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Dynamic programming in constrained Markov decision

Piunovskiy A. B.

Control and Cybernetics

2006

Vol. 35, no 3

645-660

We consider a discounted Markov Decision Process (MDP) supplemented with the requirement that another discounted loss must not exceed a specified value, almost surely. We show that he problem can be reformulated as a standard MDP and solved using the Dynamic Programming approach. An example on a controlled queue is presented. In the last section, we briefly reinforce the connection of the Dynamic Programming approach to another close problem statement and present the corresponding example. Several other types of constraints are discussed, as well.

On global maxima in multiphase queues

Minkevicius S., Steisunas S.

Control and Cybernetics

2005

Vol. 34, no 2

575-588

The target of this research in the queueing theory is to prove the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems. In this paper, the LIL for global maxima is proved in the phases of a queueing system studied for an important probability characteristic of the system (total waiting time of a customer and waiting time of a customer).