38. Queuing Formulas

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch38

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Queuing Formulas, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch38

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242



  • Kendall-Lee notation;
  • queuing models


Queuing theory provides a classification system and mathematical analysis of basic queuing models and this assists in the conceptual understanding, design, and operation of queuing systems. This chapter summarizes the formulas for a number of the standard mathematical queuing models. It describes various types of queuing system in terms of six characteristics. The chapter describes these characteristics, the Kendall-Lee notation, which is used to describe them, and some terms and symbols. Queuing formulas apply to steady state average values of properties such as the average length of the queue and the average time a customer spends in the queuing system. The chapter discusses some standard queuing systems such as M/M/1/G/∞/∞ system, M/M/s/G/∞/∞ system, M/G/1/G/∞/∞ system (Pollaczek-Khinchin), M/M/1/G/m/∞ system, and M/G/m/G/m/∞ system (Erlang).

Controlled Vocabulary Terms

Kendall operator