Stationary solution to a tandem fluid queue with input controlled by exponential timer. (1st January 2013)

• Record Type: Journal Article
• Authors: Vijayakumar, A.; Sophia, S.
• Is Part Of: International journal of operational research. Volume 18:Number 1(2013)
• Page Start: 71
• Page End: 90
• Publication Date: 2013-01-01
• Subjects: tandem fluid queue -- on-off source -- busy period -- exponential timer -- buffer content; Operations research -- Periodicals; 003.05
• Languages: English
• ISSNs: 1745-7645

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 j th 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.