A note on the first emptiness time of an infinite reservoir with inputs forming a Markov chain

Abstract

Summary The first emptiness time of an infinite reservoir with unit release and discrete input forming a stationary. Markov chain is investigated. The exact distribution of the first emptiness time is derived without the use of moment generating functions. The first and second moments of this distribution are given explicity. The close relationship between the process with stationary independent input and Markov chain input is emphasized. The first moment of the area beneath the sample path up to first emptiness is computed. This area is often used as a measure of total delay in traffic flow theory.