Artalejo Rodríguez, Jesús ManuelGómez-Corral, Antonio2023-06-202023-06-2019980171-646810.1007/BF01545523https://hdl.handle.net/20.500.14352/57480The authors are grateful to the referees for helpful comments. This research was supported by the DGICYT under grant PB95-0416.We consider the stochastic behaviour of a Markovian bivariate process {(C(t), N(t)), t greater than or equal to 0} whose state-space is a semi-strip S = {0, 1} x N. The intensity matrix of the process is taken to get a limit distribution P-ij = lim(t-->+infinity) P{(C(t), N(t)) = (i, j)} such that {P-0j, j is an element of N}, or alternatively {P-lj, j is an element of 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.engjournal articlehttp://www.springerlink.com/content/j3436182445g4186/http://www.springerlink.com/restricted access519.8Birth and death processesConvolufive equationsNegative arrivalsQueues with repeated attemptsWaiting timesInvestigación operativa (Matemáticas)1207 Investigación Operativa