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Time-sensitive networks require timely and accurate monitoring of the statusof the network. To achieve this, many devices send packets periodically, whichare then aggregated and forwarded to the controller. Bounding the aggregateburstiness of the traffic is then crucial for effective resource management. Inthis paper, we are interested in bounding this aggregate burstiness forindependent and periodic flows. A deterministic bound is tight only when flowsare perfectly synchronized, which is highly unlikely in practice and would beoverly pessimistic. We compute the probability that the aggregate burstinessexceeds some value. When all flows have the same period and packet size, weobtain a closed-form bound using the Dvoretzky-Kiefer-Wolfowitz inequality. Inthe heterogeneous case, we group flows and combine the bounds obtained for eachgroup using the convolution bound. Our bounds are numerically close tosimulations and thus fairly tight. The resulting aggregate burstiness estimatedfor a non-zero violation probability is considerably smaller than thedeterministic one: it grows in $\sqrt{n\log{n}}$, instead of $n$, where $n$ isthe number of flows.

Quasi-Deterministic Burstiness Bound for Aggregate of Independent, Periodic Flows