RATE CONTROL UNDER HEAVY TRAFFIC WITH STRATEGIC SERVERS

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Budhiraja, Amarjit; Cohen, Asaf
• 署名单位: University of Michigan System; University of Michigan; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of Haifa
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1349
• 发表日期: 2019
• 页码: 1-35
• 关键词: mean-field games; semi-lagrangian scheme; differential-equations; CONVERGENCE; systems; propagation; THEOREM; limit

摘要

We consider a large queueing system that consists of many strategic servers that are weakly interacting. Each server processes jobs from its unique critically loaded buffer and controls the rate of arrivals and departures associated with its queue to minimize its expected cost. The rates and the cost functions in addition to depending on the control action, can depend, in a symmetric fashion, on the size of the individual queue and the empirical measure of the states of all queues in the system. In order to determine an approximate Nash equilibrium for this finite player game, we construct a Lasry-Lions-type mean-field game (MFG) for certain reflected diffusions that governs the limiting behavior. Under conditions, we establish the convergence of the Nash-equilibrium value for the finite size queuing system to the value of the MFG.