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Some Transient Results on the M/SM/1 Special Semi-Markov Model in Risk and Queueing Theories

Published online by Cambridge University Press:  29 August 2014

Jacques Janssen
Jacques Janssen*
Affiliation:
Université Libre de Bruxelles
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Abstract

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We consider a usual situation in risk theory for which the arrival process is a Poisson process and the claim process a positive (J — X) process inducing a semi-Markov process. The equivalent in queueing theory is the M/SM/1 model introduced for the first time by Neuts (1966).

For both models, we give an explicit expression of the probability of non-ruin on [o, t] starting with u as initial reserve and of the waiting time distribution of the last customer arrived before t. “Explicit expression” means in terms of the matrix of the aggregate claims distributions.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 11 , Issue 1 , June 1980 , pp. 41 - 51
Copyright
Copyright © International Actuarial Association 1980

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