Results 1  10
of
14
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 ..."
Abstract

Cited by 20 (11 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
(Show Context)
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.
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.
On the scaling of nonasymptotic capacity in multiaccess networks with bursty traffic
 IN PROC. IEEE ISIT
, 2011
"... The practicality of available (throughput) capacity results in multiaccess networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these li ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
The practicality of available (throughput) capacity results in multiaccess networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these limitations by providing capacity results in nonasymptotic regimes, i.e., holding at all time scales and network sizes, for the very broad class of exponentially bounded burstiness (EBB) traffic sources. Both upper and lower bounds on capacity are derived in terms of probability distributions, which immediately yield all the moments. The explicit and closedform nature of the results enable the investigation of the impact of burstiness on nonasymptotic network capacity. In particular, the results show that for the EBB class the nonasymptotic endtoend capacity rate decays linearly in the number of hops.
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
(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 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
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
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.
On the catalyzing effect of randomness on the perflow throughput in wireless networks
, 2013
"... This paper investigates the throughput capacity of a flow crossing a multihop wireless network, whose geometry is characterized by general randomness laws including Uniform, Poisson, HeavyTailed distributions for both the nodes ’ densities and the number of hops. The key contribution is to demons ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
This paper investigates the throughput capacity of a flow crossing a multihop wireless network, whose geometry is characterized by general randomness laws including Uniform, Poisson, HeavyTailed distributions for both the nodes ’ densities and the number of hops. The key contribution is to demonstrate how the perflow throughput depends on the distribution of 1) the number of nodes Nj inside hops ’ interference sets, 2) the number of hops K, and 3) the degree of spatial correlations. The randomness in both Nj ’s and K is advantageous, i.e., it can yield larger scalings (as large as Θ(n)) than in nonrandom settings. An interesting consequence is that the perflow capacity can exhibit the opposite behavior to the network capacity, which was shown to suffer from a logarithmic decrease in the presence of randomness. In turn, spatial correlations along the endtoend path are detrimental by a logarithmic term.
Stochastic service curve and delay bound analysis: a single node case
 Computer Science from University of Kaiserslautern
, 2013
"... ar ..."
(Show Context)
Robust Queueing Theory
 SUBMITTED TO OPERATIONS RESEARCH
"... We propose an alternative approach for studying queueing systems by employing robust optimization as opposed to stochastic analysis. While traditional stochastic queueing theory relies on Kolmogorov’s axioms of probability and models arrivals and services as renewal processes, we use the limit laws ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We propose an alternative approach for studying queueing systems by employing robust optimization as opposed to stochastic analysis. While traditional stochastic queueing theory relies on Kolmogorov’s axioms of probability and models arrivals and services as renewal processes, we use the limit laws of probability as the axioms of our methodology and model the queueing systems primitives by uncertainty sets. In this framework, we obtain closed form expressions for the steadystate waiting times in multiserver queues with heavytailed arrival and service processes. These expressions are not available under traditional stochastic queueing theory for heavytailed processes, while they lead to the same qualitative insights for independent and identically distributed arrival and service times. We also develop an exact calculus for analyzing a network of queues with multiple servers based on the following key principle: a) the departure from a queue, b) the superposition, and c) the thinning of arrival processes have the same uncertainty set representation as the original arrival processes. We show that our approach, which we call the Robust Queueing Network Analyzer (RQNA) a) yields results with error percentages in single digits (for all experiments we performed) relative to simulation, b) performs significantly better than the Queueing Network Analyzer (QNA) proposed in Whitt (1983), and c) is to a large extent insensitive to the number of servers per queue, the network size, degree of feedback, traffic intensity, and somewhat sensitive to the degree of diversity of external arrival distributions in the network.
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