Busy Period Analysis of GI/G/c and MAP/G/c Queues


Kusum Deep, Madhu Jain, Said Salhi

Document Type

Book Chapter

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Publication Title

Performance Prediction and Analytics of Fuzzy, Reliability and Queuing Models : Theory and Applications


The busy period analysis of queueing systems, in general, is very involved and complicated. Even for the simplest queueing model, namely M / M / 1, the probability density function of the busy period is obtained in terms of modified Bessel function. A number of approaches using complex analysis, combinatorics, lattice path, and matrix-analytic methods have been applied to study some selected queueing models. While the steady-state analysis involving queue length and waiting times of queueing models, in general, has been receiving considerable and significant attention in the literature from both analytical and algorithmic points of view, the same cannot be said (relatively speaking) about busy period analysis. This is inherent in the nature of the busy period more than by choice. In this paper, after establishing the complexity involved in the study of the busy period, we record some interesting observations on the busy period under a wide variety of scenarios through simulation approach. The main purpose is to help researchers to look for novel theoretical and/or numerical approach to solving functional equations which naturally arise in the study of busy periods and use the simulated results here as one of the ways to confirm/validate their results.

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Print ISBN 978-981-13-0856-7 Online ISBN 978-981-13-0857-4


Part of the Asset Analytics book series (ASAN).


© Springer Nature Singapore Pte Ltd. 2019