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Chernishova E. N., Lisovskaya E. Y. On a Total Resource Amounts at the System with Parallel Service and MMPP Arrivals. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 3, pp. 400-410. DOI: 10.18500/1816-9791-2020-20-3-400-410, EDN: PTIYON
On a Total Resource Amounts at the System with Parallel Service and MMPP Arrivals
In this paper, we consider a resource system with an unlimited resources and servers number, with parallel customers servicing, arriving at the system according to the MMPP. Using a combination of multidimensional dynamic screening methods and asymptotic analysis, it is proved that the joint asymptotic probability distribution of the total resource amounts converges to a bi-dimensional Gaussian distribution under conditions of increasing intensity of MMPP. The parameters of the asymptotic probability distribution are found. A numerical analysis of the approximation accuracy is carried out.
- Gajdamaka Yu. V., Zaripova E. R., Orlov Yu. N. Analysis of the impact the batch size distribution on parameters of the SIP-server queueing model with batch arrivals. KIAM Preprint, Moscow, 2015, no. 27. 16 p. (in Russian). Available at: http://library.keldysh.ru/preprint.asp?id=2015-27 (accessed 07 May 2019).
- Еfrosinin D. V. Metody analiza upravlyaemykh dinamicheskikh system [Methods of analysis of controlled dynamic systems]. Diss. Dr. Sci. (Phis. and math.). Moscow, 2013. 332 p. (in Russian).
- Galileyskaya A. On the Total Amount of the Occupied Resources in the Multi-Resource QS with Renewal Arrival Process. Informatsionnye tekhnologii i matematicheskoe modelirovanie (ITMM-2019): materialy XVIII Mezhdunar. konf. im. A. F. Terpugova [Information Technology and Mathematical Modeling (ITMM-2019). Materials of the XVIII Int. conf. named after A. F. Terpugov]. Tomsk, Izd-vo NTL, 2019, pt. 2, pp. 80–85.
- Lisovskaya Е. Yu., Moiseev A. N., Moiseeva S. P., Pagano M. Modeling of processing of physics experimental data in the form of non-Markovian multi-resource queuing system. Izvestiya vuzov. Fizika, 2018, vol. 61, no. 12 (732), pp. 39–46 (in Russian).
- Mandelbaum A., Zeltyn S. The impact of customers’ patience on delay and abandonment: Some empirically-driven experiments with the M/M/n + G queue. OR Spectrum, 2004, vol. 26, pp. 377–411. DOI: https://doi.org/10.1007/s00291-004-0164-8
- Neuts M. F. Models based on the Markovian arrival process. IEICE Trans. Comm., 1992, vol. E-75B, no. 12, pp. 1255–1265.
- Lucantoni D. M. New results on single server queue with a batch Markovian arrival process. Stoch. Models, 1991, vol. 7, no. 1, pp. 1–46. DOI: https://doi.org/10.1080/15326349108807174
- Simulation model of an infinitely linear system for servicing requirements of a random volume with an input flow MMP / Е. Yu. Lisovskaya, S. P. Moiseeva, M. Pagano; copyright holder National Research Tomsk State University (RU). No. 2017612202; declared 17.03.2017; register in the Register of computer programs 12.05.2017 (in Russian).
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