We consider the stochastic behaviour of a Markovian bivariate process {(C(t), (N(t)), t ≥ 0} whose state-space is a semi-strip S = {0, 1} × ℕ. The intensity matrix of the process is taken to get a limit distribution Pij = limt→+∞ P{(C(t), (N(t)) = (i, j)} such that {P0j, j ∈ ℕ}, or alternatively {P1j, j ∈ ℕ}, satisfies a system of equations of ‘birth and death’ type. We show that this process has applications to queues with repeated attempts and queues with negative arrivals. We carry out an extensive analysis of the queueing process, including classification of states, stationary analysis, waiting time, busy period and number of customers served.
