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2 results

  • A storage process by semi-Markov input

  • Lajos Takács
  • Journal:
    Advances in Applied Probability / Volume 7 / Issue 4 / December 1975
    Published online by Cambridge University Press:
    01 July 2016, pp. 830-844
    Print publication:
    December 1975

  • A sequence of random variables η0, η1, …, ηn, … is defined by the recurrence formula ηn = max (ηn–1 + ξn, 0) where η0 is a discrete random variable taking on non-negative integers only and ξ1, ξ2, … ξn, … is a semi-Markov sequence of discrete random variables taking on integers only. Define Δ as the smallest n = 1, 2, … for which ηn = 0. The random variable ηn can be interpreted as the content of a dam at time t = n(n = 0, 1, 2, …) and Δ as the time of first emptiness. This paper deals with the determination of the distributions of ηn and Δ by using the method of matrix factorisation.