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Finite Population Models—Single Station Queues

  1. Raja Jayaraman1,
  2. Timothy I. Matis2

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0325

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Jayaraman, R. and Matis, T. I. 2011. Finite Population Models—Single Station Queues. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. 1

    University of Arkansas, Department of Industrial Engineering, Fayetteville, Arkansas

  2. 2

    Texas Tech University, Department of Industrial Engineering, Lubbock, Texas

Publication History

  1. Published Online: 14 JAN 2011

Abstract

A finite population queueing model consists of service requests generated by finite number of customers handled by either a single or multiple number of servers. There are several practical applications of finite-source models including the machine–repairman model, multiprocessor systems, time-sharing systems, telecommunication models, vacation models, reliability models, and so on. In this article, we review several applications of finite-source models, and analyze the classical machine–repairman model in steady state to discuss related performance measures. Variations to the underlying characteristics and assumptions of this model lead to the development and analysis of a broader class of queueing problems motivated by these applications, for which we present extensions and suggestions for further reading.

Keywords:

  • queueing models;
  • machine–repairman model;
  • birth–death process;
  • steady state;
  • machine failure