Fluid queues have been used to model the performance of a network switch,[10] a router,[11] the IEEE 802.11 protocol,[12] Asynchronous Transfer Mode (the intended technology for B-ISDN),[13][14] peer-to-peer file sharing,[15] optical burst switching,[16] and has applications in civil engineering when designing dams.
[23][24] For a simple system where service has a constant rate μ and arrival fluctuate between rates λ and 0 (in states 1 and 2 respectively) according to a continuous time Markov chain with generator matrix the stationary distribution can be computed explicitly and is given by[6] and average fluid level[25] The busy period is the period of time measured from the instant that fluid first arrives in the buffer (X(t) becomes non-zero) until the buffer is again empty (X(t) returns to zero).
[31] There are two main approaches to solving for the busy period in general, using either spectral decomposition or an iterative recurrent method.
[32] A quadratically convergent algorithm for computing points of the transform was published by Ahn and Ramaswami.
[40] The ordered Schur factorization can be used to efficiently compute the stationary distribution of such a model.
[41] Second order fluid queues (sometimes called Markov modulated diffusion processes or fluid queues with Brownian noise[42]) consider a reflected Brownian motion with parameters controlled by a Markov process.