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36
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
On Superlinear Scaling of Network Delays
"... We investigate scaling properties of endtoend delays in packet networks for a flow that traverses a sequence of H nodes and that experiences cross traffic at each node. When the traffic flow and the cross traffic do not satisfy independence assumptions, we find that delay bounds scale faster than ..."
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Cited by 14 (7 self)
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We investigate scaling properties of endtoend delays in packet networks for a flow that traverses a sequence of H nodes and that experiences cross traffic at each node. When the traffic flow and the cross traffic do not satisfy independence assumptions, we find that delay bounds scale faster than linearly. More precisely, for exponentially bounded packetized traffic we show that delays grow with Θ(H log H) in the number of nodes on the network path. This superlinear scaling of delays is qualitatively different from the scaling behavior predicted by a worstcase analysis or by a probabilistic analysis assuming independence of traffic arrivals at network nodes.
Delay bounds in communication networks with heavytailed and selfsimilar traffic
 IEEE Transactions on Information Theory
, 2012
"... Traffic with selfsimilar and heavytailed characteristics has been widely reported in communication networks, yet, the stateoftheart of analytically predicting the delay performance of such networks is lacking. We address a particularly difficult type of heavytailed traffic where only the first ..."
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Cited by 12 (3 self)
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Traffic with selfsimilar and heavytailed characteristics has been widely reported in communication networks, yet, the stateoftheart of analytically predicting the delay performance of such networks is lacking. We address a particularly difficult type of heavytailed traffic where only the first moment can be computed, and present nonasymptotic endtoend delay bounds for such traffic. The derived performance bounds are nonasymptotic in that they do not assume a steady state, large buffer, or many sources regime. The analysis follows a network calculus approach where traffic is characterized by envelope functions and service is described by service curves. Our analysis considers a multihop path of fixedcapacity links with heavytailed selfsimilar cross traffic at each node. A key contribution of the analysis is a novel probabilistic samplepath bound for heavytailed arrival and service processes, which is based on a scalefree sampling method. We explore how delays scale as a function of the length of the path, and compare them with lower bounds. A comparison with simulations illustrates pitfalls when simulating selfsimilar heavytailed traffic, providing further evidence for the need of analytical bounds. I.
Network calculus and queueing theory: two sides of one coin
 in Proc. 4th International Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS
, 2009
"... Network calculus is a theory dealing with queueing type problems encountered in computer networks, with particular focus on quality of service guarantee analysis. Queueing theory is the mathematical study of queues, proven to be applicable to a wide area of problems, generally concerning about the ( ..."
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Cited by 11 (5 self)
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Network calculus is a theory dealing with queueing type problems encountered in computer networks, with particular focus on quality of service guarantee analysis. Queueing theory is the mathematical study of queues, proven to be applicable to a wide area of problems, generally concerning about the (average) quantities in an equilibrium state. Since both network calculus and queueing theory are analytical tools for studying queues, a question arises naturally as is if and where network calculus and queueing theory meet. In this paper, we explore queueing principles that underlie network calculus and exemplify their use. Particularly, based on the network calculus queueing principles, we show that for GI/GI/1, similar inequalities in the theory of queues can be derived. In addition, we prove that the endtoend performance of a tandem network is independent of the order of servers in the network even under some general settings. Through these, we present a network calculus perspective on queues and relate network calculus to queueing theory. 1.
On Theta (H log H) scaling of network delays
 in Proc. of IEEE INFOCOM
"... Abstract — A recent result in network calculus theory provided statistical delay bounds for exponentially bounded traffic that grow as O(H log H) with the number of nodes on the network path. 1 In this paper we establish the corresponding lower bound which shows that under these assumptions, typical ..."
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Cited by 8 (7 self)
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Abstract — A recent result in network calculus theory provided statistical delay bounds for exponentially bounded traffic that grow as O(H log H) with the number of nodes on the network path. 1 In this paper we establish the corresponding lower bound which shows that under these assumptions, typical endtoend delays can indeed grow as Θ (H log H). The lower bound is obtained by analyzing the endtoend delay in a tandem network. A critical assumption is that each packet maintains the same service time at each traversed node. The results of this paper provide conclusive evidence that, in general, delays have a qualitatively different scaling behavior than is suggested by a worstcase analysis or by assuming independence on the service obtained at network nodes. I.
A Foundation for Stochastic Bandwidth Estimation of Networks with Random Service
, 1008
"... We develop a stochastic foundation for bandwidth estimation of networks with random service, where bandwidth availability is expressed in terms of bounding functions with a defined violation probability. Exploiting properties of a stochastic maxplus algebra and system theory, the task of bandwidth ..."
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Cited by 7 (3 self)
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We develop a stochastic foundation for bandwidth estimation of networks with random service, where bandwidth availability is expressed in terms of bounding functions with a defined violation probability. Exploiting properties of a stochastic maxplus algebra and system theory, the task of bandwidth estimation is formulated as inferring an unknown bounding function from measurements of probing traffic. We derive an estimation methodology that is based on iterative constant rate probes. Our solution provides evidence for the utility of packet trains for bandwidth estimation in the presence of variable cross traffic. Taking advantage of statistical methods, we show how our estimation method can be realized in practice, with adaptive train lengths of probe packets, probing rates, and replicated measurements required to achieve both high accuracy and confidence levels. We evaluate our method in a controlled testbed network, where we show the impact of cross traffic variability on the timescales of service availability, and provide a comparison with existing bandwidth estimation tools. 1
Scaling Properties in the Stochastic Network Calculus
, 2007
"... Modern networks have become increasingly complex over the past years in terms of control algorithms, applications and service expectations. Since classical theories for the analysis of telephone networks were found inadequate to cope with these complexities, new analytical tools have been conceived ..."
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Cited by 6 (2 self)
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Modern networks have become increasingly complex over the past years in terms of control algorithms, applications and service expectations. Since classical theories for the analysis of telephone networks were found inadequate to cope with these complexities, new analytical tools have been conceived as of late. Among these, the stochastic network calculus has given rise to the optimism that it can emerge as an elegant mathematical tool for assessing network performance. This thesis argues that the stochastic network calculus can provide new analytical insight into the scaling properties of network performance metrics. In this sense it is shown that endtoend delays grow as Θ(H log H) in the number of network nodes H, as opposed to the Θ(H) order of growth predicted by other theories under simplifying assumptions. It is also shown a comparison between delay bounds obtained with the stochastic network calculus and exact results available in some productform queueing networks. The main technical contribution of this thesis is a construction of a statistical network service curve that expresses the service given to a flow by a network as if the flow traversed a single node only. This network service curve enables the proof of the O(H log H) scaling
An Analysis on Error Servers for Stochastic Network Calculus
"... Abstract—Network calculus is a recently developed theory dealing with queuing systems found in computer networks with focus on service guarantee analysis. In the current network calculus literature, the behavior of a server is typically modeled with the cumulative amount of service it successfully d ..."
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Abstract—Network calculus is a recently developed theory dealing with queuing systems found in computer networks with focus on service guarantee analysis. In the current network calculus literature, the behavior of a server is typically modeled with the cumulative amount of service it successfully delivers, and the successfulness of service delivery implies no error in the delivered service. However, there are many networks such as wireless networks, where, not only is the service prone to error due to multiaccess contention and/or random error on the communication link, but different error handling methods may also be applied. In such cases, it is difficult to directly apply the existing network calculus results due to lack of server models taking error into account. In this paper, an error server model is proposed for stochastic network calculus, based on which, an analysis on error servers is performed. Particularly, the corresponding concatenation property is derived, which shows that under some general conditions, the tandem of error servers can be treated as an equivalent error server. In addition, to demonstrate the use and implication of the proposed error server model, performance bounds are derived and compared for a simple network. The study of the simple network shows that error handling may have significant impact on the performance bounds, and the proposed error server model can facilitate the analysis. I.
Sharp PerFlow Delay Bounds for Bursty Arrivals: The Case of FIFO, SP, and EDF Scheduling
"... Abstract—The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper, it is uncovered that for bursty arrival processes (specifically MarkovModulated OnOff (MMOO)), whose amenability to perflow analysis i ..."
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Abstract—The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper, it is uncovered that for bursty arrival processes (specifically MarkovModulated OnOff (MMOO)), whose amenability to perflow analysis is typically proclaimed as a highlight of SNC, the bounds can unfortunately be very loose (e.g., by several orders of magnitude off). In response to this uncovered weakness of SNC, the (Standard) perflow bounds are herein improved by deriving a general samplepath bound, using martingale based techniques, which accommodates FIFO, SP, and EDF scheduling. The obtained (Martingale) bounds capture an extra exponential decay factor of O
On the Delay Performance Analysis in A LargeScale Wireless Sensor Network
"... Abstract—We present a comprehensive delay performance measurement and analysis in an operational largescale urban wireless sensor network. We build a lightweight delay measurement system in such a network and present a robust method to calculate perpacket delay. Through analysis of delay and syst ..."
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Abstract—We present a comprehensive delay performance measurement and analysis in an operational largescale urban wireless sensor network. We build a lightweight delay measurement system in such a network and present a robust method to calculate perpacket delay. Through analysis of delay and system metrics, we seek to answer the following fundamental questions: what are the spatial and temporal characteristics of delay performance in a real network? what are the most important impacting factors and is there any practical model to capture those factors? what are the implications to protocol design? In this paper, we explore the important factors from the data in presence of various metrics and randomness, and show that the important factors are not necessarily the same with that in Internet. Further, we propose a delay model to capture those factors and validate it in the network. We revisit several prevalent protocol designs such as Collection Tree Protocol, opportunistic routing and Dynamic Switching based Forwarding, and show the implications to protocol designs. I.