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.

The gradient descent to a local minimum is the key ingredient of deep neural networks learning techniques. We consider a function Lm(.) in dimension n with a random set of m absolute minima. When log m = o(n), we show that a gradient descent from an initial random point quasi always ends on a unique local minimum approximately at the centroid of the absolute minima. This fake minimum acts like an absorbing node, but its value by function Lm(.) can be far above the values obtained by Lm(.) on the absolute minima and sometimes gives very bad coefficients for the neural network. Fortunately in most cases the fake minimum leads to a neural network with not so bad prediction, with an error rate of order n-1/4. The only way to escape the fake minimum is to start a new gradient descent from a new random point and we show that finding a good initial point takes in average time which is at least proportional to ebn/mn2for some b > 0.

The evolution of LTE and advent of 5G networks increases further the bandwidth requirements for RAN. In parallel, the deployment of Centralized RAN architecture raises new challenges on the FrontHaul network. The inflexibility of the legacy CPRI is the primary challenge to Virtualized RAN deployments, and there is currently a strong trend towards the use of packetized transport methods, together with flexible split RAN based architectures. Functional splits within the real-time functions of the RAN have very stringent requirements on latency and jitter. This paper analyzes the jitter produced in the switching nodes of the FrontHaul network, and proposes dimensioning rules.

The maximum independent set (MIS) problem is a well-studied combinatorial optimization problem that naturally arises in many applications, such as wireless communication, information theory and statistical mechanics.

In this paper, we compute the actual worst-case end-to-end delay for a flow in a feed-forward network of first-in-first-out (FIFO)-multiplexing service curve nodes, where flows are shaped by piecewise-affine concave arrival curves, and service curves are piecewise affine and convex. We show that the worst-case delay problem can be formulated as a mixed integer linear programming problem, whose size grows exponentially with the number of nodes involved. Furthermore, we present approximate solution schemes to find upper and lower delay bounds on the worst-case delay. Both only require to solve just one linear programming problem and yield bounds that are generally more accurate than those found in the previous work, which are computed under more restrictive assumptions.

Nowadays, telecommunication systems are growing more and more complex, generating a large amount of alarms that cannot be effectively managed by human operators. The problem is to detect significant combinations of alarms describing an issue in real-time. In this article, we present a powerful heuristic algorithm that constructs dependency graphs of alarm patterns. More precisely, it highlights patterns extracted from an alarm flow obtained from a learning process with a small footprint on network management system performance. This algorithm helps to detect issues in real-time by effectively delivering concise alarm patterns. Furthermore, it allows the proactive analysis of the functioning of a network by computing the general trends of this network. We evaluate our algorithm on an optical network alarm data set of an existing operator. We find similar results as the expert analysis performed for this operator by Alcatel-Lucent Customer Services.

Cyber-Physical Systems require distributed architectures to support safety critical real-time control. Kopetz' Time-Triggered Architectures (TTA) have been proposed as both an architecture and a comprehensive paradigm for systems architecture, for such systems. To relax the strict requirements on synchronization imposed by TTA, Loosely Time-Triggered Architectures (LTTA) have been recently proposed. In LTTA, computation and communication units at all triggered by autonomous, non synchronized, clocks. Communication media act as shared memories between writers and readers and communication is non blocking. In this paper we pursue our previous work by providing a unified presentation of the two variants of LTTA (token- and time-based), with simplified analyses. We compare these two variants regarding performance and robustness and we provide ways to combine them.

Network Calculus theory aims at evaluating worst-case performances in communication networks. It provides methods to analyze models where the traffic and the services are constrained by some minimum and/or maximum envelopes (service/arrival curves). While new applications come forward, a challenging and inescapable issue remains open: achieving tight analyzes of networks with aggregate multiplexing. The theory offers efficient methods to bound maximum end-to-end delays or local backlogs. However as shown recently, those bounds can be arbitrarily far from the exact worst-case values, even in seemingly simple feed-forward networks (two flows and two servers), under blind multiplexing (i.e. no information about the scheduling policies, except FIFO per flow). For now, only a network with three flows and three servers, as well as a tandem network called sink tree, have been analyzed tightly. We describe the first algorithm which computes the maximum end-to-end delay for a given flow, as well as the maximum backlog at a server, for any feed-forward network under blind multiplexing, with concave arrival curves and convex service curves. Its computational complexity may look expensive (possibly super-exponential), but we show that the problem is intrinsically difficult (NP-hard). Fortunately we show that in some cases, like tandem networks with cross-traffic interfering along intervals of servers, the complexity becomes polynomial. We also compare ourselves to the previous approaches and discuss the problems left open.

Over the last few years, Real-Time Calculus has been used extensively to model and analyze embedded systems processing continuous data/event streams. Towards this, bounds on the arrival process of streams and bounds on the processing capacity of resources serve as inputs to the model, which are used to calculate end-to-end delays suffered by streams, maximum backlog, utilization of resources, etc. This "functional'' model, although amenable to computationally inexpensive analysis methods, has limited modeling capability. In particular, "state-based'' processing, e.g. blocking write - where the processing depends on the "state'' or fill-level of the buffer - cannot be modeled in a straightforward manner. This has led to a number of recent proposals on using automata-theoretic models for stream processing systems (e.g. Event Count Automata [RTSS 2005]). Although such models offer better modeling flexibility, they suffer from the usual state-space explosion problem. In this paper we show that a number of complex state-dependencies can be modeled in a lightweight manner, using a feedback control technique. This avoids explicit state modeling, and hence the state-space explosion problem. Our proposed modeling and analysis therefore extend the original Real-Time Calculus-based functional modeling in a very useful way, and cover much larger problem domain compared to what was previously possible without explicit state-modeling. We illustrate its utility through two case studies and also compare our analysis results with those obtained from detailed system simulations (which are significantly more time consuming).