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A fluid queue driven by an infinite-state birth-death process E.A. van Doorn and W.R.W. Scheinhardt
 

Summary: 465
A fluid queue driven by an infinite-state birth-death process
E.A. van Doorn and W.R.W. Scheinhardt
Faculty of Applied Mathematics, University of Twente,
P.O. Box 217, 7500 AE Enschede, The Netherlands
E-mail: {doorn, w.r.w.scheinhardt}@math.utwente.nl
We describe an approach to analysing the stochastic behaviour of the content of a buffer
which receives and releases fluid flows at rates which are determined by the state of an
infinite-state birth-death process evolving in the background. The approach is illustrated
by a concrete example.
1. INTRODUCTION
In the performance analysis of telecommunication systems fluid flows have been widely
used as models of information flows, see, e.g., [18,3,16,19,9,32,27,24]. This modelling ap-
proach ignores the discrete nature of the real information flow and treats it as a continuous
stream. In particular in the ATM environment, where the fixed cell size is small and the
interarrival time between cells at the time of generation is constant for several contiguous
cells, this modelling approach has been found to be quite effective, see, e.g., [30,6,26,28].
The rate at which information arrives to a switch or multiplexer usually fluctuates
randomly, often with a high degree of correlation in time. The information is buffered
for service (the server typically being a communication channel) and the service rate

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering