Activity rates with very heavy tails

Thomas Mikosch and Sidney Resnick

Stochastic Processes and their Applications, 2006, vol. 116, issue 2, 131-155

Abstract: Consider a data network model in which sources begin to transmit at renewal time points {Sn}. Transmissions proceed for random durations of time {Tn} and transmissions are assumed to proceed at fixed rate unity. We study M(t), the number of active sources at time t, a process we term the activity rate process, since M(t) gives the overall input rate into the network at time t. Under a variety of heavy-tailed assumptions on the inter-renewal times and the duration times, we can give results on asymptotic behavior of M(t) and the cumulative input process .

Keywords: Regular; variation; Infinite; first; moment; Stable; Lévy; motion (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (5)

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