International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 24, Pages 1509-1528
doi:10.1155/S0161171203203203
Fluid queues driven by a discouraged arrivals queue
Department of Mathematics, Indian Institute of Technology, Madras 600 036, Chennai, India
Received 20 March 2002
Copyright © 2003 P. R. Parthasarathy and K. V. Vijayashree. 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.
Abstract
We consider a fluid queue driven by a discouraged arrivals queue
and obtain explicit expressions for the stationary distribution
function of the buffer content in terms of confluent
hypergeometric functions. We compare it with a fluid queue driven
by an infinite server queue. Numerical results are presented to
compare the behaviour of the buffer content distributions for both
these models.