Cost sharing of cooperating queues in a Jackson network

Abstract

We consider networks of queues in which the independent operators of individual queues may cooperate to reduce the amount of waiting. More specifically, we focus on Jackson 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 known from the literature how the operators should share the available service capacity to minimize the long run total cost. This paper deals with the question whether or not (the operators of) the individual queues will indeed cooperate in this way, and if so, how they could share the cost in the new situation such that each operator never pays more than his own cost without cooperation. For the particular case of a tandem network with two or three nodes it is known from previous work that cooperation is indeed beneficial, but for larger tandem networks and for general Jackson networks this question was still open. The main result of this paper gives for any Jackson network an explicit cost allocation that is beneficial for all operators. The approach we use also works for other cost functions, such as the server utilization.