Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6894425 | European Journal of Operational Research | 2018 | 8 Pages |
Abstract
We consider a tandem network of queues with a Poisson arrival process to the first queue. Service times are assumed to be exponential. In cases where they are not, we additionally assume a processor sharing service discipline in all servers. Consecutive servers may cooperate by pooling resources which leads to the formation of a single combined server that satisfies the aggregated service demands with a greater service rate. On this basis we define a cooperative game with transferable utility, where the cost of a coalition is the steady-state mean total number of customers in the system formed by its members. We show that the game is subadditive, leading to full cooperation being socially optimal. We then show the non-emptiness of the core, despite the characteristic function being neither monotone, nor concave. Finally, we derive several well-known solution concepts, including the Shapley value, the Banzhaf, value and the nucleolus, for the case where servers have equal mean service demands. In particular, we show that all three values coincide in this case.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Dan Bendel, Moshe Haviv,