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In this paper, we present (in terms of roots) a simple closed-form analysis for evaluating system-length distribution at three epochs of time (arbitrary, pre-arrival, and post-departure) and queueing-time distribution (virtual and actual) of the MAP/R/1 queue, where R represents the class of distributions whose Laplace–Stieltjes transforms are rational functions. Our analysis is based on roots of...
In recent years, queueing models with Markovian arrival process have attracted interest among researchers due to their applications in telecommunications. Such models are generally dealt with matrix-analytic method which appears to be powerful analytically despite the fact that it has numerical difficulties. However, analyzing such queues with the method of roots is always a neglected part since it...
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