Infinite-server queueing tandem with mmpp arrivals and random capacity of customers

Tandem of two queueing systems with infinite number of servers is considered. Customers arrive at the first stage of the tandem according to Markovian modulated Poisson process, and after a completion of their services, they go to the second stage. Each customer carries some data package with a random value (capacity of the customer). Service time does not depend on the customers' capacities in this study, capacities are used just to fix some additional characteristic of the system evolution. It is shown that two-dimensional probability distribution of total capacities at the stages of the system is two-dimensional Gaussian under the asymptotic condition of a high rate of arrivals. Presented numerical experiments and simulations allow to determine an applicability area of the asymptotic result. © ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi,Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors).