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In this paper, we study optimal control problems for multiclass GI/M/n+Mqueues in an alternating renewal (up-down) random environment in theHalfin-Whitt regime. Assuming that the downtimes are asymptotically negligibleand only the service processes are affected, we show that the limits of thediffusion-scaled state processes under non-anticipative, preemptive,work-conserving scheduling policies, are controlled jump diffusions driven by acompound Poisson jump process. We establish the asymptotic optimality of theinfinite-horizon discounted and long-run average (ergodic) problems for thequeueing dynamics.  Since the process counting the number of customers in each class is notMarkov, the usual martingale arguments for convergence of mean empiricalmeasures cannot be applied. We surmount this obstacle by demonstrating theconvergence of the generators of an augmented Markovian model whichincorporates the age processes of the renewal interarrival times and downtimes.We also establish long-run average moment bounds of the diffusion-scaledqueueing processes under some (modified) priority scheduling policies. This isaccomplished via Foster-Lyapunov equations for the augmented Markovian model.

Optimal scheduling of critically loaded multiclass GI/M/n+M queues in an alternating renewal environment