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Equivalence, reversibility and symmetry properties in Fork/Join queueing networks with blocking

Yves Dallery · Zhen Liu · Don Towsley · 06 - Valbonne (France). Unite de Recherche de Sophia-Antipolis Institut National de Recherche en Informatique et en Automatique (INRIA)

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Advanced Queuing Theory Analysis Interconnection Networks and Systems Petri Nets in System Modeling

Abstract

In this paper we study quantitative as well as qualitative properties of Fork/Join queueing networks with blocking (FJQN/B's). Specifically, we prove theorems regarding the equivalence of the behavior of a FJQN/B and that of its duals of a circuit-free FJQN/B, and a strongly connected marked graph. In addition, we obtain general conditions that must be satisfied by the service times to guarantee the existence of a long term throughput and its independence on the initial configuration. We also establish conditions under which the reverse of a FJQN/B has the same throughput as the original network. Last, by combining the equivalence results for duals and the reversibility results, we establish a symmetry property for the throughput of a FJQN/B.

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