Algorithm of Balance Equations Decomposition and Investigation of Poisson Flows in Jackson Networks

  • Gurami TsitsiashviliEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


In this paper a decomposition of a solution of balance equations for intensities of flows departing from nodes of the Jackson network is constructed. Procedures of the decomposition are based on a definition of classes of cyclically equivalent nodes and on a construction of acyclic directed graph consistent with the Jackson network and these classes. Then classes of cyclically equivalent nodes are arranged in the acyclic graph accordingly with maximal ways lengths from the source node to all others nodes classes. An algorithm of maximal ways lengths calculation is represented as an analogy of the Floyd-Steinberg algorithm of minimal ways lengths calculation.

Sets of independent stationary Poisson flows departing from nodes of Jackson network are enumerated. These sets are defined by non-return sets in the acyclic directed graph which is composed of cyclic equivalence classes of the Jackson network nodes. Special algorithm of an enumeration of non-return nodes sets is constructed. This algorithm is constructed accordingly with partial order of the equivalence classes in the acyclic directed graph of the equivalence classes of nodes.


The Jackson network A system of balance equations A class of cyclic equivalent nodes A directed graph A non-return set of nodes 



This paper is supported by Russian Fund for Basic Researches, project 17-07-00177.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Applied Mathematics of Far Eastern Branch of RASVladivostokRussia
  2. 2.Far Eastern Federal UniversityVladivostokRussia

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