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

摘要

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.