A Differential Game for a Multiclass Queueing Model in the Moderate-Deviation Heavy-Traffic Regime
研究了中等偏差重流量下多类单服务器排队控制问题的微分博弈，通过自由边界问题刻画博弈并给出最优策略的半显式解，对排队论和风险控制研究者有参考价值。
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.