Incentives for Shared Services: Multiserver Queueing Systems with Priorities

Problem definition: We study shared service whereby multiple independent service providers collaborate by pooling their resources into a shared service center (SSC). The SSC deploys an optimal priority scheduling policy for their customers collectively by accounting for their individual waiting costs and service-level requirements. We model the SSC as a multiclass $M/M/c$ queueing system subject to service-level constraints. Academic/practical relevance: Shared services are increasingly popular among firms for saving operational costs and improving service quality. One key issue in fostering collaboration is the allocation of costs among different firms. Methodology: To incentivize collaboration, we investigate cost allocation rules for the SSC by applying concepts from cooperative game theory. Results: To empower our analysis, we show that a cooperative game with polymatroid optimization can be analyzed via simple auxiliary games. By exploiting the polymatroidal structures of the multiclass queueing systems, we show when the games possess a core allocation. We explore the extent to which our results remain valid for some general cases. Managerial implications: We provide operational insights and guidelines on how to allocate costs for the SSC under the multiserver queueing context with priorities.