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

P. R. Parthasarathy and K. V. Vijayashree

 Department of Mathematics, Indian Institute of Technology, Madras 600 036, Chennai, India
Received 20 March 2002

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.