期刊
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
卷 130, 期 11, 页码 6733-6756出版社
ELSEVIER
DOI: 10.1016/j.spa.2020.06.008
关键词
Controlled jump diffusions; ergodic Hamilton-Jacobi-Bellman (HJB) equation; Stable Markov optimal control; Pathwise optimality; Approximate HJB equation; Spatial truncation
资金
- Army Research Office [W911NF17-1-001]
- National Science Foundation [DMS-1715210, CMMI-1635410, DMS-1715875]
- Office of Naval Research [N00014-16-1-2956]
We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of Arapostathis et al. (2019) 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 characterizations 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. (C) 2020 Elsevier B.V. All rights reserved.
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