Title: Stationary solution to a tandem fluid queue with input controlled by exponential timer

Authors: A. Vijayakumar; S. Sophia

Addresses: Department of Science and Humanities, RMK Engineering College, Tamilnadu, India ' Department of Mathematics, SSN College of Engineering, Tamilnadu, India

Abstract: A tandem fluid queue with multiple consecutive buffers connected in series is considered. The output of the (j − 1)th buffer is the input to the jth buffer and the first buffer is fed by a number of independent homogeneous on-off sources. The sources have exponentially distributed silent periods, active periods following general distribution and are controlled by an exponential timer. The buffer contents are obtained for the first and subsequent buffers in terms of Laplace transforms. Explicit expressions for the buffer content of the first buffer fed by a single source are obtained for the fluid queue driven by M/M/1 and M/M/2 queues. Expressions are also found for the contents of subsequent buffers when the first buffer is fed by multiple sources. Some of the known results are deduced from the results obtained. Numerical illustrations are provided to display the trend of the average buffer content for the models under consideration.

Keywords: tandem fluid queues; on-off source; busy period; exponential timer; buffer content.

DOI: 10.1504/IJOR.2013.055541

International Journal of Operational Research, 2013 Vol.18 No.1, pp.71 - 90

Received: 14 Dec 2011
Accepted: 06 Jul 2012
Published online: 29 Jul 2014 *

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