Abstract
We study a general multi-server system in which each customer has service time and a random volume. We consider two main cases: (i) the total volume of the present customers is unlimited and (ii) this volume is upper bounded by a finite constant. For this system, using the regenerative approach, we develop performance analysis. We establish a solidarity property of the basic processes: accumulated volume, waiting time (workload) and queue size. In case (i), we prove an analog of Little’s formula and, provided the system is single-server and the input is Poisson, the Pollaczeck-Khintchine formula. In case (ii), we suggest an approximation of the Pollaczeck-Khintchine formula, which is then verified by simulation.
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Research is supported by Russian Foundation for Basic Research, projects 15-07-02341, 15-07-02354, 15-07-02360 and the Program of Strategy Development of Petrozavodsk State University.
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Morozov, E., Potakhina, L., Tikhonenko, O. (2016). Regenerative Analysis of a System with a Random Volume of Customers. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2016. Communications in Computer and Information Science, vol 638. Springer, Cham. https://doi.org/10.1007/978-3-319-44615-8_23
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DOI: https://doi.org/10.1007/978-3-319-44615-8_23
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