Abstract
Processor sharing (PS) queuing systems and particularly their well-known class of egalitarian processor (EPS) sharing are widely investigated by research community and applied for the analysis of wire and wireless communication systems and networks. The same can be said for queuing systems in random environment, with unreliable servers, interruptions, pre-emption mechanisms. Nevertheless, only few works focus on queues with both PS discipline and unreliable servers. In the paper, compared with the previous results we analyse a finite capacity PS queuing system with unreliable server and an upper limit of the number of customers it serves simultaneously. For calculating the mean sojourn time, unlike a popular but computational complex technique of inverse Laplace transform we use an effective method based on embedded Markov chains. The paper also includes a practical numerical example of web browsing in a wireless network when the corresponding low priority traffic can be interrupted by more priority applications.
Keywords
- Queuing system
- Processor sharing
- Egalitarian processor sharing
- Unreliable server
- Interruption
- Probability distribution
- Recursive algorithm
- Mean sojourn time
- Embedded Markov chain
- Web browsing
The reported study was funded by RFBR according to the research projects No. 16-07-00766 16-37-60103 and 16-37-00421 and by Ministry of Education and Science of the Russian Federation (No. 2987.2016.5).
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Acknowledgment
The authors wish to thank the referees for their useful comments. We are grateful to the research group coordinator of the Wireless System Laboratory at the Brno University of Technology (Czech Republic) Dr. Jiri Hosek for the advice on the numerical case study.
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Samouylov, K., Naumov, V., Sopin, E., Gudkova, I., Shorgin, S. (2016). Sojourn Time Analysis for Processor Sharing Loss System with Unreliable Server. In: Wittevrongel, S., Phung-Duc, T. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2016. Lecture Notes in Computer Science(), vol 9845. Springer, Cham. https://doi.org/10.1007/978-3-319-43904-4_20
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DOI: https://doi.org/10.1007/978-3-319-43904-4_20
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