Geodesic
On a total resource amounts at the system with parallel service and MMPP arrivals
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 20 (2020) no. 3, pp. 400-410

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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. 
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     author = {E. N. Chernishova and E. Yu. Lisovskaya},
     title = {On a total resource amounts at the system with parallel service and {MMPP} arrivals},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {400--410},
     publisher = {mathdoc},
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E. N. Chernishova; E. Yu. Lisovskaya. On a total resource amounts at the system with parallel service and MMPP arrivals. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 20 (2020) no. 3, pp. 400-410. http://geodesic.mathdoc.fr/item/ISU_2020_20_3_a10/