Birth-Death Processes With Catastrophes
by
Alan Krinik
California State Polytechnic University, Pomona

For processes defined on the countable state space, 0, 1, 2, 3, …, the problem of finding transient probability functions of irreducible birth-death processes with catastrophes is reduced to determining the transient probability function of a related, irreducible, birth-death process on state space 0, 1, 2, 3, …. This connection comes from a fundamental result on dual processes. Our reduction also holds for processes having multiple types of catastrophes. The correspondence is illustrated for the classical queueing systems M/M/1 and M/M/2 with catastrophes.

Date received: August 31, 2003