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

  • Authors:

  • Predrag Jelenković;Petar Momčilović

  • Affiliations:

  • Department of Electrical engineering, Columbia University, 500 West 120th Street, New York, NY;Department of Electrical engineering, Columbia University, 500 West 120th Street, New York, NY

  • Venue:
  • Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
  • Year:
  • 2002

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Abstract

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 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 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 ≠ iρj 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.