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

Networking and Internet Architecture