The study of scheduling problems has a long history in the academic literature.  However, many classic models used to study scheduling problems do not incorporate customer impatience.  Furthermore, many of the ones that do assume the time a customer is willing to wait for service is exponentially distributed.  The issue is that that assumption can lead to poor scheduling decisions.

Our objective is to study the interplay between customer impatience and scheduling decisions when managing heterogeneous customer classes.  We do this in the context of a many server queue, and develop results in as general a framework as possible.  First, we use the solution of an approximating diffusion control problem to propose and numerically evaluate a scheduling policy.  Under certain conditions, we see a novel “U-shape” structure emerge.  Second, we consider how to prove an asymptotic optimality result.  For this, the first step is to understand fluid-scale behavior.  That leads to an interesting closed-form non-linear relationship between the queue-length and the server effort allocation.

**This is based on separate joint works, one with Ramandeep Randhawa and Jeunghyun Kim (downloadable from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2722085), and one with Amber Puha (manuscript in preparation).