The Annals of Applied Probability

Rate control under heavy traffic with strategic servers

Erhan Bayraktar, Amarjit Budhiraja, and Asaf Cohen

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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.

Article information

Source
Ann. Appl. Probab., Volume 29, Number 1 (2019), 1-35.

Dates
Received: February 2017
Revised: August 2017
First available in Project Euclid: 5 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1544000424

Digital Object Identifier
doi:10.1214/17-AAP1349

Mathematical Reviews number (MathSciNet)
MR3909999

Zentralblatt MATH identifier
07039120

Subjects
Primary: Heavy traffic limits queuing systems strategic servers mean-field games rate control reflected diffusions

Keywords
60K25 91A13 60K35 93E20 60H30 60F17

Citation

Bayraktar, Erhan; Budhiraja, Amarjit; Cohen, Asaf. Rate control under heavy traffic with strategic servers. Ann. Appl. Probab. 29 (2019), no. 1, 1--35. doi:10.1214/17-AAP1349. https://projecteuclid.org/euclid.aoap/1544000424


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