Asymptotic Loss Probability in a Finite Buer Fluid Queue with Heterogeneous Heavy-Tailed On-O Processes

Consider a uid queue with a nite buer B and capacity c fed by a superposition of N independent On-O processes. An On-O process consists of a sequence of alternating indepen-dent activity and silence periods. Successive activity, as well as silence, periods are identically distributed. The process is active with probability p and during its activity period produces uid at constant rate r. For this queueing system, under the assumption that the excess ac-tivity periods are intermediately regularly varying, we derive explicit and asymptotically exact formulas for approximating the stationary over ow probability and loss rate. In the case of homogeneous processes with excess activity periods equal in distribution to e, the queue loss rate is asymptotically, as B!1, equal to