Abstract
We consider routing and scheduling systems consisting of a number of parallel homogeneous servers with finite capacities. Assuming that jobs belong to multiple classes, we represent the interconnection of arrival streams (servers) to stations by abipartite graph, called therouting (resp.scheduling) digraph. By developing an algebraic structure on the interconnection pattern embedded in the digraph, we identify certain classes of symmetric routing and scheduling systems for which a simple control policy such as theShortest Queue policy can be shown to be optimal in the sense of optimizing the departure and loss counting processes. A counterexample is shown for systems described by digraphs with a cyclic structure.
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Sparaggis, P.D., Towsley, D. & Cassandras, C.G. Optimal control of multiclass parallel service systems. Discrete Event Dyn Syst 6, 139–158 (1996). https://doi.org/10.1007/BF01797236
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DOI: https://doi.org/10.1007/BF01797236