Finite buffer queue with generalized processor sharing and heavy-tailed input processes

We consider a set of N fluid On–Off flows that share a common server of capacity c and a finite buffer B. The server capacity is allocated using the generalized processor sharing scheduling discipline. Each flow has a minimum service rate guarantee that exceeds its long-term average demand qi. 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 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 P j61⁄4i qj and buffer B, where this flow is served in isolation. In particular, the system behaves as if it had N times bigger buffer. This new insight on buffer multiplexing gain offers an additional tradeoff in distributing buffers between core and edge switching elements. 2002 Elsevier Science B.V. All rights reserved.