Strategic timing of arrivals to a queueing system with scheduled customers

This paper examines a single-server queueing system that serves both scheduled and strategic walk-in customers. The service discipline follows a first-come, first-served policy, with scheduled customers granted non-preemptive priority. Each walk-in customer strategically chooses their arrival time to minimize their expected waiting time, taking into account the reservation schedule and the decisions of other walk-in customers. We derive the Nash equilibrium arrival distribution for walk-in customers and investigate the implications of allowing early arrivals. By analysing various appointment schedules, we assess their effects on equilibrium arrival patterns, waiting times, and server idle time. Additionally, we develop an optimisation approach using the Differential Evolution algorithm, which demonstrates measurable improvements in system performance compared to traditional equally-spaced scheduling.