Incentives for Shared Services: Multi-Server Queueing Systems with Priorities

Abstract

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 multi-class 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 SSC under the multi-server queueing context with priorities.

Keywords: resource pooling, shared service, multiclass queueing systems, priority rules, polymatroid, cooperative game theory