Symmetry property of the throughput in closed tandem queueing networks with finite buffers

Authors:
Y Dallery;D Towsley
Affiliations:
Laboratoire MASI, Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05, France;Department of Computer & Information Science, University of Amherst, Amherst, MA 01002, USA
Venue:
Operations Research Letters
Year:
1991

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Abstract

In this paper we consider closed tandem queueing networks with finite buffers and blocking before service. With this type of blocking, a server is allowed to start processing a job only if there is an empty space in the next buffer. It was recently conjectured that the throughput of such networks is symmetrical with respect to the population of the network. That is, the throughput of the network with population N is the same as that with population C - N, where C is the total number of buffer spaces in the network. The main purpose of this paper is to prove this result in the case where the service time distributions are of phase type (PH-distribution). The proof is based on the comparison of the sample paths of the network with populations N and C - N. Finally, we also show that this symmetry property is related to a reversibility property of this class of networks.