Asymptotic behavior of the loss rate for Markov-modulated fluid queue with a finite buffer
The paper considers a stochastic fluid queue with a finite buffer, where the fluid flow is modulated by a background Markov chain with a finite state space. It is assumed that the transition probabilities of the background Markov chain change when the buffer content is empty or full. The objective of the paper is twofold. The authors derive the asymptotic loss rate of the Markov-modulated fluid queue with a finite buffer. When the mean drift of the net fluid flow is not null, this was studied earlier. The paper includes the null drift case. The authors consider the density of the stationary buffer content distribution and derive it in matrix exponential form. This density is particularly useful for getting the asymptotic loss rate for the null drift case. Deriving the stationary distribution in tractable form is the second purpose.
scientific article; zbMATH DE number 5710665