Summary: Statistics & Probability Letters 10 (1990) 427-430
THE `BIRTH-AND-ASSASSINATION' PROCESS
David ALDOUS *
The Unrversity of California, Berkeley, CA, USA
William B. KREBS
Florrda State University, Talahnssee, FL, USA
Received January 1989
Revised September 1989
Abstract: A new variant of a branching process is introduced, with sufficient conditions for it to persist and to die out. The
model is applied to discuss the asymptotic stability of a new type of queuing process.
Keywords: Branching processes, multi-server queues.
Consider a system of particles evolving according to the following rules:
(a) Particles j have random (i.i.d.) lifetimes K,;
(b) During its lifetime, a particle has offspring at the times of a Poisson (rate h) process.
This is a well-studied type of branching process. The populations in successive generations behave as
the simple Galton-Walton branching process with mean offspring equal to hEK, and so the process is
subcritical or supercritical according as this mean is less than or greater than 1.
We study a variation in which the `clock' which counts down time until a particle's death does not start