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1 results

  • Infinite dams with discrete additive inputs

  • M. S. Ali Khan
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 170-180
    Print publication:
    March 1977

  • This paper considers an infinite dam fed by a discrete input Xt during the time interval [t, t + 1), t = 0, 1, 2, ···. At time t – 0 there is an output Yt = min(Zt–1, + Xt–1, r) from the dam leaving behind the amount Zt = max(0, Zt–1, + Xt–1, r). The probability Pr(Zt = i), i = 0, 1, 2, ··· is discussed under the strict assumption that r > 1 and the given initial condition that Z0 = u, u = 1, 2, ···. The generating function technique has been used throughout the paper.