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1 results

  • A finite dam with variable release rate

  • G. F. Yeo
  • Journal:
    Journal of Applied Probability / Volume 12 / Issue 1 / March 1975
    Published online by Cambridge University Press:
    14 July 2016, pp. 205-211
    Print publication:
    March 1975

  • This note considers a finite dam fed by independently and identically distributed (i.i.d.) inputs, being either (i) of at least size β (> 0) or (ii) negative exponentially distributed, occurring in a Poisson process. The instantaneous release rate may be a function r(·) of the content; additional and numerical results are given for the special case where r(x) = µxα (0 ≦ α<∞, 0 < µ <∞) is proportional to the αth power of the content. The basic method used in [7] for the special case r(x) = µx for obtaining the distribution of the number of steps and of the time to first overflowing is shown to carry over almost completely in case (i), but only partially so in case (ii).