Strategic Queues with Priority Classes

2025-02-09

AI Summary

This paper investigates strategic behavior of two customer classes (Class A has priority over Class B) in an M/M/1 queue: customers decide whether to join, whether to renege after joining, and when to renege. Using game-theoretic analysis and continuous-time Markov chain modeling, we characterize the structure of Nash equilibrium strategies and compare socially optimal solutions with and without priority constraints. Our key contribution is the first joint modeling—within a priority queueing framework—of strategic joining decisions and dynamic reneging behavior. Results show that priority significantly exacerbates equilibrium efficiency loss (i.e., price of anarchy). The unconstrained social optimum becomes infeasible under priority rules, necessitating a trade-off between fairness and system efficiency. Moreover, we quantify the structural impact of priority on both equilibrium performance metrics and the feasible region of socially optimal policies.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Search and Optimization: Evaluation and Analysis

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We consider a strategic M/M/1 queueing model under a first-come-first-served regime, where customers are split into two classes and class $A$ has priority over class $B$. Customers can decide whether to join the queue or balk, and, in case they have joined the queue, whether and when to renege. We study the equilibrium strategies and compare the equilibrium outcome and the social optimum in the two cases where the social optimum is or is not constrained by priority.

Problem

• Strategic M/M/1 queue model
• Priority classes A and B
• Equilibrium vs social optimum

Innovation

• Strategic M/M/1 queueing model
• Priority classes A and B
• Equilibrium strategies analysis