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Fundamentals of Queuing Systems : Statistical Methods for Analyzing Queuing Models / by Nick T. Thomopoulos
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Boston, MA : Springer US, 2012Description: Online-Ressource (XIII, 170p. 4 illus, digital)ISBN:- 9781461437130
- 519.8/2
- 330.015195
- QA276-280
Contents:
Summary: Introduction -- Preliminary Concepts -- One Server, Infinite Queue (M/M/1) -- One Server, Finite Queue (M/M/1/N) -- One Server, No Queue (M/M/1/1) -- Multi Servers, Infinite Queue (M/M/k) -- Multi Servers, Finite Queue (M/M/k/N) -- Multi Servers, No Queue (M/M/k/k) -- One Server, Arbitrary Service (M/G/1) -- 2 Populations, One Server, Arbitrary Service (M/G/1/2) -- M Machines, One Repairman (M/M/1/M) -- M Machines, R Repairmen (M/M/R/M) -- One Server, Repeat Service (M/M/1/q) -- Multi Servers, Repeat Service (M/M/k/θ) -- Tandem Queues (M/M/1 : M/M/1) -- Priority System, One Server, Infinite Queue (M/M/1//P) -- Priority, One Server, Arbitrary Service (M/G/1/P) -- One Server, Constant Service (M/D/1) -- Exponential Arrivals, Erlang Service (M/E2/1) -- Erlang Arrivals, Exponential Service (E2/M/1) -- Erlang Arrivals, Erlang Service (E2/E2/1) -- Waiting Time Density, One Server (M/M/1) -- Waiting Time Density, Multi Servers (M/M/k) -- Bibliography -- Problems -- Solutions.Summary: Waiting in lines is a staple of everyday human life. Without really noticing, we are doing it when we go to buy a ticket at a movie theater, stop at a bank to make an account withdrawal, or proceed to checkout a purchase from one of our favorite department stores. Oftentimes, waiting lines are due to overcrowded, overfilling, or congestion; any time there is more customer demand for a service than can be provided, a waiting line forms. Queuing systems is a term used to describe the methods and techniques most ideal for measuring the probability and statistics of a wide variety of waiting line models. This book provides an introduction to basic queuing systems, such as M/M/1 and its variants, as well as newer concepts like systems with priorities, networks of queues, and general service policies. Numerical examples are presented to guide readers into thinking about practical real-world applications, and students and researchers will be able to apply the methods learned to designing queuing systems that extend beyond the classroom. Very little has been published in the area of queuing systems, and this volume will appeal to graduate-level students, researchers, and practitioners in the areas of management science, applied mathematics, engineering, computer science, and statistics. .PPN: PPN: 1651394520Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Fundamentals of QueuingSystems; Preface; Fundamentals of Queuing Systems; Contents; 1 Introduction; Abstract; 1.1…Introduction; 1.2…The Queuing System; 1.3…Early Literature; 1.4…Some Applications; 1.5…Chapter Summaries; Bibliography; 2 Preliminary Concepts; Abstract; 2.1…Introduction; 2.2…Some Useful Relations; 2.3…Exponential Distribution; 2.4…Poisson Distribution; 2.5…Relation Between the Exponential and Poisson Distributions; 2.6…Convolution of Two Poisson Variables; 2.7…ErlangErlang Distribution; 2.8…Memory-Less Property of the Exponential Distribution
2.9…Cumulative Distribution for a Small Increment h2.10…Probability Postulates; 2.11…Difference Equations; 2.12…Differential Equations; 2.13…Equilibrium Equations; 2.14…Reduced Equations; 2.15…Probability of n Units in the System (Pn); 2.16…Performance Measures; 2.17…Wait Time in Queue Given a Delay (WqWqvprime); 2.18…Little's Law; 2.19…Kendall's Notation; Bibliography; 3 One Server, Infinite Queue (M/M/1); Abstract; 3.1…Introduction; 3.2…Difference Equations; 3.3…Equilibrium Equations; 3.4…Reduced Equations; 3.5…Probability on n Units in the Systemsystem; 3.6…Probability the System is Idle
3.7…Expected Units in the Service Facility (LsLs)3.8…Expected Units in the Queue (LqLq); 3.9…Expected Units in the System (LL); 3.10…Expected Time in Service (WsWs), Queue (WqWq) and System (WW); 3.11…Expected Time in the Queue Given a Delay (WqWqvprime); 3.12…Service Level; 4 One Server, Finite Queue (M/M/1/N); Abstract; 4.1…Introduction; 4.2…Difference Equations; 4.3…Equilibrium Equations; 4.4…Reduced Equations; 4.5…Probability on n Units in the System; 4.6…Probability the System is Idle; 4.7…Expected Units in the Service Facility (LsLs); 4.8…Lambda and Rho Effective
4.9…Expected Unitsunits in the Queue (LqLq)4.10…Expected Units in the System (LL); 4.11…Expected Time in Service (WsWs), Queue (WqWq) and System (WW); 4.12…Expected Time in the Queue Given a Delay (WqWqvprime); 4.13…Service Level (SL) and Loss Probability (Ploss); 5 One Server, No Queue (M/M/1/1); Abstract; 5.1…Introduction; 5.2…Difference Equations; 5.3…Equilibrium Equations; 5.4…Reduced Equation; 5.5…Probability on n Units in the System; 5.6…Probability the System is Empty; 5.7…Expected Units in the Service Facility (LsLs); 5.8…Lambda and Rho Effective
5.9…Expected Units in the Queue (LqLq)5.10…Expected Units in the System (LL); 5.11…Expected Time in Service (WsWs), Queue (WqWq) and System (WW); 5.12…Service Level and Loss Probability; 6 Multi Servers, Infinite Queue (M/M/k); Abstract; 6.1…Introduction; 6.2…Difference Equations; 6.3…Equilibrium Equations; 6.4…Reduced Equations; 6.5…Probability on n Units in the System; 6.6…Expected Units in the Service Facility (LsLs); 6.7…Expected Units in the Queue (LqLq); 6.8…Expected Units in the System (LL); 6.9…Expected Time in Service (WsWs), Queue (WqWq) and System (WW)
6.10…Expected Time in the Queue Given a Delay (WqWqvprime)
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