wait in line for fueling, inspection, a particular gate, a specific flight route, an assigned crew, food loading, verified passenger count...
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...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 the...
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...* Management optimization of bank’s queuing system * Abstract Nowadays the queue phenomenon in the bank offices is a common and troublesome issue that nearly occurs everyday in the banks of China. The rapid tempo of life makes people pay much attention to the time management, they don’t willing to spend much time on queuing and gradually lose confidence in banks. In order to improve the efficiency and the satisfy degree of customers and finally increase the profit of banks, the banks have to do something about their current queuing system. This proposal aims at analyzing the current queuing system of the China banks, finding out existing problems and carrying out some effective measures based on the previous researches, the principle of queuing and statistic method. Under the premise of less increasing the operation cost of the banks to improve the service efficiency in order to realize the win-win result of customers satisfaction and banks profit. Background Every person no matter he is young or old may have some painful experiences waiting in the banks of China. Customers still have to wait for a period of time even when they avoid the busy hours of the banks. Not alone the busy operation time or the peak period of the banks people have to wait for ages. I also had the similar experiences when I was an undergraduate student. As a student we need to pay our tuition fee through a certain bank such as Bank of China before a semester begins. However so many students...
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...Chapter 18 Management of Waiting Lines True / False Questions 1. Waiting lines occur even in under loaded systems because of variability in service rates and/or arrival rates. TRUE Difficulty: Easy TLO: 1 Taxonomy: Knowledge 2. A system has one service facility that can service 10 customers per hour. The customers arrive at a variable rate, which averages 6 per hour. Since there is excess capacity, no waiting lines will form. FALSE Difficulty: Easy TLO: 1 Taxonomy: Knowledge 3. The goal of queuing analysis is to help eliminate customer waiting lines. FALSE Difficulty: Easy TLO: 2 Taxonomy: Knowledge 4. The cost of customer waiting is easy to estimate, the number waiting multiplied by the wait cost per minute. FALSE Difficulty: Easy TLO: 3 Taxonomy: Knowledge 5. In a theme park like Disney world, reservation systems are a win-lose situation since only those holding reservations are satisfied. FALSE Difficulty: Medium TLO: 2 Taxonomy: Knowledge 6. The point that minimizes total queuing system costs is that point where waiting costs and capacity costs are equal. FALSE Difficulty: Medium TLO: 2 Taxonomy: Knowledge 7. A multiple channel system assumes that each server will have its own waiting line and line changing is not permitted. FALSE Difficulty: Medium TLO: 4 Taxonomy: Knowledge 8. A dental office with two professionals (one dentist, one hygienist) who work together...
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...Minnesota. His major concern was the number of workers to assign to his single unloading dock. After he began contracting with motor carriers for deliveries, he found that they were assessing him stiff penalties if their trucks had wait time to be unloaded. Wayne started adding larger crews at the unloading dock, but often, they seemed idle because there were no trucks to unload. Wayne recalled from college that queuing theory might be applicable to such a problem. The theory of queuing is an analysis of the probabilities associated with waiting in line, assuming that orders, customers, and so on arrive in some pattern (often a random pattern) to stand in line. A common situation is that on the average, a facility may have excess capacity, but oftentimes, it is more than full, with a backlog of work to be done. Often, this backlog has costs associated with it, including penalties to be paid or customers who walk away rather than wait. If a firm expands its capacity to reduce waiting times, then its costs go up and must be paid even when the facility is idle. Queuing theory is used to find the best level of capacity, the one that minimizes the costs of providing a service and the costs of those waiting to use the service. After some further research specific to his firm, Wayne determined the following facts. 1. Trucks arrive randomly at the average rate of four per hour, with a deviation of plus or minus one. 2. A team of two warehouse workers can unload trucks at the rate...
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...Operational Laws and Mean Value Analysis Nirdosh Bhatnagar 1. Introduction Operational technique can be used to analyse both computer and networking systems. We …rst introduce basics of operational analysis. This technique is then extended to open and closed queueing networks. The closed queueing network considered has single servers at its queueing centers. 2. Operational Analysis Basics The word operational means measurable. The analysis presented in this chapter assumes that the performance metrics of a computer can be directly inferred by measurable quantities. The measurable quantities are called operational quantities. The laws which relate operational quantities are called operational laws. Operational laws for computer systems will be studied in this note. We …rst introduce some notation. Notation: M =Number of queueing centers in the network. T = Finite observation period. Ai = Number of arrivals at queue i (device i) during observation period. Bi = Total busy period of queue i during observation period. Ci = Number of service completions at queue i during observation period. Di = Total service demand by a customer at device i. Qi = Queue length at device i (including the job in service) Ri = Response time per visit to the ith device. Si = Average service time per customer visit to queue i during observation period. Ui = Utilization of queue i during observation period. Vi = Average number of visits to queue i by a customer before it leaves the system during observation...
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...RELATIONSHIP BETWEEN FACILITY, VARIETY OF MENU, PRICE, LOCATION AND SERVICE WITH WILLINGNESS OF QUEUING IN ITB CANTEENS This paper is a prerequsite of graduation Business Research Method lecture By Rizky Rahmany 19011055 Ersha Nuranjasari 19011094 Wedda Le 19011139 Arizal Khoironi 19011032 Sweeta Elfonsia 19011087 (Study Program Business Management) INSTITUT TEKNOLOGI BANDUNG 2012 RELATIONSHIP BETWEEN FACILITY, VARIETY OF MENU, PRICE, LOCATION AND SERVICE WITH WILLINGNESS OF QUEUING IN ITB CANTEENS This paper is a prerequsite of graduation Business Research Method lecture By Rizky Rahmany 19011055 Ersha Nuranjasari 19011094 Wedda Le 19011139 Arizal Khoironi 19011032 Sweeta Elfonsia 19011087 (Study Program Business Management) INSTITUT TEKNOLOGI BANDUNG 2012 ABSTRACT RELATIONSHIP BETWEEN FACILITY, VARIETY OF MENU, PRICE, LOCATION AND SERVICE WITH WILLINGNESS OF QUEUING IN ITB CANTEENS By Rizky Rahmany 19011055 Ersha Nuranjasari 19011094 Wedda Le 19011139 Arizal Khoironi 19011032 Sweeta Elfonsia 19011087 (Study Program Business Management) Institut Teknologi Bandung When we talk about queuing, there are many questions come up from our mind such “what kind of thing is happening there so people want to queue?” Talking about queuing is not always about staying in the line, no guarantee that people want to keep staying for...
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...In queueing theory, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953[1] where A denotes the time between arrivals to the queue, S the size of jobs and c the number of servers at the node. It has since been extended to A/S/c/K/N/D where K and D the capacity of the queue and queueing discipline[2] and N the size of the population of jobs to be served.[3][4] When the final three parameters are not specified (e.g. M/M/1 queue), it is assumed K = ∞, N = ∞ and D = FIFO. In queueing theory, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953[1] where A denotes the time between arrivals to the queue, S the size of jobs and c the number of servers at the node. It has since been extended to A/S/c/K/N/D where K and D the capacity of the queue and queueing discipline[2] and N the size of the population of jobs to be served.[3][4] When the final three parameters are not specified (e.g. M/M/1 queue), it is assumed K = ∞, N = ∞ and D = FIFO. In queueing theory, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953[1]...
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...Queuing Theory Significance There is a very significant reason why Queuing Theory exists. Not only does it apply to a wide variety of topic, many within the business and supply chain industries, it also helps prove cause and effect. In addition to this, it provides a very logical idea of what a solution to a problem it has discovered should be. Measuring and understanding both order rate and service rate can potentially be the difference between business success and business failure. For example, if a company has too slow of a service rate, it is going to lose business because of the long wait times. On the opposite end of the spectrum, if a company focuses too much on improving its service rate instead of understanding its ratio compared to order rate, it will be misusing its very valuable resources. It is also important to have knowledge of all different types of queuing systems. Importance of Queuing Configuration As one can imagine, the importance of a queuing system configuration is very significant as well. As stated above, there are several different types of queuing systems and queuing configurations. If a business uses an improper queuing system or queuing configuration, it can suffer from one of many different negative consequences. Some examples of different types of queuing systems/queuing configurations are First Come First Served, First In First Out, Round Robin, Service in Random order, and many more. Queuing systems and configurations also vary by the number...
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...management deals with cases where the customer arrival is random; therefore, service rendered to them is also random. A service organization can reduce cost and thus improve profitability by efficient queue management. A cost is associated with customer waiting in line and there is cost associated with adding new counters to reduce service time. Queue management looks to address this trade off and offer solutions to management. Queuing System To solve problems related to queue management it is important to understand characteristics of the queue. Some common queue situations are waiting in line for service in super-market or banks, waiting for results from computer and waiting in line for bus or commuter rail. General premise of queue theory is that there are limited resources for a given population of customers and addition of a new service line will increase the cost aspect to the business. A typical queue system has the following: Arrival Process: As the name suggests an arrival process look at different components of customer arrival. Customer arrival could in single, batch or bulk, arrival as distribution of time, arrival in finite population or infinite population. Service Mechanism: this looks at available resources for customer service, queue structure to avail the service and preemption of service. Underlining assumption here is that service time of customers is independent of arrival to the queue. Queue Characteristics: this looks at selection of customers...
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