How to share the cost of cooperating queues in a tandem network?

Abstract

We consider networks of queues in which the different operators of individual queues may cooperate to reduce the amount of waiting. More specifically, as a first step we focus on Jackson tandem networks in which the total capacity of the servers can be redistributed over all queues in any desired way. If we associate a cost to waiting that is linear in the queue lengths, it is not difficult to see that the long run total cost is minimized when the operators equally share the available service capacity. The main question we try to answer is whether or not (the operators of) the individual queues will indeed cooperate in this way, and if so, how they will share the cost in the new situation. We find answers to this question for two- and three-node networks.

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