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Sharp bounds in stochastic network calculus
 CORR
, 2013
"... 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 typicall ..."
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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 indeed 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 disciplines. The obtained (Martingale) bounds capture an additional exponential decay factor of O e−αn in the number of flows n, and are remarkably accurate even in multiplexing scenarios with few flows.
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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Cited by 3 (3 self)
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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
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.
On Multiplexing Flows: Does it Hurt or Not?
"... Abstract—This paper analyzes queueing behavior subject to multiplexing a stochastic process M(n) of flows, and not a constant as conventionally assumed. By first considering the case when M(n) is iid, it is shown that flows ’ multiplexing ‘hurts’ the queue size (i.e., the queue size increases in dis ..."
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Abstract—This paper analyzes queueing behavior subject to multiplexing a stochastic process M(n) of flows, and not a constant as conventionally assumed. By first considering the case when M(n) is iid, it is shown that flows ’ multiplexing ‘hurts’ the queue size (i.e., the queue size increases in distribution). The simplicity of the iid case enables the quantification of the ‘best’ and ‘worst ’ distributions of M(n), i.e., minimizing/maximizing the queue size. The more general, and also realistic, case when M(n) is Markovmodulated reveals an interesting behavior: flows ’ multiplexing ‘hurts ’ but only when the multiplexed flows are sufficiently long. An important caveat raised by such observations is that the conventional approximation of M(n) by a constant can be very misleading for queueing analysis. I.
ServiceMartingales: Theory and Applications to the Delay Analysis of Random Access Protocols
"... Abstract—This paper proposes a martingale extension of effectivecapacity, a concept which has been instrumental in teletraffic theory to model the linklayer wireless channel and analyze QoS metrics. Together with a recently developed concept of an arrivalmartingale, the proposed servicemartingal ..."
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Abstract—This paper proposes a martingale extension of effectivecapacity, a concept which has been instrumental in teletraffic theory to model the linklayer wireless channel and analyze QoS metrics. Together with a recently developed concept of an arrivalmartingale, the proposed servicemartingale concept enables the queueing analysis of a bursty source sharing a MAC channel. In particular, the paper derives the first rigorous and accurate stochastic delay bounds for a Markovian source sharing either an Aloha or CSMA/CA channel, and further considers two extended scenarios accounting for 1) insource scheduling and 2) spatial multiplexing MIMO. By leveraging the powerful martingale methodology, the obtained bounds are remarkably tight and improve stateoftheart bounds by several orders of magnitude. Moreover, the obtained bounds indicate that MIMO spatial multiplexing is subject to the fundamental poweroftwo phenomena. I.
On Capacity Dimensioning in Dynamic Scenarios: The Key Role of Peak Values
"... Abstract—This paper analyzes queueing behavior in queues with a random number of parallel flows, and not static as typically assumed. By deriving upper and lower bounds on the queue size distribution, the paper identifies extremal properties in such dynamic queues. The extremal bestcase distributio ..."
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Abstract—This paper analyzes queueing behavior in queues with a random number of parallel flows, and not static as typically assumed. By deriving upper and lower bounds on the queue size distribution, the paper identifies extremal properties in such dynamic queues. The extremal bestcase distribution (minimizing the queue) is simply the constant, whereas the worstcase distribution (maximizing the queue) has a bimodal structure. From a more practical point of view, this paper highlights an idiosyncrasy of dynamic queues: unlike in static queues whereby capacity dimensioning is dominated by averagevalues (subject to certain safety margins), in dynamic queues the capacity dimensioning is dominated instead by peakvalues. I.
TOWARDS A STATISTICAL NETWORK CALCULUS– DEALING WITH UNCERTAINTY IN ARRIVALS
"... Abstract. The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In m ..."
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Abstract. The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In many situations it is hard, if possible at all to make such assumptions a priori. A more practical approach would be to base the SNC operations on measurements of the arrival processes (preferably even online). In this report, we develop this idea and incorporate measurements into the framework of SNC taking the further uncertainty resulting from estimation errors into account. This is a crucial step towards a statistical network calculus (StatNC) eventually lending itself to a selfmodelling operation of networks with a minimum of a priori assumptions. In numerical experiments, we are able to substantiate the novel opportunities by StatNC. 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.
1Towards a Statistical Network Calculus– Dealing with Uncertainty in Arrivals
"... Abstract—The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In ma ..."
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Abstract—The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In many situations it is hard, if possible at all, to make such assumptions a priori. A more practical approach would be to base the SNC operations on measurements of the arrival processes (preferably even online). In this paper, we develop this idea and incorporate measurements into the framework of SNC taking the further uncertainty resulting from estimation errors into account. This is a crucial step towards a statistical network calculus (StatNC) eventually lending itself to a selfmodelling operation of networks with a minimum of a priori assumptions. In numerical experiments, we are able to substantiate the novel opportunities by StatNC.
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.