On the weak convergence of departures from an infinite series of \(\cdot{}/M /1\) queues
Given a stationary point process \(A\) indexed by two-sided time, the authors construct a stationary output process obtained from passing \(A\) through an independent single-server queue whose service times are independent and identically distributed exponentials of rate \(l\). They prove an old conjecture, viz., if \(A\) is a stationary, ergodic point process of rate \(\alpha < 1\), then \(A^n\) converges in distribution to a Poisson process of rate \(\alpha\).
scientific article; zbMATH DE number 780983