Decomposition and Customer Streams of Feedback Queueing Networks in Equilibrium,

Abstract

P. J. Burke and E. Reich independently showed the output of a M/M/1 queue in equilibrium to be a Poisson process. Consequently, analysis of tandem exponential servers with a Poisson input stream can be reduced to consideration of a series of M/M/1 queues. This work generalizes the above results to so-called Jackson networks, which consists of exponential servers with mutually independent Poisson exogenous inputs and random customer routings permitting customer feedback. The authors prove that traffic on all exit arcs is Poisson; moreover, the customer streams leaving any exit set are mutually independent.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1975
Accession Number
ADA021238

Entities

People

  • Benjamin Melamed
  • Frederick J. Beutler

Organizations

  • University of Michigan

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Chemical Reaction Properties
  • Chemical Reactions
  • Decomposition
  • Dissociation
  • Feedback
  • Interdisciplinary Science
  • Queueing Theory

Readers

  • Computer Networking
  • Mathematical Modeling and Probability Theory.