A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime

Rami Atar; Asaf Cohen

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arXiv · 1412.6773

A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime

Rami Atar·Asaf Cohen

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Abstract

We study a differential game that governs the moderate-deviation heavy-traffic asymptotics of a multiclass single-server queueing control problem with a risk-sensitive cost. We consider a cost set on a finite but sufficiently large time horizon, and show that this formulation leads to stationary feedback policies for the game. Several aspects of the game are explored, including its characterization via a (one-dimensional) free boundary problem, the semi-explicit solution of an optimal strategy, and the specification of a saddle point. We emphasize the analogy to the well-known Harrison-Taksar free boundary problem which plays a similar role in the diffusion-scale heavy-traffic literature.

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Rami Atar, Asaf Cohen. 2014-12-21. A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime. https://arxiv.org/abs/1412.6773

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