Results 1  10
of
20
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 ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
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
"... 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 ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
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
Scheduling Analysis with Martingales
, 2014
"... This paper proposes a new characterization of queueing systems by bounding a suitable exponential transform with a martingale. The constructed martingale is quite versatile in the sense that it captures queueing systems with Markovian and autoregressive arrivals in a unified manner; the second clas ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
This paper proposes a new characterization of queueing systems by bounding a suitable exponential transform with a martingale. The constructed martingale is quite versatile in the sense that it captures queueing systems with Markovian and autoregressive arrivals in a unified manner; the second class is particularly relevant due to Wold’s decomposition of stationary processes. Moreover, using the framework of stochastic network calculus, the martingales allow for a simple handling of typical queueing operations: 1) flows’ multiplexing translates into multiplying the corresponding martingales, and 2) scheduling translates into timeshifting the martingales. The emerging calculus is applied to estimate the perflow delay for FIFO, SP, and EDF scheduling. Unlike stateoftheart results, our bounds capture a fundamental exponential leading constant in the number of multiplexed flows, and additionally are numerically tight.
Stochastic service curve and delay bound analysis: a single node case
 Computer Science from University of Kaiserslautern
, 2013
"... ar ..."
(Show Context)
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 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
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.
A MartingaleEnvelope and Applications
"... ABSTRACT In the framework of stochastic network calculus we present a new envelopebased approach which uses martingales to characterize a queueing system. We show that this setting allows a simple handling of multiplexing and scheduling: whereas multiplexing of several sources results in multiplic ..."
Abstract
 Add to MetaCart
(Show Context)
ABSTRACT In the framework of stochastic network calculus we present a new envelopebased approach which uses martingales to characterize a queueing system. We show that this setting allows a simple handling of multiplexing and scheduling: whereas multiplexing of several sources results in multiplication of the corresponding martingales, perflow analysis in a scheduled system can be done by shifting the martingales to a certain point in time. Applying this calculus to Markov Arrival Processes, it is shown that the performance bounds can become reasonably tight.
Applying Stochastic Network Calculus In Scenarios With Incomplete Knowledge
, 2013
"... The deterministic network calculus (DNC) and its probabilistic counterpart stochastic network calculus (SNC) are promising theories which provide methodologies to analyse and design networked systems. As the “little brother” of queuing theory, the main goal of network calculus has always been the w ..."
Abstract
 Add to MetaCart
The deterministic network calculus (DNC) and its probabilistic counterpart stochastic network calculus (SNC) are promising theories which provide methodologies to analyse and design networked systems. As the “little brother” of queuing theory, the main goal of network calculus has always been the wellfounded design of future networks, since its origins in the 1990’s [17]. Therefore, the analysis of a network with (S)NC is always static as it is aimed to provide (performance) guarantees for all points in time. Moreover, a complete knowledge about the system topology and structure of arrival flows is necessary in order to provide the desired bounds. However, in realworld scenarios the structure of arrivals is, in contrast to the topology, hardly known. In order to fill this gap, in this thesis a first approach for arrival estimation is proposed and interleaved with the traditional performance
On Using Storage and Genset for Mitigating Power Grid Failures
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Although modern society is critically reliant on power ..."
Abstract
 Add to MetaCart
(Show Context)
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Although modern society is critically reliant on power grids, even modern power grids are subject to unavoidable outages due to storms, lightning strikes, and equipment failures. The situation in developing countries is even worse, with frequent load shedding lasting several hours a day due to unreliable generation. We study the use of battery storage to allow a set of homes in a single residential neighbourhood to avoid power outages. Due to the high cost of storage, our goal is to choose the smallest battery size such that, with high target probability, there is no loss of power despite a grid outage. Recognizing that the most common approach today for mitigating outages is to use a diesel generator (genset), we study the related problem of minimizing the carbon footprint of genset operation. Drawing on recent results, we model both problems as buffer sizing problems that can be addressed using stochastic network calculus. We show that this approach greatly improves battery sizing in contrast to prior approaches. Specifically, a numerical study shows that, for a neighbourhood of 100 homes, our approach computes a battery size, which is less than 10 % more than the minimum possible size necessary to satisfy a one day in ten years loss probability (2.7∗104). Moreover, we are able to estimate the carbon footprint reduction, compared to an exact numerical analysis, within a factor of 1.7. We also study the genset scheduling problem when the rate of genset fuel consumption is given by an affine function instead of a linear function of the current power. We give alternate scheduling, an online scheduling strategy that has a competitive ratio of k1
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 ..."
Abstract
 Add to MetaCart
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.
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 ..."
Abstract
 Add to MetaCart
(Show Context)
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