For multiclass many-server queues with alternating service interruptions and renewal arrivals in the Halfin-Whitt regime, the paper proves that the optimal diffusion-scale costs converge to the optimal costs of a limiting compound-Poisson jump-diffusion control problem.
Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis
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abstract
We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of [SIAM J. Control Optim. 57 (2019), no. 2, 1516-1540] to running costs that are not near-monotone. This generality is needed in applications such as optimal scheduling of large-scale parallel server networks. We provide a full characterization of optimality via the Hamilton-Jacobi-Bellman (HJB) equation, for which we additionally exhibit regularity of solutions under mild hypotheses. In addition, we show that optimal stationary Markov controls are a.s. pathwise optimal. Lastly, we show that one can fix a stable control outside a compact set and obtain near-optimal solutions by solving the HJB on a sufficiently large bounded domain. This is useful for constructing asymptotically optimal scheduling policies for multiclass parallel server networks.
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Optimal scheduling of critically loaded multiclass GI/M/n+M queues in an alternating renewal environment
For multiclass many-server queues with alternating service interruptions and renewal arrivals in the Halfin-Whitt regime, the paper proves that the optimal diffusion-scale costs converge to the optimal costs of a limiting compound-Poisson jump-diffusion control problem.