AI Insight
This paper introduces Discrete Event Population Updates (DEPU), a new computational method that combines discrete event simulation with evolutionary game theory to analyze strategic behavior in complex queueing systems. The approach eliminates the need for closed-form mathematical expressions by coupling a single long simulation run directly to evolutionary population dynamics, making it applicable to a much wider range of queueing systems. When tested on a multi-server jockeying model, DEPU achieved comparable precision tens of times faster than traditional nested simulation methods.
Why it matters
This method enables researchers to analyze strategic behavior in realistic queueing systems that were previously too complex to study, such as hospital emergency departments, call centers, and transportation networks. The computational efficiency gains make systematic exploration of different system parameters practical, potentially improving the design of service systems where customer behavior affects overall performance.
Understand the Science
Abstract: Strategic behaviour in queueing systems has been studied extensively in the behavioural queueing literature, but almost exclusively for systems that admit closed-form expressions for the cost or utility experienced by a strategic user. Evolutionary game theory offers a mature framework for analysing populations whose individual payoffs depend on the composition of the population itself, and would in principle apply to a much wider class of queueing systems; its application has, however, been constrained by the same closed-form requirement. We introduce Discrete Event Population Updates (DEPU), a general algorithmic framework that couples a single long run of a discrete event simulation (DES) directly to an evolutionary population update rule, removing that constraint. We present two implementations: Discrete Event Replicator Dynamics (DERD), which follows an Euler discretisation of the replicator dynamics equation, and Discrete Event Moran Replacement (DEMR), which maintains a finite population updated via Moran-style copying events. Both are applied to a multi-server jockeying model for which no closed-form fitness expressions are available. On the jockeying model considered, DEPU reaches comparable precision tens of times faster than the standard practice of nesting short simulations inside an outer evolutionary loop, and because each operating point then costs only a single simulation run it also makes systematic parameter sweeps tractable. This brings the toolkit of evolutionary dynamics within reach of any system a modeller can build in a discrete event simulator.