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In this paper, we study the nth-bias optimality problem for finite continuous-time Markov decision processes (MDPs) with a multichain structure. We first provide nth-bias difference formulas for two policies and present some interesting characterizations of an nth-bias optimal policy by using these difference formulas. Then, we prove the existence of an nth-bias optimal policy by using nth-bias optimal...
Semi-markov decision processes (SMDP) are continuous time generalizations of discrete time Markov Decision Process. A number of value and policy iteration algorithms have been developed for the solution of SMDP problem. But solving SMDP problem requires prior knowledge of the deterministic kernels, and suffers from the curse of dimensionality. In this paper, we present the steepest descent direction...
In the previous works, we have shown that policy iteration algorithms in performance optimization follow directly from performance difference formulas. In this paper, we show that based on this idea, we can develop policy iteration type of optimization algorithms for "policies" that depend on system parameters. We illustrate this idea with a load-dependent closed Jackson network, where the...
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