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The Laws of Conservation of Flows in Acyclic Queueing Networks

  • Gurami TsitsiashviliEmail author
  • Marina Osipova
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1109)

Abstract

In this paper we consider open acyclic queuing network with few input flows, multi-server nodes and service discipline when a presence of customers in a node leads to a work of some its server. Input flows are Poisson and service times in all nodes have exponential distribution. It is proved that in stationary regime input and output flows coincide by their distributions. These results are based on generalization of Burke theorem and on rearrangement of acyclic open network nodes into some classes of nodes \(J_p,\;p=1,\ldots ,s,\) so that transition of customer may be only from node of class \(J_p\) to node of class \(J_{p+1},\;p=1,\ldots ,s-1.\)

Keywords

Acyclic queuing network Output flow Law of conservation 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.IAM FEB RASVladivostokRussia
  2. 2.Far Eastern Federal UniversityVladivostokRussia

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