Asymptotic Loss Probability in a Finite Buffer Fluid Queue with Heterogeneous Heavy-Tailed On-Off Pr

Consider a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent On–Off processes. An On–Off process consists of a sequence of alternating independent periods of activity and silence. Successive periods of activity, as well as silence, are identically distributed. The process is active with probability p and during its activity period produces fluid at constant rate r . For this queueing system, under the assumption that the excess activity periods are intermediately regularly varying, we derive explicit and asymptotically exact formulas for approximating the stationary overflow probability and loss rate. In the case of homogeneous processes with excess activity periods equal in distribution to τe , the queue loss rate is asymptotically, as B → ∞, equal to

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