Optimal control of multiclass parallel service systems with and without state information

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 a bipartite graph, called the routing (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 the shortest queue or the randomized round-robin policy can be shown to be optimal -in the sense of optimizing the departure and loss counting processes. Thus, our results apply to systems with control procedures which may or may not use state (queue length) information. A counter example is shown for systems described by digraphs with a cyclic structure