Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 2, Pages 143-158
Transient analysis of a fluid queue driven by a birth and death process suggested by a chain sequence
1Department of Mathematics, Indian Institute of Technology, Madras Chennai 600 036, India
2IRISA-INRIA, Campus Universitaire de Beaulieu, Rennes Cedex 35042, France
Received 31 March 2004; Revised 30 August 2004
Copyright © 2005 P. R. Parthasarathy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We analyse the transient behaviour of a fluid queue driven by a
birth and death process (BDP) whose birth and death rates are
suggested by a chain sequence. For the BDP suggested by a chain
sequence, the stationary probabilities do not exist and
hence the stationary buffer content distribution for fluid queues driven by such BDP does not exist.
However, their transient distribution is obtained in a simple
closed form by two different approaches: the first is
the continued fraction approach and the second is an approach
in terms of recurrence relation by an analysis similar
to that of Sericola (1998). The probability for the
buffer content to be empty at an arbitrary time is also studied.
The variations in this performance measure are revealed in the
form of graphs. Numerical illustrations are included.