Standard Article

Batch Arrivals and Service—Single Station Queues

  1. Raja Jayaraman1,
  2. Timothy I. Matis2

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0095

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. Batch Arrivals and Service—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

Queueing models characterized by bulk (or batch, group) arrivals or service performed in batches of either fixed or variable sizes can be commonly found in models of traffic and transportation, complex computer and telecommunication systems, inventory replenishment systems, and many other real-life applications. In this article, we study single-server bulk Markovian queueing models, followed by extensions to general distributions for both arrivals and services. We discuss important performance measures in steady state including waiting time characteristics, stochastic ordering properties, approximations, and bounds. We then review methods commonly employed to extend the study of bulk queueing models to more general systems, and present further reading references.

Keywords:

  • queueing models;
  • batch arrival queues;
  • batch service queues;
  • partial batch model;
  • full batch model