Equilibrium Arrival Times to a Queue with Order Penalties

TL;DR

This paper analyzes how customers strategically choose arrival times to a queue considering both congestion and order penalties, providing a game-theoretic characterization of equilibrium arrival patterns.

Contribution

It introduces a novel queueing model incorporating order penalties and derives the symmetric Nash equilibrium arrival process.

Findings

Characterization of equilibrium arrival times considering order penalties.

Analysis of how order penalties influence customer arrival strategies.

Insights into queue management with strategic customer behavior.

Abstract

Suppose customers need to choose when to arrive to a congested queue with some desired service at the end, provided by a single server that operates only during a certain time interval. We study a model where the customers incur not only congestion (waiting) costs but also penalties for their index of arrival. Arriving before other customers is desirable when the value of service decreases with every admitted customer. This may be the case for example when arriving at a concert or a bus with unmarked seats or going to lunch in a busy cafeteria. We provide game theoretic analysis of such queueing systems with a given number of customers, specifically we characterize the arrival process which constitutes a symmetric Nash equilibrium.