On the reversible counters system of Lampard

Abstract

The paper considers some properties of the reversible counters system of Lampard [1]. Lampard considers the properties of the process imbedded at the epochs when the counter receiving pulses from the ‘down’ process reaches zero. We consider here the time-dependent and stationary distributions of the original process. Their derivation gives rise to some interesting functional equations, besides being useful for studying queues with Markov-dependent inter-arrival or service times.