Queueing Systems: Theory and Applications
A Markov Renewal Approach to M/G/1 Type Queues with Countably Many Background States
Queueing Systems: Theory and Applications
On a class of stochastic models with two-sided jumps
Queueing Systems: Theory and Applications
Queues with boundary assistance: the effects of truncation
Queueing Systems: Theory and Applications
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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.