A Differential Game for a Multiclass Queueing Model in the Moderate-Deviation Heavy-Traffic Regime

作者：Atar Rami^*; Cohen Asaf

来源：Mathematics of Operations Research, 2016, 41(4): 1354-1380.

DOI：10.1287/moor.2016.0780

• multiclass single-server queue
• moderate deviations
• heavy traffic
• risk-sensitive cost
• the Harrison-Taksar free boundary problem

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.

• 出版日期2016-11