Using simulation to study service-rate controls to stabilize performance in a single-server queue with time-varying arrival rate

Simulation is used to evaluate the performance of alternative service-rate controls designed to stabilize performance in a queue with time-varying arrival rate, service in order of arrival and unlimited waiting space. Both Markovian and non-Markovian models are considered. Customer service requirements are specified separately from the service rate, which is subject to control. New versions of the inverse method exploiting tables constructed outside the simulation are developed to efficiently generate both the arrival times and service times. The simulation experiments show that a rate-matching service-rate control successfully stabilizes the expected queue length, but not the expected waiting time, while a new square-root servicerate control, based on a assuming that a pointwise-stationary approximation is appropriate, successfully stabilizes the expected waiting time when the arrival rate changes slowly compared to the expected service time.

1 Introduction

In this paper we study alternative service-rate controls to stabilize performance in a single-server queue with time-varying arrival rate and independent and identically distributed (i.i.d.) service requirements specified separately from the service rate actually provided. Our study parallels Liu and Whitt (2012), He, Liu, and Whitt (2015) and earlier papers cited there that develop time-varying staffing levels (number of servers) to stabilize performance in multi-server queues with flexible staffing.