Laws of Little in an open queueing network

Saulius Minkevičius, Stasys Steišūnas
2012 Nonlinear Analysis: Modelling and Control  
The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of
more » ... ed theorems laws of Little in OQN are presented.
doi:10.15388/na.17.3.14059 fatcat:bbbd5bidcrbpvk73b6mxvx55ke