Published online by Cambridge University Press: 09 April 2009
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
.