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Probability and Computational Finance Seminar
Erhan Bayraktar
University of Michigan
Title: Rate Control under Heavy Traffic with Strategic Servers

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. In general closed form solutions of such MFG are not available and thus numerical methods are needed. We use the Markov chain approximation method to construct approximations for the solution of the MFG and establish convergence of the numerical scheme over a small time interval.

Joint work with Amarjit Budhiraja and Asaf Cohen.

Date: Monday, May 1, 2017
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Steve Shreve