期刊
QUEUEING SYSTEMS
卷 43, 期 4, 页码 329-347出版社
SPRINGER
DOI: 10.1023/A:1023261830362
关键词
busy period; catastrophe waiting time; Wiener process; first-passage time
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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