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Jackson Networks

  • Hong Chen
  • David D. Yao
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 46)

Abstract

A Jackson network consists of J nodes (or stations), each with one or several servers. The processing times of jobs at each node are i.i.d., following an exponential distribution with unit mean. The service rate, i.e., the rate by which work is depleted, at each node i can be both node-dependent and state-dependent. Specifically, whenever there are x i jobs at node i, the processing rate is μ i (x i ),where μ i (·)is a function Z + ↦ ℜ+, with μ i (0)= 0 and μ i (x) > 0 for all x > 0. Jobs travel among the nodes following a routing matrix P:= (p ij ), where, for i, j = 1,..., J,p ij is the probability that a job leaving node i will go to node j.

Keywords

Service Rate Equilibrium Distribution Original Network Closed Network Stationary Markov Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Hong Chen
    • 1
  • David D. Yao
    • 2
  1. 1.Faculty of Commerce and Business AdministrationUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Operations Research and Industrial EngineeringColumbia UniversityNew YorkUSA

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