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Abstract
With the advent of highly integrated transmission networks, the transmission of data, such as audio, video, video streaming are transmitted over a common medium in smaller file sizes. These files have variable transmission time requirement which is of deterministic in nature. Further, the traffic generated from various sources is bursty and correlated. This particular scenario can be best modelled as a single-server queueing system with arrivals following a Markovian arrival process and service-time deterministic distribution taking one of the N possible values. For this model, we present a closed-form (in terms of roots) analysis for evaluating queueing/system-time distributions using an inversion method which is based on the roots of associated characteristic equation. Several numerical examples are presented with complete discussion.
Acknowledgements
The authors thank the anonymous referees for their valuable comments and suggestions that helped to improve the presentation of the paper in the current form. The first author is grateful to the National Board for Higher Mathematics (NBHM), Department of Atomic Energy, Government of India for the financial support. The second author acknowledges the Department of Science and Technology, Govt. of India, for the financial support under the project grant SR/S4/MS:789/12. The last author acknowledges the partial support provided by NSERC 172877-02.