Abstract
In this paper, a queueing system with multicast service, random resource requirements and general probability distributions of busy and idle periods is considered. Motivated by challenges from practical applications in the area of performance analysis of telecommunication systems, the model is built on the basis of well-known resource queueing systems theory. Two distinctive features of the model related to resource requirements are: the volume of a requirement, which is random with a given probability distribution function, and the resource requirements which overlap with each other. The first feature comes from the analysis of wireless networks, where the volume of resource depends on the location of the mobile equipment, type of telecommunication service, required data bitrate and radio signal path loss. The second feature relates to the multicast approach to data delivery in modern telecommunication networks. The stationary probability distribution of the number of customers in the system is derived. The main characteristics for the performance analysis of multicast telecommunication systems including the blocking probability, the mean number of customers in the system and the mean of the total amount of occupied resources are proposed. The analytical formulas for the performance calculations are obtained for the Fréchet-type distribution of a requested resources volume.
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Acknowledgements
The publication was supported by the Ministry of Education and Science of the Russian Federation (Project No. 2.3397.2017/4.6). The authors thank their colleague Prof. Valeriy Naumov, Service Innovation Research Institute, Finland, who provided insight and expertise that greatly assisted the research. We also sincerely thank the anonymous reviewers for their helpful comments, which have significantly improved the quality of the paper.
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Samouylov, K., Gaidamaka, Y. Analysis of loss systems with overlapping resource requirements. Stat Papers 59, 1463–1470 (2018). https://doi.org/10.1007/s00362-018-1041-x
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DOI: https://doi.org/10.1007/s00362-018-1041-x