In this paper, we study optimal control problems for multiclass \(GI/M/n+M\) queues in an alternating renewal (up–down) random environment in the Halfin–Whitt regime. Assuming that the downtimes are asymptotically negligible and only the service processes are affected, we show that the limits of the diffusion-scaled state processes under non-anticipative, preemptive, work-conserving scheduling policies, are controlled jump diffusions driven by a compound Poisson jump process. We establish the asymptotic optimality of the infinite-horizon discounted and long-run average (ergodic) problems for the queueing dynamics. Since the process counting the number of customers in each class is not Markov, the usual martingale arguments for convergence of mean empirical measures cannot be applied. We surmount this obstacle by demonstrating the convergence of the generators of an augmented Markovian model which incorporates the age processes of the renewal interarrival times and downtimes. We also establish long-run average moment bounds of the diffusion-scaled queueing processes under some (modified) priority scheduling policies. This is accomplished via Foster–Lyapunov equations for the augmented Markovian model.

在本文中，我们研究了多类\（GI / M / n + M \）的最优控制问题在Halfin-Whitt政权的交替续约（上下）随机环境中排队。假设停机时间可以渐近地忽略不计，并且仅影响服务过程，我们表明在非预期，先占，节省工作的调度策略下，扩散规模状态过程的限制是由复合泊松跳跃驱动的受控跳跃扩散处理。我们为排队动力学建立了无限水平折现和长期平均（遍历）问题的渐近最优性。由于计算每个类别中的客户数量的过程不是马尔可夫，因此无法应用通常的关于均值经验测度趋同的arguments论点。我们通过展示增强的马尔可夫模型的生成器的收敛性克服了这一障碍，该模型融合了更新的到达间隔时间和停机时间的年龄过程。我们还建立了一些（修改的）优先级调度策略下的扩散规模排队过程的长期平均矩边界。这是通过Foster–Lyapunov方程来完成的，用于增强的马尔可夫模型。