Network Multiplexer with Generalized Processor Sharing and Heavy-tailed On-Off Flows

We consider a set of fluid On-Off flows that share a common server of capacity c and a finite buffer B. The server capacity is divided using Generalized Processor Sharing scheduling discipline. Each flow has a minimum service rate guarantee that exceeds its long term average demand ρi. The buffer sharing is unrestricted as long as there is available space; if the buffer is full, the necessary amount of fluid from the most demanding flows is discarded. When the On periods are heavy-tailed, we show that the loss rate of a particular flow i is asymptotically equal to the loss rate in a reduced system with capacity c − Σj 6=iρj and buffer B, where this flow is served in isolation. In particular, each flow perceives to have the whole buffer B to itself. This insight provides a new guideline for efficiently engineering differentiated quality of service in integrated multimedia networks.