Optimal Policy in Single-Server Multi-Class Queuing Systems with Abandonment

Abstract

We study a multi-class queuing system with a single server and customer abandonment. We fully characterize the structure of the server's optimal scheduling policy that minimizes the long-run average customer abandonment cost. We show that the optimal service policy is a static priority policy. We derive sufficient conditions under which the so-called b.mu-rule is optimal. Under the b.mu-rule, it is optimal to give priority to the customer type that has higher service rate (mu) and higher abandonment cost (b), i.e., higher index b.mu.

Keywords: Queuing System, Server Scheduling, Abandonment, Markov Decision Process, Infomercial Call Centers

JEL Classification: C44