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1 results

  • The basic equations for a supplemented GSMP and its applications to queues

  • Masakiyo Miyazawa, Genji Yamazaki
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue 3 / September 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 565-578
    Print publication:
    September 1988

  • A supplemented GSMP (generalized semi-Markov process) is a useful stochastic process for discussing fairly general queues including queueing networks. Although much work has been done on its insensitivity property, there are only a few papers on its general properties. This paper considers a supplemented GSMP in a general setting. Our main concern is with a system of Laplace–Stieltjes transforms of the steady state equations called the basic equations. The basic equations are derived directly under the stationary condition. It is shown that these basic equations with some other conditions characterize the stationary distribution. We mention how to get a solution to the basic equations when the solution is partially known or inferred. Their applications to queues are discussed.