Uniqueness of the solution for optimal static routing in open BCMP queueing networks

Authors:
H. Kameda;Y. Zhang
Affiliations:
Institute of Information Sciences and Electronics University of Tsukuba, Tsukuba Science City, Ibaraki 305, Japan;Department of Computer Science and Information Mathematics The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182, Japan
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1995

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Abstract

Optimal static routing problems in open BCMP queueing networks with state-independent arrival and service rates are studied. They include static routing problems in communication networks and optimal static load balancing problems in distributed computer systems. We consider an overall optimal policy that is the routing policy whereby the overall mean response (or sojourn) time of a job is minimized. We obtain the routing decisions of the overall optimal policy and show that they may not be unique, but that the utilization of each service center is uniquely determined by the overall optimal policy. We also consider an individually optimal policy whereby jobs are routed so that each job may feel that its own expected response time is minimized if it knows the mean delay time for each path.