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4395 results in Advances in Applied Probability

Page 182 of 220

  • A rate-conservative principle for stationary piecewise Markov processes

  • Tomasz Rolski
  • Journal:
    Advances in Applied Probability / Volume 10 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    01 July 2016, pp. 392-410
    Print publication:
    June 1978

  • A stationary process yt, t ∈ R1 is considered which is Markov between points of changeover from a stationary point process, and at these points it changes over according to a distribution dependent only on the value of yt just before the change is analysed. An explicit form of a rate-conservative principle is stated, and its relationship with formulae relating the distribution of the process at an instant t and the distribution at a point of changeover is shown. The theory is applied to discrete state processes and to processes which are generalizations of the Takács processes, and is also applied in the theory of G/M/l and G/G/k queues to obtain relations between distributions of a process and some process imbedded in it.

  • Invariant problems in discounted dynamic programming

  • David Assaf
  • Journal:
    Advances in Applied Probability / Volume 10 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    01 July 2016, pp. 472-490
    Print publication:
    June 1978

  • Discounted dynamic programming problems whose transition mechanism depends only on the action taken and does not depend on the current state are considered. A value determination operation and method of obtaining optimal policies for the case of finite action space (and arbitrary state space) are presented.

    The solution of other problems is reduced to this special case by a suitable transformation. Results are illustrated by examples.

Page 182 of 220