Mathematical Problems in Engineering 
Volume 2004 (2004), Issue 5, Pages 469-489
doi:10.1155/S1024123X0420103X

Fluid queues driven by a birth and death process with alternating flow rates

P. R. Parthasarathy,1 K. V. Vijayashree,1 and R. B. Lenin2

 1Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India
2Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, Antwerpen 2610, Belgium
Received 18 January 2002; Revised 15 July 2002

Abstract

Fluid queue driven by a birth and death process (BDP) with only one negative effective input rate has been considered in the literature. As an alternative, here we consider a fluid queue in which the input is characterized by a BDP with alternating positive and negative flow rates on a finite state space. Also, the BDP has two alternating arrival rates and two alternating service rates. Explicit expression for the distribution function of the buffer occupancy is obtained. The case where the state space is infinite is also discussed. Graphs are presented to visualize the buffer content distribution.