Abstract
This paper uses submodularity to obtain monotonicity results for a class of Markovian queueing network service rate control problems. Nonlinear costs of queueing and service are allowed. In contrast to Weber and Stidham [14], our monotonicity theorem considers arbitrary directions in the state space (not just control directions), arrival routing problems, and certain uncontrolled service rates. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions. The theory is applied to queueing networks that arise in a manufacturing system that produces to a forecast of customer demand, and also to assembly and disassembly networks.
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Veatch, M.H., Wein, L.M. Monotone control of queueing networks. Queueing Syst 12, 391–408 (1992). https://doi.org/10.1007/BF01158810
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DOI: https://doi.org/10.1007/BF01158810