Asymptotic behavior of loss rate for feedback finite fluid queue with downward jumps

Abstract

We consider a feedback fluid queue with a finite buffer and downward jumps, where the net flow rate and the jump size for the buffer content are controlled by a background Markov chain with a finite state space. The feedback means that the transition structure of the background Markov chain may change when the buffer content becomes empty or full. In this chapter, we show that the loss rate for this fluid queue decays exponentially as the buffer size gets large under a negative drift condition. © Springer Science+Business Media LLC 2009.