We consider a queueing system with batch MMPP arrivals and an unlimited number of servers. An arriving group of customers occupies necessary number of free servers for a random time determined by a given probability distribution function. At the end of the service, the whole group releases all the servers at the same time. In the paper, we obtain the probability distribution of the number of customers in the system. To solve the problem, we use the dynamic screening method and asymptotic analysis such condition of high intensity of arrivals. It is shown that under condition the probability distribution of the number of customers in the system is Gaussian. The parameters of this Gaussian distribution are obtained in the paper.
Infinite-server bulk queue with mmpp arrivals
Pagano M.;
2020-01-01
Abstract
We consider a queueing system with batch MMPP arrivals and an unlimited number of servers. An arriving group of customers occupies necessary number of free servers for a random time determined by a given probability distribution function. At the end of the service, the whole group releases all the servers at the same time. In the paper, we obtain the probability distribution of the number of customers in the system. To solve the problem, we use the dynamic screening method and asymptotic analysis such condition of high intensity of arrivals. It is shown that under condition the probability distribution of the number of customers in the system is Gaussian. The parameters of this Gaussian distribution are obtained in the paper.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
