On relation of two processes with independent increments applied in queueing systems

Abstract

In the paper, by using two processes ?t and ? (t), t ? 0 with independent increments, one of which is without negative overshoots and the second one is homogeneous in time, we study a homogeneous Markov process ?t, t ? 0, and we find the Laplace transform of the generating function of transitional probabilities of the process ?t, t ? 0.