Abstract
For the M/M/1 queue in the presence of catastrophes the transition probabilities, densities of the busy period and of the catastrophe waiting time are determined. A heavy-traffic approximation to this discrete model is then derived. This is seen to be equivalent to a Wiener process subject to randomly occurring jumps for which some analytical results are obtained. The goodness of the approximation is discussed by comparing the closed-form solutions obtained for the continuous process with those obtained for the M/M/1 catastrophized queue.
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Di Crescenzo, A., Giorno, V., Nobile, A. et al. On the M/M/1 Queue with Catastrophes and Its Continuous Approximation. Queueing Systems 43, 329–347 (2003). https://doi.org/10.1023/A:1023261830362
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DOI: https://doi.org/10.1023/A:1023261830362