Fluid queue driven by an \(M/M/1\) queue (Q1331299)

The present paper deals with a Markov-modulated \(M/M/1\) queue where the well-known spectral decomposition technique can be applied. The novelty in this system is the nature of the spectrum which is shown to be composed of a continuous part and one or two discrete points depending on whether the load of the fluid queue is less or greater than the output to the input rate ratio. The solution for the buffer content distribution is obtained as a simple integral expression. Numerical examples illustrate the problem in question.