Large Buffer Asymptotics for Fluid Queues with Heterogeneous M/G/∞ Weibullian Inputs

  • Authors:

  • Nikolay Likhanov;Ravi R. Mazumdar;Ozcan Ozturk

  • Affiliations:

  • Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow, Russia;School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA mazum@ecn.purdue.edu;School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2003

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Abstract

In this paper we consider a generalization of the so called M/G/∞ model where M types of sessions enter a buffer. The instantaneous rates of the sessions are functions of the occupancy of an M/G/∞ system with Weibullian G distributions. In particular we assume that a session of type i transmits ri cells per unit time and lasts for a random time τ with a Weibull distribution given by Pr (τx)∼e−γixαi, where 0ii0. We show that the complementary buffer occupancy distribution for large buffer size is Weibullian whose parameters can be determined as the solution of a deterministic nonlinear knapsack problem. For αi