Strategic timing of arrivals to a queueing system with scheduled customers

TL;DR

This paper analyzes a queueing system with scheduled and strategic walk-in customers, deriving equilibrium arrival patterns and optimizing appointment schedules to improve system performance using evolutionary algorithms.

Contribution

It introduces a model for strategic customer arrivals in scheduled queueing systems and applies Differential Evolution for schedule optimization, a novel approach in this context.

Findings

Equilibrium arrival distributions are characterized analytically.

Allowing early arrivals impacts waiting times and server idle time.

Optimized schedules outperform traditional fixed appointment intervals.

Abstract

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.