Heterogeneous System MMPP/GI(2)/∞ with Random Customers Capacities

Autor: Moiseeva, Svetlana P., Farhadov, Mais P., Moiseev, Alexander N., Pankratova, Ekaterina V.
Rok vydání: 2019
Předmět:
Zdroj: Journal of Siberian Federal University. Mathematics and Physics. 2019. Vol. 12, № 2. P. 231-239
ISSN: 2313-6022
1997-1397
DOI: 10.17516/1997-1397-2019-12-2-231-239
Popis: A heterogeneous queuing system with an infinite number of servers is considered in this paper. Customers arrive in the system according to a Markov Modulated Poisson Process. The type of incoming customer is defined as i-type with probability pi (i = 1, 2). Each customer carries a random quantity of work (capacity of the customer). In this study service time does not depend on the customers capacities. It is shown that the joint probability distribution of the customers number and total capacities in the system is multidimensional Gaussian distribution under the asymptotic condition of an infinitely growing service time. Simulation results allow us to determine an applicability area of the asymptotic result.
Databáze: OpenAIRE