Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs

Abstract

For queueing systems with multiple customer types differing in service time distributions and costs for waiting, it is known that giving priority to one type over others minimizes the long-run average waiting costs when waiting is penalized linearly in time. However, when waiting costs are nonlinear, which is typically a more reasonable depiction of reality, it is not clear whether policies that ignore the type information such as the first-come-first-serve policy (FCFS) should be replaced with type-based priority policies. To shed some light on to this problem, we study a single-server queueing system with two types of customers under static queueing policies that use information on customers’ types and order of arrival. Our main theorem ranks the type-based priority policies and FCFS according to their long-run average waiting costs under nonlinear cost functions. We then apply this result to polynomial cost functions and generate insights into when prioritization is advantageous. For example, we find that when customers are similar in terms of their service time distributions, then the parameter region where FCFS is more preferable over type-based priority policies under quadratic costs increases with traffic intensity. We also conduct a numerical study to compare the best static policy with a well-known dynamic policy that requires information on the current waiting times of customers. We find that the best static policy performs comparably with (sometimes even better than) this dynamic policy except when the traffic is heavy and it is not clear which type should receive priority.