The object of this research in the queueing theory is a theorem about theStrong-Law-of-Large-Numbers (SLLN) under the conditions of heavy traffic in a multiserveropen queueing network. SLLN is known as a fluid limit or fluid approximation. In thiswork, we prove that the long-term average rate of growth of the queue length process of amultiserver open queueing network under heavy traffic strongly converges to a particularvector of rates. SLLN is proved for the values of an important probabilisticcharacteristic of the multiserver open queueing network investigated as well as the queuelength of jobs.
