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.
Author(s): Thomopoulos, Nicholas T
Publisher: Springer
Year: 2012
Language: English
Pages: 182
City: New York
Tags: Statistics for Business/Economics/Mathematical Finance/Insurance; Operations Research/Decision Theory; Operations Research, Management Science
Front Matter....Pages i-xviii
Introduction....Pages 1-8
Preliminary Concepts....Pages 9-18
One Server, Infinite Queue (M/M/1)....Pages 19-25
One Server, Finite Queue (M/M/1/N)....Pages 27-33
One Server, No Queue (M/M/1/1)....Pages 35-40
Multi Servers, Infinite Queue (M/M/k)....Pages 41-48
Multi Servers, Finite Queue (M/M/k/N)....Pages 49-56
Multi Servers, No Queue (M/M/k/k)....Pages 57-63
One Server, Arbitrary Service (M/G/1)....Pages 65-71
2 Populations, One Server, Arbitrary Service (M/G/1/2)....Pages 73-78
M Machines, One Repairman (M/M/1/M)....Pages 79-84
M Machines, R Repairmen (M/M/R/M)....Pages 85-91
One Server, Repeat Service (M/M/1/θ)....Pages 93-96
Multi Servers, Repeat Service (M/M/k/θ)....Pages 97-101
Tandem Queues (M/M/1: M/M/1)....Pages 103-107
Priority System, One Server, Infinite Queue (M/M/1//P)....Pages 109-113
Priority, One Server, Arbitrary Service (M/G/1//P)....Pages 115-121
One Server, Constant Service (M/D/1)....Pages 123-127
Exponential Arrivals, Erlang Service (M/E2/1)....Pages 129-138
Erlang Arrivals, Exponential Service (E2/M/1)....Pages 139-146
Erlang Arrivals, Erlang Service (E2/E2/1)....Pages 147-154
Waiting Time Density, One Server (M/M/1)....Pages 155-158
Waiting Time Density, Multi Servers (M/M/k)....Pages 159-162
Back Matter....Pages 163-182
