Abstract

Consider a system of two queues in parallel, one of which is M/M/1 single-server infinite capacity queue, and the other M/M(N)/K batch service queue,where batch size N ≧ 2 and K ＜ ∞. In the network, a stream of Poisson arrivals choose which queue to join, after observing the current state of the system, and so as to minimize their own expected delay. We show that a user optimal policy exists, and that it possesses various monotonicity properties. In addition, we give examples where state-dependent routing mitigates the Downs-Thomson effect observed under probabilistic routing.

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