Abstract
In this paper a model of a heterogeneous resource queueing system with a Markovian arrival process is considered. The customer accepted for servicing occupies random amount of resource with a given distribution function depending on the class of the customer and on the type of service it needs. At the end of the service, the customer leaves the system and releases the occupied resource. In this work, asymptotic formulas for calculating the main probability characteristics of the model, including the joint distribution functions of the customers number and the total resource amounts occupied by them, are obtained. Finally, the accuracy of the approximation is verified by using simulation.
The publication has been prepared with the support of the “RUDN University Program 5-100” (recipient E. Lisovskaya, mathematical model development). The reported study was funded by RFBR, project number 18-07-00576 (Y. Gaidamaka, simulation model development) and 17-07-00845 (Y. Gaidamaka, problem formulation and analysis) and the University of Pisa PRA 2018–2019 Research Project “CONCEPT Communication and Networking for vehicular Cyber-Physical systems” (recipient M. Pagano, simulation and numerical analysis).
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Lisovskaya, E., Pankratova, E., Gaidamaka, Y., Moiseeva, S., Pagano, M. (2019). Heterogeneous Queueing System MAP/GI\(^{(n)}\)/\(\infty \) with Random Customers’ Capacities. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2019. Lecture Notes in Computer Science(), vol 11965. Springer, Cham. https://doi.org/10.1007/978-3-030-36614-8_24
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