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.

翻译：时间敏感网络需要及时准确地监控网络状态。为实现这一目标，许多设备定期发送数据包，这些数据包随后被聚合转发至控制器。对流量聚合突发性进行界定对资源管理至关重要。本文旨在为独立且周期性的流界定这一聚合突发性。确定性界仅在流完全同步时成立，这在实践中极不可能且过于悲观。我们计算了聚合突发性超过某值的概率。当所有流具有相同周期和数据包大小时，我们利用Dvoretzky-Kiefer-Wolfowitz不等式得到了闭式界。在异构情况下，我们对流进行分组，并通过卷积界合并每组所得结果。我们的数值结果与仿真接近，因而较为紧凑。基于非零违规概率估计的聚合突发性远小于确定性界：其增长阶为$\sqrt{n\log{n}}$，而非$n$，其中$n$为流的数量。