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The paper is devoted to the analysis of queueing systems in the context of the network and communication theory (called a multi-server multi-core open queueing network). The ob ject of this research on the queueing theory is theorems about the Functional Strong Laws of Large Numbers (FSLLN) in multi-server multi-core open queueing networks, working under overload heavy trac conditions. FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for extreme values of important probabilistic characteristics of the multi-server multicore open queueing network, investigated as well as the virtual waiting time of a job and the queue length of jobs. As applications of the proved theorems Little’s laws in a multi-server multi-core open queueing network are presented.

Little's laws for extreme values in multi-server multi-core open queueing networks