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## H-Probe: Estimating Traffic Correlations from Sampling and Active Network Probing

### Citations

3977 |
Handbook of Mathematical Functions
- ABRAMOWITZ, STEGUN
- 1965
(Show Context)
Citation Context ... obtained using this software package. Fig. 7 depicts the experimental setup in our Emulab-based testbed4. The topology comprises two relevant links, denoted link 1 and 2. Two traffic senders Si, i ∈ =-=[1, 2]-=- transmit LRD cross traffic traces with defined Hurst parameter H to the receivers Ri. The traces were synthesized by superposition of 105 heavy tailed on-off sources with tail index α. The relation b... |

2207 | On the selfsimilar nature of ethernet traffic
- Leland, Taqqu, et al.
- 1995
(Show Context)
Citation Context ...comprehensive measurement studies, based on recorded network traces, have revealed that aggregate Internet traffic possesses long memory correlations, so-called long range dependence (LRD) [8], [12], =-=[19]-=-, [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], [25], [26], [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally differen... |

1769 | Wide-Area Traffic: The Failure of Poisson Modeling
- Paxson
- 1995
(Show Context)
Citation Context ...hensive measurement studies, based on recorded network traces, have revealed that aggregate Internet traffic possesses long memory correlations, so-called long range dependence (LRD) [8], [12], [19], =-=[30]-=-. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], [25], [26], [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally different beha... |

1413 | Self-similarity in world wide web traffic, evidence and possible causes. Sigmetrics - Crovella, Bestavros - 1996 |

1033 |
Statistics for long-memory processes
- Beran
- 1994
(Show Context)
Citation Context ...respectively, to estimate the Hurst parameter H from from the slope of cY (τ) on a log-log scale. Numerous other methods exist for estimating the Hurst parameter from LRD and self-similar time series =-=[4]-=-, [39], [42]. In addition to (1), we consider two established methods for estimating the Hurst parameter H [4], [39]. First, we consider the aggregate variance method, that relies on the convergence r... |

741 | Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level
- Willinger, Taqqu, et al.
- 1995
(Show Context)
Citation Context ...f sources with heavy tailed on and off periods yields self-similar LRD traffic. This notion corresponds to file transfers from heavy tailed file size distributions as observed on storage systems [8], =-=[45]-=-. An experimental validation of the relation between self-similarity and heavy-tailed distributions is carried out in [23] on a largescale experimental facility. Given a stationary process Y (t), LRD ... |

413 | End-to-end available bandwidth: measurement methodology, dynamics, and relation with TCP throughput
- Jain, Dovrolis
- 2002
(Show Context)
Citation Context ... packet delays or inter packet times are metrics commonly used to estimate network characteristics such as the average available bandwidth or even to reconstruct statistics of the cross-traffic [17], =-=[18]-=-, [33], [38]. Under the assumption of FIFO scheduling, cross traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], [21], [22], [38]. Cross traffic estimation of L... |

346 | Experimental queueing analysis with longrange dependent packet traffic.
- Erramilli, Narayan, et al.
- 1996
(Show Context)
Citation Context ...ternet traffic possesses long memory correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], =-=[11]-=-, [20], [25], [26], [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuous logg... |

313 | D.Moore, “What do Packet Dispersion Techniques Measure
- Dovrolis, Ramanathan
- 2001
(Show Context)
Citation Context ...construct statistics of the cross-traffic [17], [18], [33], [38]. Under the assumption of FIFO scheduling, cross traffic intensity can be estimated from the dispersion of back-to-back probing packets =-=[9]-=-, [21], [22], [38]. Cross traffic estimation of LRD traffic using active measurements was discussed, in [16], [32]. The authors of [16] carry out a numerical simulation to interpolate cross traffic fr... |

293 | A measurement study of available bandwidth estimation tools
- Strauss, Katabi, et al.
- 2003
(Show Context)
Citation Context ...ys or inter packet times are metrics commonly used to estimate network characteristics such as the average available bandwidth or even to reconstruct statistics of the cross-traffic [17], [18], [33], =-=[38]-=-. Under the assumption of FIFO scheduling, cross traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], [21], [22], [38]. Cross traffic estimation of LRD traffic u... |

290 | Proof of a fundamental result in self-similar traffic modeling
- Taqqu, Willinger, et al.
- 1997
(Show Context)
Citation Context ...butions on different time scales except for a rescaling factor which depends on H . The aggregation of multiple traffic sources offers a possible explanation of these characteristics. It was shown in =-=[40]-=- that aggregating many on-off sources with heavy tailed on and off periods yields self-similar LRD traffic. This notion corresponds to file transfers from heavy tailed file size distributions as obser... |

278 | On the use of fractional Brownian motion in the theory of connectionless networks.
- Norros
- 1995
(Show Context)
Citation Context ... long memory correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], [25], [26], =-=[28]-=-, [34], [35]. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuous logging and evaluation of al... |

271 | Dynamics of IP traffic: A study of the role of variability and the impact of control,”
- Feldmann, Gilbert, et al.
- 1999
(Show Context)
Citation Context ...erous comprehensive measurement studies, based on recorded network traces, have revealed that aggregate Internet traffic possesses long memory correlations, so-called long range dependence (LRD) [8], =-=[12]-=-, [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], [25], [26], [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally di... |

209 | Large deviations and overflow probabilities for the general single server queue, with application
- Duffield, O’Connell
- 1995
(Show Context)
Citation Context ...ate Internet traffic possesses long memory correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., =-=[10]-=-, [11], [20], [25], [26], [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuou... |

202 |
Pathchar: A Tool to Infer Characteristics of Internet Paths. ftp://ftp. ee.lbl.gov/pathchar
- Jacobson
- 1997
(Show Context)
Citation Context ...to-end packet delays or inter packet times are metrics commonly used to estimate network characteristics such as the average available bandwidth or even to reconstruct statistics of the cross-traffic =-=[17]-=-, [18], [33], [38]. Under the assumption of FIFO scheduling, cross traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], [21], [22], [38]. Cross traffic estimatio... |

198 |
Poisson arrivals see time averages",
- Wolff
- 1982
(Show Context)
Citation Context ...s to circumvent problems, such as system inaccessibility and hardware access latency. A fundamental result often employed in the sampling context is known as PASTA, Poisson Arrivals see Time Averages =-=[46]-=-. PASTA states that the portion of Poisson arrivals that see a system in a certain state corresponds, in average, to the portion of time the system spends in that state. Further, the authors of [27] e... |

156 | Estimators for long-range dependence: an empirical study
- Taqqu, V, et al.
- 1995
(Show Context)
Citation Context ...ctively, to estimate the Hurst parameter H from from the slope of cY (τ) on a log-log scale. Numerous other methods exist for estimating the Hurst parameter from LRD and self-similar time series [4], =-=[39]-=-, [42]. In addition to (1), we consider two established methods for estimating the Hurst parameter H [4], [39]. First, we consider the aggregate variance method, that relies on the convergence rate of... |

76 | Multifractal cross-traffic estimation
- Ribeiro, Coates, et al.
- 2000
(Show Context)
Citation Context ...traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], [21], [22], [38]. Cross traffic estimation of LRD traffic using active measurements was discussed, in [16], =-=[32]-=-. The authors of [16] carry out a numerical simulation to interpolate cross traffic from probes and predict future traffic from the LRD property. In [32] the authors derive and show simulation results... |

65 | A wavelet-based joint estimator of the parameters of long-range dependence
- Veitch, Abry
- 1999
(Show Context)
Citation Context ...y, to estimate the Hurst parameter H from from the slope of cY (τ) on a log-log scale. Numerous other methods exist for estimating the Hurst parameter from LRD and self-similar time series [4], [39], =-=[42]-=-. In addition to (1), we consider two established methods for estimating the Hurst parameter H [4], [39]. First, we consider the aggregate variance method, that relies on the convergence rate of the s... |

63 |
Big queues
- Ganesh, O’Connell, et al.
(Show Context)
Citation Context ... a result, each probe yields a sample of the egress link state at time t = ts, and the observed process can be constructed as W (t) = { 1 if dp > dmin and A(t) = 1 0 otherwise. (14) It is known [11], =-=[13]-=-, that the covariance structure of LRD traffic is preserved at the output of a queue or a traffic shaper, such that W (t) permits observing the covariance of the cross traffic. We assume that the pert... |

34 |
W.: On arrivals that see time averages
- Melamed, Whitt
- 1990
(Show Context)
Citation Context ...s [46]. PASTA states that the portion of Poisson arrivals that see a system in a certain state corresponds, in average, to the portion of time the system spends in that state. Further, the authors of =-=[27]-=- establish general conditions, such that Arrivals See Time Averages (ASTA) holds, i.e., bias free estimates are not limited to Poisson sampling. In a recent work the authors of [3] coined the term NIM... |

29 |
Probability and Random Processes.
- Grimmet, Stirzaker
- 1992
(Show Context)
Citation Context ...ential distribution with parameter λ. The spectral density of A(t) is given, e.g., in [7] as ΨA(f) = λ2δ(f) + λ with the well known Dirac delta function δ(f) that is defined as∫∞ −∞ g(f)δ(f)df = g(0) =-=[14]-=-. From (12) we calculate the spectral density of the observed process W (t) as ΨW (f) = ΨA(f) ∗ΨY (f) = (λ2δ(f) + λ) ∗ΨY (f) = λ2ΨY (f) + λ ( σ2Y + µ 2 Y ) (13) The convolution λ∗ΨY (f) reduces to λ (... |

24 | The role of PASTA in network measurement
- Baccelli, Machiraju, et al.
- 2006
(Show Context)
Citation Context ...er, the authors of [27] establish general conditions, such that Arrivals See Time Averages (ASTA) holds, i.e., bias free estimates are not limited to Poisson sampling. In a recent work the authors of =-=[3]-=- coined the term NIMASTA, i.e. Nonintrusive Mixing Arrivals See Time Averages, in the context of network measurements. Using an argument on joint ergodicity, the authors prove an almost sure convergen... |

24 | Fundamental bounds on the accuracy of network performance measurements
- Roughan
- 2005
(Show Context)
Citation Context ... perturb the system leading to distorted observations. For example, measuring queueing delays of probes to determine the true queue length distribution is governed by a type of Heisenberg uncertainty =-=[36]-=-, since the probes alter the queue length. The authors describe the impact of the probing intensity on the accuracy of the result using the notion of asymptotic variance. The effect is increased in ca... |

21 |
On the automatic selection of the onset of scaling
- Veitch, Abry, et al.
- 2003
(Show Context)
Citation Context ...on using the aggregate variance method a range of scales has to be fixed for the estimation [4]. A similar observation is made in the context of Hurst parameter estimation using wavelet decomposition =-=[43]-=-. The authors in [43] describe upper and lower cutoff bounds on the time scales considered for the estimation using wavelets. Similarly, we fix the range of scales M for the H estimation with upper an... |

18 | On exploiting long-range dependency of network traffic in measuring cross-traffic on an end-to-end basis
- He, Hou
- 2003
(Show Context)
Citation Context ...cross traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], [21], [22], [38]. Cross traffic estimation of LRD traffic using active measurements was discussed, in =-=[16]-=-, [32]. The authors of [16] carry out a numerical simulation to interpolate cross traffic from probes and predict future traffic from the LRD property. In [32] the authors derive and show simulation r... |

17 | A.: Large buffer asymptotics for the queue with FBM input
- Massoulié, Simonian
- 1999
(Show Context)
Citation Context ...sesses long memory correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], [25], =-=[26]-=-, [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuous logging and evaluation... |

16 |
On Optimal Probing for Delay and Loss Measurement
- Baccelli, Machiraju, et al.
- 2007
(Show Context)
Citation Context ...to a sampling process. The target metric is specified depending on the chosen function g. Eq. (3) is satisfied when the process Y (t) is ergodic and the sampling process is mixing [3]. The authors in =-=[2]-=- show that Poisson sampling, though bias free, does not guarantee minimum variance estimates. A comparison of Poisson and periodic sampling was carried out in [37], [41]. In [41] the authors show expe... |

14 | Adding definition to active probing
- Machiraju, Veitch, et al.
- 2007
(Show Context)
Citation Context ...c. The additional challenge of active compared to passive methods is to design probes that actually permit inferring the desired traffic characteristics, which in certain cases may even be impossible =-=[24]-=-. The ultimate result of this work is to enable the online estimation of traffic correlations along network paths without network support. To this end, we present methods for extracting LRD characteri... |

14 | Multifractality in tcp/ip traffic: the case against
- Hohn, Veitch, et al.
(Show Context)
Citation Context ...Mup = 102 to ensure enough points for the variance calculation at M = Mup. We fix M low = 0.1 s. This range is consistent with the ranges reported in trace driven H estimation literature, e.g., [15], =-=[44]-=-. H=0.6 H=0.7 H=0.8 H=0.9 0.5 0.6 0.7 0.8 0.9 1 Hse st im at e Trace passive sampling active probing Fig. 8: Hurst parameter estimates from (a) offline trace analysis, (b) offline trace sampling and (... |

12 | Delay bounds in communication networks with heavy-tailed and self-similar traffic
- Liebeherr, Burchard, et al.
- 2012
(Show Context)
Citation Context ... traffic possesses long memory correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], =-=[20]-=-, [25], [26], [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuous logging an... |

12 |
Large Deviations for Gaussian Queues.
- Mandjes
- 2007
(Show Context)
Citation Context ...ic possesses long memory correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], =-=[25]-=-, [26], [28], [34], [35]. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuous logging and eval... |

12 | Poisson versus periodic path probing (or, does PASTA matter
- Tariq, Dhamdhere, et al.
- 2005
(Show Context)
Citation Context ...s is mixing [3]. The authors in [2] show that Poisson sampling, though bias free, does not guarantee minimum variance estimates. A comparison of Poisson and periodic sampling was carried out in [37], =-=[41]-=-. In [41] the authors show experimentally, that the differences between round trip times (RTT), loss rate and packet pair dispersion estimates, obtained by either Poisson or periodic probing, are in s... |

11 |
The statistical analysis of series of events. Methuen’s monographs on applied probability and statistics.
- Cox, Lewis
- 1966
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Citation Context .../b probability mass function f(τ) of the inter sample times to calculate the n-fold self-convolution f (∗n)(τ). We then calculate the autocorrelation E [A(t)A(t+ τ)] = µA ∑∞ n=1 f (∗n)(τ) as given in =-=[7]-=-, Eq. (4.6.1). We exploit the property that f (∗n) is a power series for the considered distributions and that its sum converges. The derivation of the autocorrelations used in Tab. I is given in appe... |

11 | What signals do packet-pair dispersions carry
- Liu, Ravindran, et al.
- 2005
(Show Context)
Citation Context ...ruct statistics of the cross-traffic [17], [18], [33], [38]. Under the assumption of FIFO scheduling, cross traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], =-=[21]-=-, [22], [38]. Cross traffic estimation of LRD traffic using active measurements was discussed, in [16], [32]. The authors of [16] carry out a numerical simulation to interpolate cross traffic from pro... |

11 | A comparision of Poisson and Uniform Sampling for Active Measurements
- Roughan
- 2006
(Show Context)
Citation Context ...process is mixing [3]. The authors in [2] show that Poisson sampling, though bias free, does not guarantee minimum variance estimates. A comparison of Poisson and periodic sampling was carried out in =-=[37]-=-, [41]. In [41] the authors show experimentally, that the differences between round trip times (RTT), loss rate and packet pair dispersion estimates, obtained by either Poisson or periodic probing, ar... |

10 | Investigating self-similarity and heavy-tailed distributions on a large-scale experimental facility,”
- Loiseau, Goncalves, et al.
- 2010
(Show Context)
Citation Context ...from heavy tailed file size distributions as observed on storage systems [8], [45]. An experimental validation of the relation between self-similarity and heavy-tailed distributions is carried out in =-=[23]-=- on a largescale experimental facility. Given a stationary process Y (t), LRD manifests itself in the slow decay of the autocovariance1 cY (τ) such that cY (τ) ∼ σ2Y τ2H−2 for τ →∞, (1) where σ2Y is t... |

7 | Radon spectroscopy of inter-packet delay
- Broido, King, et al.
- 2003
(Show Context)
Citation Context ...istinct periodicities on different timescales, as exemplified in Fig. 9(c). Periodic behavior in offline Internet traces due to various protocol implementations has been previously reported, e.g., in =-=[6]-=-. Fig. 10 depicts estimated H using the aggregate variance method from Sect. IV-A. The Hurst parameter estimates indicate a diurnal behavior. We provide additional data sets and results in the appendi... |

5 |
Non-asymptotic end-to-end performance bounds for networks with long range dependent fbm cross traffic
- Rizk, Fidler
(Show Context)
Citation Context ... correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], [25], [26], [28], [34], =-=[35]-=-. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuous logging and evaluation of all relevant n... |

4 |
Random sampling of long-memory stationary processes
- Philippe, Viano
(Show Context)
Citation Context ...are in some cases not significant. Depending on the autocovariance of the sampled process, Poisson or periodic sampling can be superior. This is shown in [37] using the metric asymptotic variance. In =-=[31]-=- it is shown that for correlation lags tending to infinity, random sampling captures the long memory of the original processes, as long as the sampling distribution has a finite mean. C. Active networ... |

3 | A queueing-theoretic foundation of available bandwidth estimation: single-hop analysis,”
- Liu, Ravindran, et al.
- 2007
(Show Context)
Citation Context ...tatistics of the cross-traffic [17], [18], [33], [38]. Under the assumption of FIFO scheduling, cross traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], [21], =-=[22]-=-, [38]. Cross traffic estimation of LRD traffic using active measurements was discussed, in [16], [32]. The authors of [16] carry out a numerical simulation to interpolate cross traffic from probes an... |

2 |
Revisiting coexistence of Poissonity and Self-similarity in Internet traffic.
- Gupta, Mahanti, et al.
- 2009
(Show Context)
Citation Context ...e., T/Mup = 102 to ensure enough points for the variance calculation at M = Mup. We fix M low = 0.1 s. This range is consistent with the ranges reported in trace driven H estimation literature, e.g., =-=[15]-=-, [44]. H=0.6 H=0.7 H=0.8 H=0.9 0.5 0.6 0.7 0.8 0.9 1 Hse st im at e Trace passive sampling active probing Fig. 8: Hurst parameter estimates from (a) offline trace analysis, (b) offline trace sampling... |

2 | Optimal sampling strategies for multiscale stochastic processes
- Ribeiro, Riedi, et al.
- 2006
(Show Context)
Citation Context ...t delays or inter packet times are metrics commonly used to estimate network characteristics such as the average available bandwidth or even to reconstruct statistics of the cross-traffic [17], [18], =-=[33]-=-, [38]. Under the assumption of FIFO scheduling, cross traffic intensity can be estimated from the dispersion of back-to-back probing packets [9], [21], [22], [38]. Cross traffic estimation of LRD tra... |

2 | Multiscale queuing analysis
- Ribeiro, Riedi, et al.
(Show Context)
Citation Context ...memory correlations, so-called long range dependence (LRD) [8], [12], [19], [30]. The impact of LRD on network performance was investigated in several works, e.g., [10], [11], [20], [25], [26], [28], =-=[34]-=-, [35]. Networks fed with LRD traffic exhibit a fundamentally different behavior compared to systems fed with memoryless or Markovian traffic. In practice continuous logging and evaluation of all rele... |

1 | H-probe software, 2012. Available at: http://www.ikt.uni-hannover.de/h-probe - Bozakov, Rizk, et al. |