4 research outputs found
Worst-case Delay Analysis of Time-Sensitive Networks with Deficit Round-Robin
In feed-forward time-sensitive networks with Deficit Round-Robin (DRR),
worst-case delay bounds were obtained by combining Total Flow Analysis (TFA)
with the strict service curve characterization of DRR by Tabatabaee et al. The
latter is the best-known single server analysis of DRR, however the former is
dominated by Polynomial-size Linear Programming (PLP), which improves the TFA
bounds and stability region, but was never applied to DRR networks. We first
perform the necessary adaptation of PLP to DRR by computing burstiness bounds
per-class and per-output aggregate and by enabling PLP to support non-convex
service curves. Second, we extend the methodology to support networks with
cyclic dependencies: This raises further dependency loops, as, on one hand, DRR
strict service curves rely on traffic characteristics inside the network, which
comes as output of the network analysis, and on the other hand, TFA or PLP
requires prior knowledge of the DRR service curves. This can be solved by
iterative methods, however PLP itself requires making cuts, which imposes other
levels of iteration, and it is not clear how to combine them. We propose a
generic method, called PLP-DRR, for combining all the iterations sequentially
or in parallel. We show that the obtained bounds are always valid even before
convergence; furthermore, at convergence, the bounds are the same regardless of
how the iterations are combined. This provides the best-known worst-case bounds
for time-sensitive networks, with general topology, with DRR. We apply the
method to an industrial network, where we find significant improvements
compared to the state-of-the-art
Quasi-Deterministic Burstiness Bound for Aggregate of Independent, Periodic Flows
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 , instead of , where is
the number of flows
Interleaved Weighted Round-Robin: A Network Calculus Analysis
Weighted Round-Robin (WRR) is often used, due to its simplicity, for scheduling packets or tasks. With WRR, a number of packets equal to the weight allocated to a flow can be served consecutively, which leads to a bursty service. Interleaved Weighted Round-Robin (IWRR) is a variant that mitigates this effect. We are interested in finding bounds on worst-case delay obtained with IWRR. To this end, we use a network calculus approach and find a strict service curve for IWRR. The result is obtained using the pseudo-inverse of a function. We show that the strict service curve is the best obtainable one, and that delay bounds derived from it are tight (i.e., worst-case) for flows of packets of constant size. Furthermore, the IWRR strict service curve dominates the strict service curve for WRR that was previously published. We provide some numerical examples to illustrate the reduction in worst-case delays caused by IWRR compared to WRR