Four relations are defined the use of which allow a reliability network to be expressed as a mathematical statement. Series and active and standby redundancy connections are allowed. The possibility of requiring more than one of the active branches to be operative is included. At the very least the result allows for typing in place of drawing a network description.

http://ieeexplore.ieee.org/iel5/24/5216426/05216446.pdf

Network Calculus

Compositional schedulability analysis of hierarchical scheduling frameworks is a well studied problem, as it has wide-ranging applications in the embedded systems domain. Several techniques, such as periodic resource model based abstraction and composition, have been proposed for this problem. However these frameworks are sub-optimal because they incur bandwidth overhead. In this work, we introduce the explicit deadline periodic (EDP) resource model, and present compositional analysis techniques under EDF and DM. We show that these techniques are bandwidth optimal, in that they do not incur any bandwidth overhead in abstraction or composition. Hence, this framework is more efficient when compared to existing approaches.

/pdf/compositional-analysis-framework-using-edp-resource-models-jirar0q6b2.pdf

Compositional Analysis Framework Using EDP Resource Models

In recent years service curves have proven a powerful and versatile model for performance analysis of network elements, such as schedulers, links, and traffic shapers, up to entire computer networks, like the Internet. The elegance of the concept of service curve is due to intuitive convolution formulas that determine the data departures of a system from its arrivals and its service curve. This fundamental relation constitutes the basis of the network calculus and relates it to systems theory, however, under a different, so-called min-plus algebra. As in systems theory, the particular strength of the minplus convolution is the ability to concatenate tandem systems along a network path. This facilitates the notion of network service curve that has the expressiveness to characterize whole networks by a single transfer function. This paper surveys the state-of-the-art of the deterministic and the recent probabilistic network calculus. It discusses the concept of service curves, its use in the network calculus, and the relation to systems theory under the min-plus algebra. Service curve models of common schedulers and different types of networks are reviewed and methods for identification of a system's service curve representation from measurements are discussed. After recapitulating the state of knowledge on time-varying min-plus systems theory, stochastic service curve models are surveyed. These models allow utilizing the statistical multiplexing gain in a network calculus framework that features end-to-end network analysis by convolution of service curves.

Survey of deterministic and stochastic service curve models in the network calculus

Deterministic and stochastic service curve models in the network calculus

Time-sensitive wireless sensor network (WSN) applications require finite delay bounds in critical situations. This paper provides a methodology for the modeling and the worst-case dimensioning of cluster-tree WSNs. We provide a fine model of the worst-case cluster-tree topology characterized by its depth, the maximum number of child routers and the maximum number of child nodes for each parent router. Using Network Calculus, we derive "plug-and-play " expressions for the end-to-end delay bounds, buffering and bandwidth requirements as a function of the WSN cluster-tree characteristics and traffic specifications. The cluster-tree topology has been adopted by many cluster-based solutions for WSNs. We demonstrate how to apply our general results for dimensioning IEEE 802.15.4/Zigbee cluster-tree WSNs. We believe that this paper shows the fundamental performance limits of cluster-tree wireless sensor networks by the provision of a simple and effective methodology for the design of such WSNs

/pdf/modeling-and-worst-case-dimensioning-of-cluster-tree-3lqsgng4kj.pdf

Modeling and Worst-Case Dimensioning of Cluster-Tree Wireless Sensor Networks

Tight end-to-end per-flow delay bounds in FIFO multiplexing sink-tree networks

In this paper we investigate the problem of scalable admission control for real-time traffic in sink-tree networks employing per-aggregate resource management policies, like MPLS or DiffServ. Every traffic flow entering the network at an ingress node, and flowing towards a given egress node, specifies its leaky-bucket parameters and a required delay bound for traversing the network. We propose an algorithm that admits a new flow if a guarantee can be given that the required delay bound, besides those of other already established flows, are not exceeded. We identify properties of sink-tree networks based on which we considerably reduce the complexity of the proposed algorithm, and we show that the latter approaches the theoretical lower bound on the worst case complexity of any algorithm working under the same hypotheses. Finally, we show that the algorithm lends itself to a distributed implementation, thus allowing for better scalability.

A novel approach to scalable CAC for real-time traffic in sink-tree networks with aggregate scheduling

In a DiffServ architecture, packets with the same marking are treated as an aggregate at core routers, independently of the flow they belong to. Nevertheless, for the purpose of QoS provisioning, derivation of upper bounds on the delay of individual flows is required. In this paper, we consider the derivation of per-flow end-to-end delay bounds in DiffServ domains where peregress (or sink-tree) FIFO aggregation is in place. We expose a general methodology to derive delay bounds, and we instantiate it on a case study. We show that the methodology yields a tighter bound than those available from the literature, and we express a worst-case scenario for the case study network, in which the bound is actually achieved.

A Methodology for Deriving Per-Flow End-to-End Delay Bounds in Sink-Tree DiffServ Domains with FIFO Multiplexing

In this paper we propose an admission control algorithm which is suitable for real time traffic in a sink-tree network in which per-aggregate resource management is in place. Every flow specifies its leaky-bucket parameters and a required delay bound, and the algorithm admits a new flow if a guarantee can be given that the delay bound for every established flow is not exceeded. The algorithm is based on a formula, derived through Network Calculus, that relates the worst-case delay of a single flow to the transmission rate provisioned for the aggregate and to the leaky-bucket parameters of flows at the ingress of the network. We describe the algorithm and the employed data structures, and we evaluate its complexity.

Linda Martorini

Papers

Tight end-to-end per-flow delay bounds in FIFO multiplexing sink-tree networks

A novel approach to scalable CAC for real-time traffic in sink-tree networks with aggregate scheduling

A Methodology for Deriving Per-Flow End-to-End Delay Bounds in Sink-Tree DiffServ Domains with FIFO Multiplexing

Exploiting Network Calculus for Delay-Based Admission Control in a Sink-Tree Network