Customer and cost sharing in a Jackson network

In this paper we consider a Jackson network of independent service stations. To improve upon the total expected waiting time, the stations may redistribute the total arrival rate of customers over all queues. We investigate this situation by means of arrival rate games. These are cooperative TU cost games in which the stations are the players and the total cost of a coalition is linear in the total expected waiting time. We show that these games are totally balanced; cooperation is beneficial to all stations. Further, we provide a tailor-made cost allocation rule that belongs to the core of the game