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Value iteration and optimization of multiclass queueing networks. (English) Zbl 0949.90020
Summary: This paper considers the scheduling problem for multiclass queueing networks, and optimization of Markov decision processes. It is shown that the value iteration algorithm may perform poorly when the algorithm is not initialized properly. The most typical case where the initial value function is taken to be zero may be a particularly bad choice. In contrast, if the value iteration algorithm is initialized with a stochastic Lyapunov function, then the following hold: (i) a stochastic Lyapunov function exists for each intermediate policy, and hence each policy is regular (a strong stability condition), (ii) intermediate costs converge to the optimal cost, and (iii) any limiting policy is average cost optimal. It is argued that a natural choice for the initial value function is the value function for the associated deterministic control problem based upon a fluid model, or the approximate solution to Poisson’s equation obtained from the LP of P. R. Kumar and S. P. Meyn [IEEE Trans. Autom. Control 40, 251-260 (1995)]. Numerical studies show that either choice may lead to fast convergence to an optimal policy.
MSC:
90B22Queues and service (optimization)
60K25Queueing theory
93C95Applications of control theory
90B10Network models, deterministic (optimization)
90C40Markov and semi-Markov decision processes
90C39Dynamic programming