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On the distribution of the time to first emptiness of a store with stochastic input

Published online by Cambridge University Press:  09 April 2009

A. M. Hasofer
A. M. Hasofer
Affiliation:
University of Tasmania, Australia.
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Kendall [4] has given for the distribution of the time to first emptiness in a store with an input process which is homogeneous and has non-negative independent increments and an output of one unit per unit time the formula . In this formula, z is the initial content of the store, g(t, z) is the density function of the time to first emptiness τ(z), defined by and k(t, x) is the density function of the input process ξ(t), defined by .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 4 , November 1964 , pp. 506 - 517
Copyright
Copyright © Australian Mathematical Society 1964

References

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