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February 2019 Rate control under heavy traffic with strategic servers
Erhan Bayraktar, Amarjit Budhiraja, Asaf Cohen
Ann. Appl. Probab. 29(1): 1-35 (February 2019). DOI: 10.1214/17-AAP1349

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.

Citation

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Erhan Bayraktar. Amarjit Budhiraja. Asaf Cohen. "Rate control under heavy traffic with strategic servers." Ann. Appl. Probab. 29 (1) 1 - 35, February 2019. https://doi.org/10.1214/17-AAP1349

Information

Received: 1 February 2017; Revised: 1 August 2017; Published: February 2019
First available in Project Euclid: 5 December 2018

zbMATH: 07039120
MathSciNet: MR3909999
Digital Object Identifier: 10.1214/17-AAP1349

Subjects:

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

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 1 • February 2019
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