Steffen Bondorf

Boosting sensor network calculus by thoroughly bounding cross-traffic

Sensor Network Calculus (SensorNC) provides a framework for worst-case analysis of wireless sensor networks. The analysis proceeds in two steps: For a given flow, (1) the network is reduced to a tandem of nodes by computing the arrival bounds of cross-traffic; (2) the flow is separated from the cross-traffic by subtracting cross-flows and concatenating nodes on its path. While the second step has seen much treatment, the first step has not at all. This is in sharp contrast to the fact that arrival bounding takes roughly 80% of the total analysis time and is equally crucial for the tightness of the bounds. Therefore, we turn our attention to this first SensorNC analysis step with the goal to boost the performance and applicability of the overall framework. The main technical contribution is a generalized version of the concatenation theorem within the SensorNC setting. This generalization is instrumental in simplifying and streamlining the cross-traffic arrival bound computations such that run times can be reduced by more than a factor of 5. Even more important, it enables a localization of the information necessary to execute the calculations at the node level, thus enabling a distribution of the SensorNC analysis within a self-modeling WSN.

Calculating Accurate End-to-End Delay Bounds - You Better Know Your Cross-Traffic

Bounds on the end-to-end delay of data flows play a crucial role in different areas, ranging from certification of hard real-time communication capabilities to quality of experience assurance for end users. Deterministic Network Calculus (DNC) allows to derive worst-case delay bounds; for instance, DNC is applied by the avionics industry to formally verify aircraft networks against strict delay requirements. Calculating tight end-to-end delays, however, was proven to be NP-hard. As a result, analyses focus on deriving fairly accurate bounds with feasible effort. Previous work constantly improved on capturing flow scheduling and cross-traffic multiplexing effects on the analyzed flows path. In contrast, we present an enhanced analysis of the cross-traffic itself to decrease the bound on its worst-case data arrivals that interfere with the analyzed flow. This improvement is beneficial for both of effects, scheduling and multiplexing. By replacing the currently used procedure to bound cross-traffic arrivals with our new method, we can improve network calculus accuracy considerably - we demonstrate improvements that reduce the worst-case delay bound by more than factor 6.

Pay bursts only once holds for (some) non-FIFO systems

Non-FIFO processing of flows by network nodes is not a rare phenomenon. Unfortunately, the state-of-the-art analytical tool for the computation of performance bounds in packet-switched networks, network calculus, cannot deal well with non-FIFO systems. The problem lies in its conventional service curve definitions. Either the definition is too strict to allow for a concatenation and consequent beneficial end-to-end analysis, or it is too loose and results in infinite delay bounds. Hence, in this paper, we propose a new service curve definition and demonstrate its strength with respect to achieving both finite delay bounds and a concatenation of systems resulting in a favorable end-to-end delay analysis. In particular, we show that the celebrated pay bursts only once phenomenon is retained even without any assumptions on the processing order of packets. This seems to contradict previous work [15]; the reasons for this are discussed.

Improving Cross-Traffic Bounds in Feed-Forward Networks – There is a Job for Everyone

Network calculus provides a mathematical framework for deterministically bounding backlog and delay in packet-switched networks. The analysis is compositional and proceeds in several steps. In the first step, a general feed-forward network is reduced to a tandem of servers lying on the path of the flow of interest. This requires to derive bounds on the cross-traffic for that flow. Tight bounds on cross-traffic are crucial for the overall analysis to obtain tight performance bounds. In this paper, we contribute an improvement on this first bounding step in a network calculus analysis. This improvement is based on the so-called total flow analysis (TFA), which so far saw little usage as it is known to be inferior to other methods for the overall delay analysis. Yet, in this work we show that TFA actually can bring significant benefits in bounding the burstiness of cross-traffic. We investigate analytically and numerically when these benefits actually occur and show that they can be considerable with several flows’ delays being improved by more than 40 % compared to existing methods – thus giving TFA’s existence a purpose finally.

Statistical response time bounds in randomly deployed wireless sensor networks

Response time bounds are important for many application scenarios of wireless sensor networks (WSN). Often, during the planning phase of a WSN its topology is not known. It rather results from a deployment process. This makes the provision of deterministic response time bounds difficult. In this paper, we strive for statistical response time bounds in WSNs that take the stochastic nature of the deployment process into account. Based on a Monte Carlo method we derive estimates for quantiles of the maximum response time distribution under uncertainty about the topology. In numerical experiments we show that the long but light tail of this distribution causes considerably lower bounds compared to the deterministic one even under small violation probabilities and, yet, on the other hand compare favourably with the median of the distribution.

Should Network Calculus Relocate? An Assessment of Current Algebraic and Optimization-Based Analyses

Network calculus (NC) offers a framework for worst-case analysis of queueing networks. It enables to derive deterministic bounds on flow delay and server backlog. The continuous evolution of NC led to a set of different analyses. In fact, it even resulted in two entirely different branches of the methodology. Both start with a common network description based on bounding functions on flow arrivals and forwarding service. Anything that follows, i.e., the actual analysis leading to a worst-case performance bound, vastly differs. For long, there was only the algebraic NC, the formalism created as a system theory for communication networks. It matured and eventually seemed to have reached its limits regarding the accuracy of bounds. The problems preventing it from attaining tight bounds in feed-forward networks were overcome with optimization-based analysis. However, this approach was proven NP-hard without an efficient analysis algorithm known for it. Therefore, it was proposed to confine to a less complex optimization-based analysis instead. Like algebraic NC analyses, it derives tight bounds for some networks and valid bounds with varying accuracy for other networks. In this paper, we investigate the consequences of this tradeoff and identify a new and crucial analysis principle that allows us to compare both NC branches more comprehensively than simply ranking delay bounds.

Generalizing Network Calculus Analysis to Derive Performance Guarantees for Multicast Flows

Guaranteeing performance bounds of data flows is an essential part of network engineering and certification of networks with real-time constraints. A prevalent analytical method to derive guarantees for end-to-end delay and bu↵er size is Deterministic Network Calculus (DNC). Due to the DNC system model, one decisive restriction is that only unicast flows can be analyzed. Previous attempts to analyze networks with multicast flows circumvented this restriction instead of overcoming it. E.g., they replaced the system model with an overly-pessimistic one that consists of unicast flows only. Such approaches impair modeling accuracy and thus inevitably result in inaccurate performance bounds. In this paper, we approach the problem of multicast flows di↵erently. We start from existing DNC analyses and generalize them to handle multicast flows. We contribute a novel analysis procedure that leaves the network model unaltered, preserves its accuracy, allows for DNC principles such as pay multiplexing only once, and therefore derives more accurate performance bounds than existing approaches.

Quality and Cost of Deterministic Network Calculus: Design and Evaluation of an Accurate and Fast Analysis

Networks are integral parts of modern safety-critical systems and certification demands the provision of guarantees for data transmissions. Deterministic Network Calculus (DNC) can compute a worst-case bound on a data flows end-to-end delay. Accuracy of DNC results has been improved steadily, resulting in two DNC branches: the classical algebraic analysis (algDNC) and the more recent optimization-based analysis (optDNC). The optimization-based branch provides a theoretical solution for tight bounds. Its computational cost grows, however, (possibly super-)exponentially with the network size. Consequently, a heuristic optimization formulation trading accuracy against computational costs was proposed. In this paper, we challenge optimization-based DNC with a novel algebraic DNC algorithm. We show that: (1) no current optimization formulation scales well with the network size and (2) algebraic DNC can be considerably improved in both aspects, accuracy and computational cost. To that end, we contribute a novel DNC algorithm that transfers the optimizations search for best attainable delay bounds to algebraic DNC. It achieves a high degree of accuracy and our novel efficiency improvements reduce the cost of the analysis dramatically. In extensive numerical experiments, we observe that our delay bounds deviate from the optimization-based ones by only 1.142% on average while computation times simultaneously decrease by several orders of magnitude.

Generalized finitary real-time calculus

Real-time Calculus (RTC) is a non-stochastic queuing theory to the worst-case performance analysis of distributed real-time systems. Workload as well as resources are modelled as piece-wise linear, pseudo-periodic curves and the system under investigation is modelled as a sequence of algebraic operations over these curves. The memory footprint of computed curves increases exponentially with the sequence of operations and RTC may become computationally infeasible fast. Recently, Finitary RTC has been proposed to counteract this problem. Finitary RTC restricts curves to finite input domains and thereby counteracts the memory demand explosion seen with pseudo periodic curves of common RTC implementations. However, the proof to the correctness of Finitary RTC specifically exploits the operational semantic of the greed processing component (GPC) model and is tied to the maximum busy window size. This is an inherent limitation, which prevents a straight-forward generalization. In this paper, we provide a generalized Finitary RTC that abstracts from the operational semantic of a specific component model and reduces the finite input domains of curves even further. The novel approach allows for faster computations and the extension of the Finitary RTC idea to a much wider range of RTC models.

The Sensor Network Calculus as Key to the Design of Wireless Sensor Networks with Predictable Performance

In this article, we survey the sensor network calculus (SensorNC), a framework continuously developed since 2005 to support the predictable design, control and management of large-scale wireless sensor networks with timing constraints. It is rooted in the deterministic network calculus, which it instantiates for WSNs, as well as it generalizes it in some crucial aspects, as for instance in-network processing. Besides presenting these core concepts of the SensorNC, we also discuss the advanced concept of self-modeling of WSNs and efficient tool support for the SensorNC. Furthermore, several applications of the SensorNC methodology, like sink and node placement, as well as TDMA design, are displayed.