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22
Perspectives on Network Calculus  No Free Lunch, but Still Good Value
, 2012
"... 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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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 expressing networks with flow transformation in convolutionform
 In Proceedings of IEEE INFOCOM
, 1979
"... Abstract—Convolutionform networks have the property that the endtoend service of network flows can be expressed in terms of a (min;+)convolution of the pernode services. This property is instrumental for deriving endtoend queueing results which fundamentally improve upon alternative results d ..."
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Abstract—Convolutionform networks have the property that the endtoend service of network flows can be expressed in terms of a (min;+)convolution of the pernode services. This property is instrumental for deriving endtoend queueing results which fundamentally improve upon alternative results derived by a nodebynode analysis. This paper extends the class of convolutionform networks with stochastic settings to scenarios with flow transformations, e.g., by loss, dynamic routing or retransmissions. In these networks, it is shown that by using the tools developed in this paper endtoend delays grow as O(n) in the number of nodes n; in contrast, by using the alternative nodebynode analysis, endtoend delays grow as O (n2). I.
1 Characterizing the Impact of the Workload on the Value of Dynamic Resizing in Data Centers
"... Abstract—Energy consumption imposes a significant cost for data centers; yet much of that energy is used to maintain excess service capacity during periods of predictably low load. Resultantly, there has recently been interest in developing designs that allow the service capacity to be dynamically r ..."
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Abstract—Energy consumption imposes a significant cost for data centers; yet much of that energy is used to maintain excess service capacity during periods of predictably low load. Resultantly, there has recently been interest in developing designs that allow the service capacity to be dynamically resized to match the current workload. However, there is still much debate about the value of such approaches in real settings. In this paper, we show that the value of dynamic resizing is highly dependent on statistics of the workload process. In particular, both slow timescale nonstationarities of the workload (e.g., the peaktomean ratio) and the fast timescale stochasticity (e.g., the burstiness of arrivals) play key roles. To illustrate the impact of these factors, we combine optimizationbased modeling of the slow timescale with stochastic modeling of the fast time scale. Within this framework, we provide both analytic and numerical results characterizing when dynamic resizing does (and does not) provide benefits.
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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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.
Nonasymptotic throughput and delay distributions in multihop wireless networks
 In Allerton Conference on Communications, Control and Computing
, 2010
"... Abstract—The class of GuptaKumar results give the asymptotic throughput in multihop wireless networks but cannot predict the throughput behavior in networks of typical size. This paper addresses the nonasymptotic analysis of the multihop wireless communication problem and provides, for the firs ..."
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Abstract—The class of GuptaKumar results give the asymptotic throughput in multihop wireless networks but cannot predict the throughput behavior in networks of typical size. This paper addresses the nonasymptotic analysis of the multihop wireless communication problem and provides, for the first time, closedform results on multihop throughput and delay distributions. The results are nonasymptotic in that they hold for any number of nodes and also fully account for transient regimes, i.e., finite time scales, delays, as well as bursty arrivals. Their accuracy is supported by the recovery of classical singlehop results, and also by simulations from empirical data sets with realistic mobility settings. Moreover, for a specific network scenario and a fixed pair of nodes, the results confirm GuptaKumar’s Ω
On the Model Transform in Stochastic Network Calculus
"... Stochastic network calculus requires special care in the search of proper stochastic traffic arrival models and stochastic service models. Tradeoff must be considered between the feasibility for the analysis of performance bounds, the usefulness of performance bounds, and the ease of their numerical ..."
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Stochastic network calculus requires special care in the search of proper stochastic traffic arrival models and stochastic service models. Tradeoff must be considered between the feasibility for the analysis of performance bounds, the usefulness of performance bounds, and the ease of their numerical calculation. In theory, transform between different traffic arrival models and transform between different service models are possible. Nevertheless, the impact of the model transform on performance bounds has not been thoroughly investigated. This paper is to investigate the effect of the model transform and to provide practical guidance in the model selection in stochastic network calculus.
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 Case for Decomposition of FIFO Networks
"... Recent studies showing that the output of traffic flows at packet switches has similar characteristics as the corresponding input enables a decomposition analysis of a network where nodes can be studied in isolation, thus simplifying an endtoend analysis of networks. However, network decomposition ..."
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Recent studies showing that the output of traffic flows at packet switches has similar characteristics as the corresponding input enables a decomposition analysis of a network where nodes can be studied in isolation, thus simplifying an endtoend analysis of networks. However, network decomposition results available today are mostly manysources asymptotics. In this paper we explore the viability of network decomposition in a nonasymptotic regime with a finite number of flows. For traffic with Exponentially Bounded Burstiness (EBB) we derive statistical bounds for the output traffic at a FIFO buffer and compare them with bounds on the input. Evaluating the accuracy of the output bounds with exact results available for special cases and by numerical illustrations we find that conditions for network decomposition appear favorable even if the number of flows is relatively small.
Sharp PerFlow Delay Bounds for Bursty Arrivals: The Case of FIFO, SP, and EDF Scheduling
"... 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 typica ..."
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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
Exponential Supermartingales for Evaluating EndtoEnd Backlog Bounds
, 2007
"... A common problem arising in network performance analysis with the stochastic network calculus is the evaluation of (min, +) convolutions. This paper presents a method to solve this problem by applying a maximal inequality to a suitable constructed supermartingale. For a network with D/M input, endt ..."
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A common problem arising in network performance analysis with the stochastic network calculus is the evaluation of (min, +) convolutions. This paper presents a method to solve this problem by applying a maximal inequality to a suitable constructed supermartingale. For a network with D/M input, endtoend backlog bounds obtained with this method improve existing results at low utilizations. For the same network, it is shown that at utilizations smaller than a certain threshold, fluidflow models may lead to inaccurate approximations of packetized models.