🤖 AI Summary
Traditional evolutionary game analysis relies on closed-form payoff expressions derived from queueing systems, which are infeasible in complex scenarios. This work proposes a Discrete-Event Population Update (DEPU) framework that directly embeds a single discrete-event simulation into the evolutionary dynamics, enabling efficient analysis of strategy evolution in systems lacking closed-form solutions without resorting to nested simulations. The framework encompasses two implementation mechanisms: Discrete-Event Replicator Dynamics (DERD) and Discrete-Event Moran Replacement (DEMR). Evaluated on a multi-server jockeying queue model, DEPU achieves computational speedups of an order of magnitude over conventional methods while preserving comparable accuracy, substantially enhancing the feasibility and efficiency of large-scale parameter sweeps.
📝 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.