THOMAS MIKOSCH AND SIDNEY RESNICK

Abstract. Consider a data network model in which sources begin to transmit at renewal time points $\{S_n\}$. Transmissions proceed for random durations of time $\{T_n\}$ 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 {\it 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 $A(t)= \int_0^t M(s)\, ds$.