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28
A Comprehensive WorstCase Calculus for Wireless Sensor Networks with
 InNetwork Processing,” in Proc. IEEE RTSS
, 2007
"... Today’s wireless sensor networks (WSN) focus on energyefficiency as the main metric to optimize. However, an increasing number of scenarios where sensor networks are considered for timecritical purposes in application scenarios like intrusion detection, industrial monitoring, or health care syste ..."
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Cited by 23 (8 self)
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Today’s wireless sensor networks (WSN) focus on energyefficiency as the main metric to optimize. However, an increasing number of scenarios where sensor networks are considered for timecritical purposes in application scenarios like intrusion detection, industrial monitoring, or health care systems demands for an explicit support of performance guarantees in WSNs and, thus, in turn for a respective mathematical framework. In [1], a sensor network calculus was introduced in order to accommodate a worstcase analysis of WSNs. This sensor network calculus focused on the communication aspect in WSNs, but had not yet a possibility to treat innetwork processing in WSNs. In this work, we now incorporate innetwork processing features as they are typical for WSNs by taking into account computational resources on the sensor nodes. Furthermore, we propose a simple, yet effective priority queue management discipline which achieves a good balance of response times across sensor nodes in the field. 1.
Perspectives on Network Calculus – No Free Lunch, but Still Good Value
"... ACM Sigcomm 2006 published a paper [26] which was perceived to unify the deterministic and stochastic branches of the network calculus (abbreviated throughout as DNC and SNC) [39]. Unfortunately, this seemingly fundamental unification—which has raised the hope of a straightforward transfer of all re ..."
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Cited by 19 (11 self)
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ACM Sigcomm 2006 published a paper [26] which was perceived to unify the deterministic and stochastic branches of the network calculus (abbreviated throughout as DNC and SNC) [39]. Unfortunately, this seemingly fundamental unification—which has raised the hope of a straightforward transfer of all results from DNC to SNC—is invalid. To substantiate this claim, we demonstrate that for the class of stationary andergodic processes, whichis prevalentin traffic modelling, the probabilistic arrival model from [26] is quasideterministic, i.e., the underlying probabilities are either zero or one. Thus, the probabilistic framework from [26] is unable to account for statistical multiplexing gain, which is in fact the raison d’être of packetswitched networks. Other previous formulations of SNC can capture statistical multiplexing
E.: Tight performance bounds in the worstcase analysis of feedforward networks
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Validating the Sensor Network Calculus by Simulations
 In Proceedings of the 2nd Performance Control in Wireless Sensor Networks Workshop at the 2007 WICON Conference
, 2007
"... Network Calculus has been proposed and customized as a framework for worstcase analysis in wireless sensor networks (WSNs). It has been demonstrated that this socalled Sensor Network Calculus (SNC) is an effective network dimensioning tool as it allows us to calculate maximum message transfer dela ..."
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Cited by 5 (2 self)
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Network Calculus has been proposed and customized as a framework for worstcase analysis in wireless sensor networks (WSNs). It has been demonstrated that this socalled Sensor Network Calculus (SNC) is an effective network dimensioning tool as it allows us to calculate maximum message transfer delays and communication related energy consumption patterns before network deployment. So far it is unclear how the SNC calculated worstcase delay bounds compare to values experienced in real deployments. Our experiments presented in this paper show that an SNC worstcase delay prediction can be as little as 2.7 % above the measured worstcase delay in a typical application scenario. Thus, it can be concluded that the SNC has a very practical relevance for dimensioning wireless sensor networks.
The DISCO Network Calculator
"... Network calculus [1, 2] was developed for use in IP and ATM networks. It aims to be a system theory for deterministic queuing, allowing to derive deterministic guarantees on throughput and delay, as well as find bounds on buffer sizes and thereby allow for lossfree transfer. Traditional queuing the ..."
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Cited by 4 (2 self)
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Network calculus [1, 2] was developed for use in IP and ATM networks. It aims to be a system theory for deterministic queuing, allowing to derive deterministic guarantees on throughput and delay, as well as find bounds on buffer sizes and thereby allow for lossfree transfer. Traditional queuing theory analyzes the average or equilibrium behavior of a network, whereas network calculus shows the worst observable case. It describes network traffic and services in terms of curves, widesense increasing functions that represent accumulated data. By using a minplus algebra, replacing the addition and multiplication in (R,+,·) by minimum and addition (R,min,+), it avoids nonlinearities in the required operations on those curves. Similar to traditional system theory, network calculus provides a concatenation result, thereby making it possible to reduce tandems of systems (respective services) to a single equivalent service. An extension of the network calculus, the sensor network calculus [3], provides results for handling crosstraffic in networks with tree topologies that are typical for sensor networks. More recent results handle effects like data scaling, which is an effect in networks that not only forward data, but also mutate it along the path. This may be
The PEGASE project: precise and scalable temporal analysis for aerospace communication systems with network calculus
 In: 4th Intl Symp. On Leveraging Applications of Formal Methods (ISoLA 2010), LNCS
, 2010
"... Abstract. With the increase of critical data exchanges in embedded realtime systems, the computation of tight upper bounds on network traversal times is becoming a crucial industrial need especially in safety critical systems. To address this need, the French project PEGASE grouping academics and ..."
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Cited by 4 (2 self)
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Abstract. With the increase of critical data exchanges in embedded realtime systems, the computation of tight upper bounds on network traversal times is becoming a crucial industrial need especially in safety critical systems. To address this need, the French project PEGASE grouping academics and industrial partners from the aerospace field has been undertaken to improve some key aspects of the Network Calculus and its implementation. 1
Network calculus: Application to switched realtime networking
 In 5th International ICST Conference on Performance Evaluation Methodologies and Tools, ValueTools
, 2011
"... In this paper, we show how Network Calculus can be used to determine whether a switched network may satisfy the time constraints of a realtime application. If switched architecture are interesting in the sense that they offer flexible design and may eliminate collisions in Ethernetbased network, ..."
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Cited by 4 (0 self)
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In this paper, we show how Network Calculus can be used to determine whether a switched network may satisfy the time constraints of a realtime application. If switched architecture are interesting in the sense that they offer flexible design and may eliminate collisions in Ethernetbased network, they are not guaranteeing endtoend performances (in particular in terms of delay), especially when crosstraffic are present. We illustrate Network Calculus usefulness by showing how the internal switching structure of an Ethernet switch simplify the analysis and which kind of traffic interdependencies are problematic.
Does Link Scheduling Matter on Long Paths?
 INTERNATIONAL CONFERENCE ON DISTRIBUTED COMPUTING SYSTEMS
, 2010
"... We seek to provide an analytical answer whether the impact of the selection of link scheduling algorithms diminishes on long network paths. The answer is provided through a detailed multinode delay analysis, which is applicable to a broad class of scheduling algorithms, and which can account for st ..."
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Cited by 3 (3 self)
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We seek to provide an analytical answer whether the impact of the selection of link scheduling algorithms diminishes on long network paths. The answer is provided through a detailed multinode delay analysis, which is applicable to a broad class of scheduling algorithms, and which can account for statistical multiplexing. The analysis is enabled by two contributions: (1) We derive a function that can characterize the available bandwidth at a node for various scheduling algorithms. The function has an accuracy that recovers necessary and sufficient conditions for satisfying worstcase delay bounds at a single node; (2) We obtain endtoend delay bounds by providing an explicit solution to an optimization problem, in which the service received at multiple nodes is subsumed into a single function. By presenting a unified analysis that captures the properties of a broad group of schedulers in a single parameter, we can provide insight how the choice of scheduling algorithms impacts endtoend delay bounds. An important finding of this paper is that some schedulers show noticeable performance differences which persist in a network setting with long paths.
Computation of a (min,+) multidimensional convolution for endtoend performance analysis
 In Proceedings of Valuetools’2008
, 2008
"... performance analysis. ..."
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Exact Worstcase Delay for FIFOmultiplexing
"... Abstract—This paper computes the actual worstcase endtoend delay for a flow in a tandem of FIFO multiplexing service curve nodes, where flows are shaped by concave, piecewise linear arrival curves, and service curves are convex and piecewise linear. Previous works only computed bounds on the abov ..."
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Cited by 1 (0 self)
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Abstract—This paper computes the actual worstcase endtoend delay for a flow in a tandem of FIFO multiplexing service curve nodes, where flows are shaped by concave, piecewise linear arrival curves, and service curves are convex and piecewise linear. Previous works only computed bounds on the above quantity, which are not always tight. We show that the solution entails taking the maximum among the optimal solution of a number of Linear Programming problems. However, the number and size of LP problems grows exponentially with the tandem length. Furthermore, we present approximate solution schemes to find both upper and lower delay bounds on the worstcase delay. Both of them only require to solve just one LP problem, and they produce bounds which are generally more accurate than those found in the previous work. Finally, we elaborate on how the worstcase scenario should be constructed. I.