Rate Control under Heavy Traffic with Strategic Servers

TL;DR

This paper models a large system of strategic servers managing their queues under heavy traffic, using mean-field game theory to approximate Nash equilibria and analyze system behavior.

Contribution

It introduces a mean-field game framework for strategic queue management in heavy traffic, establishing convergence of finite system equilibria to the mean-field limit.

Findings

Convergence of Nash-equilibrium values to the mean-field game solution.

Development of a Lasry-Lions type mean-field model for queueing systems.

Analysis of strategic server behavior under heavy traffic conditions.

Abstract

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.