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Stochastic Network Calculus for Performance Analysis of Internet Networks – An Overview and Outlook
"... Abstract—Stochastic network calculus is a theory for performance guarantee analysis of Internet networks. Originated in early 1990s, stochastic network calculus has its foundation on the minplus convolution and maxplus convolution queueing principles. Although challenging, it has shown tremendous ..."
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Abstract—Stochastic network calculus is a theory for performance guarantee analysis of Internet networks. Originated in early 1990s, stochastic network calculus has its foundation on the minplus convolution and maxplus convolution queueing principles. Although challenging, it has shown tremendous potential in dealing with queueing type problems encountered in Internet networks. By focusing on bounds, stochastic network calculus compliments the classical queueing theory. This paper provides an overview of stochastic network calculus from the queueing principle perspective and presents an outlook by discussing crucial yet still open challenges in the area. I.
A Guide to the Stochastic Network Calculus
"... Abstract—The aim of the stochastic network calculus is to comprehend statistical multiplexing and scheduling of nontrivial traffic sources in a framework for endtoend analysis of multinode networks. To date, several models, some of them with subtle yet important differences, have been explored t ..."
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Abstract—The aim of the stochastic network calculus is to comprehend statistical multiplexing and scheduling of nontrivial traffic sources in a framework for endtoend analysis of multinode networks. To date, several models, some of them with subtle yet important differences, have been explored to achieve these objectives. Capitalizing on previous works, this paper contributes an intuitive approach to the stochastic network calculus, where we seek to obtain its fundamental results in the possibly easiest way. For this purpose, we will now and then trade generality or precision for simplicity. In detail, the method that is assembled in this work uses moment generating functions, known from the theory of effective bandwidths, to characterize traffic arrivals and network service. Thereof, affine envelope functions with exponentially decaying overflow profile are derived to compute statistical endtoend backlog and delay bounds for networks. I.
A leftover service curve approach to analyze demultiplexing in queueing networks
 in Proc. of VALUETOOLS
, 2012
"... Abstract—Queueing networks are typically subject to demultiplexing operations, whereby network nodes split flows into multiple subflows. The demultiplexing operation captures relevant network aspects such as packet loss or multipath routing. In this paper we propose a novel approach to analyze q ..."
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Abstract—Queueing networks are typically subject to demultiplexing operations, whereby network nodes split flows into multiple subflows. The demultiplexing operation captures relevant network aspects such as packet loss or multipath routing. In this paper we propose a novel approach to analyze queueing networks with demultiplexing. The basic idea is to represent a network node implementing a demultiplexing operation on an output flow as an equivalent system for which the corresponding input flow is logically demultiplexed according to the demultiplexing operation at the output. In this way, the service given to one of the demultiplexed subflows at the output can be expressed in terms of a leftover service curve, and consequently performance bounds can be derived using the network calculus methodology. Using numerical illustrations, we show that the obtained bounds improve upon existing bounds, especially in the case of the rather small subflows. Index Terms—Demultiplexing, network calculus, leftover service, scaling element.
The DISCO Stochastic Network Calculator Version 1.0  When Waiting Comes to an End
 In ValueTools
, 2013
"... The stochastic network calculus (SNC) is a recent methodology to analyze queueing systems in terms of probabilistic performance bounds. It complements traditional queueing theory and features support for a large set of traffic arrivals as well as different scheduling algorithms. So far, there had ..."
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The stochastic network calculus (SNC) is a recent methodology to analyze queueing systems in terms of probabilistic performance bounds. It complements traditional queueing theory and features support for a large set of traffic arrivals as well as different scheduling algorithms. So far, there had been no tool support for SNC analyses. Therefore, we present the DISCO Stochastic Network Calculator (DISCOSNC) version 1.0, a Java library supporting the modelling and analysis of feedforward queueing networks using the SNC. The DISCOSNC allows to calculate probabilistic delay and backlog bounds given a feedforward topology consisting of workconserving servers and a set of flows traversing the network. While the DISCOSNC is still in its infancy it is designed in a modular fashion to allow for an easy extension of, e.g., traffic types and scheduling algorithms; furthermore, it performs the optimization of free parameters as they usually appear during SNC analyses due to the application of the Chernoff bound or Hölder inequality. Apart from this core functionality, the DISCOSNC also provides a flexible GUI to make the SNC accessible even for SNCunexperienced users.
Performance of innetwork processing for visual analysis in wireless sensor networks
"... AbstractNodes in a sensor network are traditionally used for sensing and data forwarding. However, with the increase of their computational capability, they can be used for innetwork data processing, leading to a potential increase of the quality of the networked applications as well as the netwo ..."
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AbstractNodes in a sensor network are traditionally used for sensing and data forwarding. However, with the increase of their computational capability, they can be used for innetwork data processing, leading to a potential increase of the quality of the networked applications as well as the network lifetime. Visual analysis in sensor networks is a prominent example where the processing power of the network nodes needs to be leveraged to meet the frame rate and the processing delay requirements of common visual analysis applications. The modeling of the endtoend performance for such networks is, however, challenging, because innetwork processing violates the flow conservation law, which is the basis for most queuing analysis. In this work we propose to solve this methodological challenge through appropriately scaling the arrival and the service processes, and we develop probabilistic performance bounds using stochastic network calculus. We use the developed model to determine the main performance bottlenecks of networked visual processing. Our numerical results show that an endtoend delay of 23 frame length is obtained with violation probability in the order of 10 −6 . Simulation shows that the obtained bounds overestimates the endtoend delay by no more than 10%.
Capacity–Delay–Error Boundaries: A Composable Model of Sources and Systems
"... Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sustain certain statistical delay guarantees with a small probability of error. We use a stochastic nonequilibr ..."
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Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sustain certain statistical delay guarantees with a small probability of error. We use a stochastic nonequilibrium approach that models the variability of traffic and service to formalize the influence of delay constraints on the effective capacity. Permitting unbounded delays, known ergodic capacity results from information theory are recovered in the limit. We prove that the model has the property of additivity, which enables composing CDE boundaries obtained for sources and systems as if in isolation. A method for construction of CDE boundaries is devised based on momentgenerating functions, which includes the large body of results from the theory of effective bandwidths. Solutions for essential sources, channels, and respective coders are derived, including Huffman coding, MPEG video, Rayleigh fading, and hybrid automatic repeat request. Results for tandem channels and for the composition of sources and channels are shown. Index Terms—Queueing analysis, information theory, channel models, time varying channels, quality of service. I.
1Delay Bounds Calculus for Variable Length Packet Transmissions under Flow Transformations
"... Abstract—A fundamental contribution of network calculus is the con volutionform representation of networks which enables tight endtoend delay bounds. Recently, this has been extended to the case where the data flow is subject to transformations on its way to the destination. Yet, the extension, ..."
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Abstract—A fundamental contribution of network calculus is the con volutionform representation of networks which enables tight endtoend delay bounds. Recently, this has been extended to the case where the data flow is subject to transformations on its way to the destination. Yet, the extension, based on socalled scaling elements, only applies to a setting of identically sized data units, e.g., bits. In practice, of course, one often has to deal with variablelength packets. Therefore, in this paper, we address this case and propose two novel methods to derive delay bounds for variablelength packets subject to flow transformations. One is a relatively direct extension of existing work and the other one represents a more detailed treatment of packetization effects. In a numerical evaluation, we show the clear superiority of the latter one and also validate the bounds by simulation results. I.
Window Flow Control in Stochastic Network Calculus
"... Abstract. Feedback is omnipresent in communication networks. One prominent example is window flow control (WFC) as, e.g., found in many transport protocols, for instance TCP. In deterministic network calculus elegant closedform solutions have been derived to provide performance bounds for WFC syst ..."
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Abstract. Feedback is omnipresent in communication networks. One prominent example is window flow control (WFC) as, e.g., found in many transport protocols, for instance TCP. In deterministic network calculus elegant closedform solutions have been derived to provide performance bounds for WFC systems. However, a treatment of WFC in stochastic network calculus (SNC) has so far been elusive. In this work, we present the first WFC analysis in SNC for subadditive and general service in the feedback loop. The subadditive case turns out as an application of existing results, switching to continuous time requires more effort. We further discuss how the condition of subadditivity is preserved under concatenation of servers and demultiplexing of flows. The key idea for the general case is to keep track of how much the service deviates from being subadditive. Both methods are illustrated in numerical examples and their properties are discussed. CHAPTER 1
Performance Modelling and Analysis of Unreliable Links with Retransmissions using Network Calculus
"... Abstract—During the last two decades, starting with the seminal work by Cruz, network calculus has evolved as an elegant system theory for the performance analysis of networked systems. It has found numerous usages as, for example, in QoSenabled networks, wireless sensor networks, switched Ethernet ..."
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Abstract—During the last two decades, starting with the seminal work by Cruz, network calculus has evolved as an elegant system theory for the performance analysis of networked systems. It has found numerous usages as, for example, in QoSenabled networks, wireless sensor networks, switched Ethernets, avionic networks, SystemsonChip, or, even to speedup simulations. One of the basic assumptions in network calculus is that links are reliable and operate lossfree. This, of course, is a major abstraction from the reality of many application scenarios, where links are unreliable and often use retransmission schemes to recover from packet losses. As of today, standard network calculus cannot analyze such links. In this paper, we take the challenge to extend the reach of network calculus to unreliable links which employ retransmissionbased loss recovery schemes. Key to this is a stochastic extension of the known data scaling element in network calculus [21], which can capture the loss process of an unreliable link. Based on this, modelling links with retransmissions results in a set of equations which are amenable to a fixedpoint solution. This allows to find the arrival constraints of each flow that corresponds to a certain number of retransmissions. Based on the description of each retransmission flow, probabilistic performance bounds can be derived. After providing the necessary theory, we illustrate this novel and important extension of network calculus with the aid of a numerical example.
EndtoEnd Delay Bounds for Variable Length Packet Transmissions under Flow Transformations
"... A fundamental contribution of network calculus is the convolutionform representation of networks which enables tight endtoend delay bounds. Recently, this has been extended to the case where the data flow is subject to transformations on its way to the destination. Yet, the extension, based on s ..."
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A fundamental contribution of network calculus is the convolutionform representation of networks which enables tight endtoend delay bounds. Recently, this has been extended to the case where the data flow is subject to transformations on its way to the destination. Yet, the extension, based on socalled scaling elements, only applies to a setting of identically sized data units, e.g., bits. In practice, of course, one often has to deal with variablelength packets. Therefore, in this paper, we address this case and propose two novel methods to derive delay bounds for variablelength packets subject to flow transformations. One is a relatively direct extension of existing work and the other one represents a more detailed treatment of packetization effects. In a numerical evaluation, we show the clear superiority of the latter one and also validate the bounds by simulation results.