On constrained optimization of the Klimov network and related Markov decision processes

A constrained version of the server allocation problem for the Klimov network is solved, and it is established that the optimal constrained schedule is obtained by randomizing between two fixed-priority schemes. This generalizes the work of P. Nain and K.W. Ross (1986) in the context of the competing queue problem and also covers the discounted cost case. In order to establish these results, a general framework is developed for optimization under a single constraint in the presence of indexlike policies. This methodology is in principle of wider applicability.<
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