In this paper, we develop a general framework to analyze the influence of system load on service times in queueing systems. Our framework unifies previous results and ties them to possible future studies to help empirical and analytical researchers to investigate and model the ways in which load impacts service times. We identify three load characteristics: changeover, instantaneous load, and extended load. The load characteristics induce behaviors, or mechanisms, in at least one of the system components: the server, the network, and the customer. A mechanism influences the service-time determinants: the work content, service speed, or in-process delay. We identify and define mechanisms that cause service times to change with load and use the framework to categorize them. We argue that an understanding of the relationship between load and service times can come about only by understanding the underlying mechanisms.

Introduction

An understanding of queueing systems is critical to the management of service, production, and supply chain systems. Queueing theory informs the planning of customer service, capacity, processing times, flow times, and delivery schedules. The queueing literature has clearly documented the influence of service times on system load. What is less well understood is the influence of load on service times. Consistent with the notion of service time in the empirical research that we review, we use “service time” in this paper to mean the time spent inside the process boundaries and “processing time” to mean the part of that time spent serving the customer. Most queueing theory models assume that service times are exogenous. That is, they assume service times are independent of the system state. Recent empirical studies have made it clear that service times are endogenous: They depend on load. The direction and magnitude of the relationship are not clear, however, and the underlying mechanisms vary across applications. The following quotes exemplify a sample of findings that at first glance appear contradictory, where denotes service times increase with load,  denotes service times decrease with load, and sequences of these symbols denote non-monotone patterns