An ε-Nash Equilibrium with High Probability for Strategic Customers in Heavy Traffic

• 成果类型: Article
• 署名作者: Atar, Rami; Saha, Subhamay
• 署名单位: Technion Israel Institute of Technology; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Guwahati
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0820
• 发表日期: 2017
• 页码: 626-647
• 关键词: systems; Servers; queues

摘要

A multiclass queue with many servers is considered, where customers make a join-or-leave decision upon arrival based on queue length information, without knowing the state of other queues. A game theoretic formulation is proposed and analyzed, that takes advantage of a phenomenon unique to heavy traffic regimes, namely, Reiman's snaphshot principle, by which waiting times are predicted with high precision by the information available upon arrival. The payoff considered is given as a random variable, which depends on the customer's decision, accounting for waiting time in the queue and penalty for leaving. The notion of an equilibrium is only meaningful in an asymptotic framework, which is taken here to be the Halfin-Whitt heavy traffic regime. The main result is the identification of an epsilon-Nash equilibrium with probability approaching 1. On the way to proving this result, new diffusion limit results for systems with finite buffers are obtained.