The Power of Letting Go: Scheduling, Rejections and Controlled Abandonments in Multi-Server Queues

Abstract: Long waiting times in service and healthcare systems reduce customer satisfaction, increase abandonment rates, and harm provider profitability and reputation. To address these issues, service providers often set class-specific service-level (SL) requirements. We study a multi-server, multi-class scheduling problem in which the operator can either reject some arriving customers or initiate controlled abandonments to minimize total operational costs while meeting SL requirements. Using a fluid approximation, we develop an asymptotically optimal index-based policy for scheduling classes that simultaneously optimizes rejection and controlled abandonment decisions. We find that under optimal capacity allocation, each class may operate in a different queue regime based on its characteristics, following either an Erlang-B or an Erlang-A queue model. When class-specific SL requirements are included, the class indices are adjusted, impacting prioritization. Under the adjusted policy, priority is no longer strict—some classes may not receive all the capacity they need, allowing remaining capacity to be allocated to classes with lower indices. Implementation of this policy in the original stochastic system results in a two-level randomized index rule. Simulation experiments confirm the effectiveness of our proposed policies.