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Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals

Artalejo, Jesús R. and Gómez-Corral, Antonio (1998) Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals. Or Spektrum, 20 (1). pp. 5-14. ISSN 0171-6468

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Abstract

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.

Item Type:Article
Additional Information:The authors are grateful to the referees for helpful comments. This research was supported by the DGICYT under grant PB95-0416.
Uncontrolled Keywords:Birth and death processes; Convolufive equations; Negative arrivals; Queues with repeated attempts; Waiting times
Subjects:Sciences > Mathematics > Operations research
ID Code:16144
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