A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime
Probability
2018-05-02 v1
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.
Keywords
Cite
@article{arxiv.1412.6773,
title = {A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime},
author = {Rami Atar and Asaf Cohen},
journal= {arXiv preprint arXiv:1412.6773},
year = {2018}
}