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A MARKOV RENEWAL APPROACH TO THE ASYMPTOTIC DECAY OF THE TAIL PROBABILITIES IN RISK AND QUEUING PROCESSES

Published online by Cambridge University Press:  21 May 2002

Masakiyo Miyazawa
Masakiyo Miyazawa
Affiliation:
Science University of Tokyo, Noda, Chiba 278-8510, Japan, E-mail: [email protected]
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Abstract

It is well known that various characteristics in risk and queuing processes can be formulated as Markov renewal functions, which are determined by Markov renewal equations. However, those functions have not been utilized as they are expected. In this article, we show that they are useful for studying asymptotic decay in risk and queuing processes under a Markovian environment. In particular, a matrix version of the Cramér–Lundberg approximation is obtained for the risk process. The corresponding result for the MAP/G/1 queue is presented as well. Emphasis is placed on a straightforward derivation using the Markov renewal structure.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 16 , Issue 2 , April 2002 , pp. 139 - 150
Copyright
© 2002 Cambridge University Press

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