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

Jacques Janssen

ASTIN Bulletin, 1980, vol. 11, issue 1, 41-51

Abstract: 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.

Date: 1980
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