Cooperative game in parallel service systems with nonexponential service times

摘要

In this paper, we employ a cooperative game to study coalition performance of a parallel service system with nonexponential service times, which is comprised of n independent parallel M/E-k/1 queues, where the service times of the coalitions are designed as a closed-form framework. For such a queueing cooperative game, we use the Erlang service time distributions to make analysis of various coalitions more feasible, and specifically, it is easy to set up a characteristic function for the coalitions under an Erlang closed-form framework. Once the characteristic function is given in the queueing cooperative game, we compute the Shapley value, the Owen value and the core whose aim is to suitably provide the cost allocation for the coalitions. Furthermore, we use numerical examples to give useful observation on the cost allocations for the coalitions through the Shapley value, the Owen value and the core.