Translating Empirical State-Dependent Service Times Into Queueing Models

Recent empirical studies suggest that human behavior in queues causes workload-dependent service times. We investigate the translation of empirical service times into state-dependent queueing models. To this end, we identify two types of state-dependent models, static and dynamic, and two types of corresponding behavioral mechanisms. For example, we view customer early task initiation as a static mechanism and social speedup pressure as a dynamic mechanism. For each model type, we discuss behavioral mechanisms consistent with the model assumptions and indicate how empirical service times can be translated into model input parameters. We illustrate how translating service times into dynamic models can result in invalid service rates, which provides evidence against dynamic mechanisms. For dynamic models, we find that mean service times are in general not the inverse of service rates, the directional change in service rates is not always the opposite of the directional change in mean service times, and workload measurement timing can drastically impact mean service time patterns. We provide closed-form equations to convert service times into service rates and vice versa, and find conditions under which monotonic mean service times imply monotonic service rates and vice versa. Our results provide guidelines for researchers to select and specify an appropriate state-dependent queueing model from service time data, and expand the scope of previously published analytical results.