## Multicast Topology Inference from Measured End-to-End Loss (2001)

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Citations: | 60 - 7 self |

### BibTeX

@MISC{Duffield01multicasttopology,

author = {N.G. Duffield and J. Horowitz and F. Lo Presti and D. Towsley},

title = {Multicast Topology Inference from Measured End-to-End Loss},

year = {2001}

}

### Years of Citing Articles

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### Abstract

The use of multicast inference on end-to-end measurement has recently been proposed as a means to infer network internal characteristics such as packet link loss rate and delay. In this paper we propose three types of algorithm that use loss measurements to infer the underlying multicast topology: (i) a grouping estimator that exploits the monotonicity of loss rates with increasing path length; (ii) a maximum likelihood estimator; and (iii) a Bayesian estimator. We establish their consistency, compare their complexity and accuracy, and analyze the modes of failure and their asymptotic probabilities.

### Citations

1245 | Statistical decision theory and Bayesian analysis - Berger - 1985 |

660 |
Large deviations techniques and applications
- Dembo, Zeitouni
- 1998
(Show Context)
Citation Context ...parent node terminates the least lossy internal link, mistakenly grouping the sibling of with one of its children. We remark that the preceding argument can be formalized using Large Deviation theory =-=[5]-=-. However, calculation of the decay rate appears computationally infeasible, although one can recover the leading exponent in the small regime. 2) Experimental Evaluation: Although we have derived the... |

538 |
Theory of Statistics
- Schervish
- 1995
(Show Context)
Citation Context ...s a consequence of the MLE property, is consistent ( with probability ), and asymptotically normal ( converges in distribution to a multivariate Gaussian random variable as ), and similarly for ; see =-=[17]-=-. (1) (2) (3) (4)DUFFIELD et al.: MULTICAST TOPOLOGY INFERENCE FROM MEASURED END-TO-END LOSS 29 III. DETERMINISTIC RECONSTRUCTION OF LOSS TREES BY GROUPING The use of estimates of shared loss rates a... |

251 | Multicast-based inference of network-internal loss characteristics
- Caceres, Duffield, et al.
- 1999
(Show Context)
Citation Context ...ch has been used to infer the per-link packet loss probabilities for logical multicast trees with a known topology. The maximum-likelihood estimator (MLE) for the link probabilities was determined in =-=[3]-=- under the assumption that probe loss occurs independently across links and between probes. This estimate is somewhat robust with respect to violations of this assumption. This approach will be discus... |

208 |
Network tomography: Estimating source-destination traffic intensities from link data
- Vardi
- 1996
(Show Context)
Citation Context ...rk tomography, we mention some recent analytic work on a different problem, namely, determination of source-destination traffic matrix from source- and destination-averaged traffic volumes; see [18], =-=[19]-=- for further details. II. LOSS TREES AND INFERENCE OF LOSS RATE We begin by reviewing the tree and loss models used to formulate the MLE for link loss probabilities in a known topology.28 IEEE TRANSA... |

155 |
Asymptotic properties of nonlinear least squares estimators
- Jennrich
- 1969
(Show Context)
Citation Context ...y of the steps that lead to the construction of node and/or node —we need to explicitly write the expression for (37) Since , the density is bounded away from zero, hence the conditions of Jennrich’s =-=[8]-=- uniform strong law of large numbers are satisfied. Thus, —almost surely (41) (38) uniformly in , whence the right-hand side of (37) converges to zero as . Proof of Theorem 9: Recall from the proof of... |

151 | An architecture for large-scale internet measurement
- Paxson, Mahdavi, et al.
- 1998
(Show Context)
Citation Context ...ds to infer the logical topology when it is not known in advance. This is motivated in part by ongoing work [1] to incorporate the loss-based MLE into the National Internet Measurement Infrastructure =-=[14]-=-. In this case, inference is performed on end-to-end measurements arising from the exchange of multicast probes between a number of measurement hosts stationed in the Internet. The methods here can be... |

83 | The use of end-to-end multicast measurements for characterizing internal network behavior
- Adams, Bu, et al.
- 2000
(Show Context)
Citation Context ...sed in more detail presently. The focus of the current paper is the extension of these methods to infer the logical topology when it is not known in advance. This is motivated in part by ongoing work =-=[1]-=- to incorporate the loss-based MLE into the National Internet Measurement Infrastructure [14]. In this case, inference is performed on end-to-end measurements arising from the exchange of multicast pr... |

68 | Multicast inference of packet delay variance at interior network links
- Duffield, Presti
(Show Context)
Citation Context ...be consistently estimated from measurements at receivers descended from that node. Examples of such quantities include the mean and variance of the cumulative delay from the root to a given node; see =-=[6]-=- and [11]. Finally, a challenging problem is to take the resulting logical multicast trees and mapping the constituent nodes onto physical routers within real networks. This remains beyond our capabil... |

63 | Organizing Multicast Receivers Deterministically According to Packet-Loss Correlation
- Levine, Paul, et al.
- 1998
(Show Context)
Citation Context ...r Related Work The mtrace [12] measurement tool, reports the route from a multicast source to a receiver, along with other information about that path such as per-hop loss statistics. The tracer tool =-=[10]-=- uses mtrace to perform topology discovery. We briefly contrast some properties of those methods with those presented here. i) Access: mtrace relies on routers to respond to explicit measurement queri... |

32 |
An overview of reliable multicast transport protocol II
- Whetten, Taskale
- 2000
(Show Context)
Citation Context ... [9] that organizing a set of receivers in a bulk transfer application into a tree can substantially improve performance. Such an organization is central component of the widely used RMTP-II protocol =-=[20]-=-. The development of tree construction algorithms for the purpose of supporting reliable multicast has been identified to be of fundamental importance by the Reliable Multicast Transport Group of the ... |

29 | The Reliable Multicast Design Space for Bulk Data Transfer
- Handley, Whetten, et al.
- 2000
(Show Context)
Citation Context ...ithms for the purpose of supporting reliable multicast has been identified to be of fundamental importance by the Reliable Multicast Transport Group of the Internet Engineeirng Task Force (IETF); see =-=[7]-=-. This motivated the work reported in [16], which was concerned with grouping multicast receivers that share the same set of network bottlenecks from the source for the purposes of congestion control.... |

29 |
The Case for Concurrent Reliable Multicasting Using Shared Ack Trees
- Levine, Lavo, et al.
- 1996
(Show Context)
Citation Context ...m for identifying the physical topology of a network. A more important motivation for this work is that knowledge of the multicast topology can be used by multicast applications. It has been shown in =-=[9]-=- that organizing a set of receivers in a bulk transfer application into a tree can substantially improve performance. Such an organization is central component of the widely used RMTP-II protocol [20]... |

18 | An em approach to od matrix estimation
- Vanderbei, Iannone
- 1994
(Show Context)
Citation Context ... network tomography, we mention some recent analytic work on a different problem, namely, determination of source-destination traffic matrix from source- and destination-averaged traffic volumes; see =-=[18]-=-, [19] for further details. II. LOSS TREES AND INFERENCE OF LOSS RATE We begin by reviewing the tree and loss models used to formulate the MLE for link loss probabilities in a known topology.28 IEEE ... |

16 |
Inference of Multicast Routing Tree Topologies and Bottleneck Bandwidths using End-to-end Measurements
- Ratnasamy, McCanne
- 1999
(Show Context)
Citation Context ...ble multicast has been identified to be of fundamental importance by the Reliable Multicast Transport Group of the Internet Engineeirng Task Force (IETF); see [7]. This motivated the work reported in =-=[16]-=-, which was concerned with grouping multicast receivers that share the same set of network bottlenecks from the source for the purposes of congestion control. Closely related to [3], the approach of [... |

5 | Statistical inference of multicast network topology - Caceres, Duffield, et al. - 1999 |

4 | Multicast-Based Inference of Network - Caceres, Duffield, et al. - 1999 |

1 |
Gradient conditions and Lagrange multipliers in nonlinear programming,” in Nonlinear Optimization: Theory and Algorithms
- Powell
- 1980
(Show Context)
Citation Context ... an asymptotic upper bound for the decay rate of the misclassification probability as increases. For each , the minimization can be carried out using the Kuhn–Tucker theorem; we use the form given in =-=[15]-=-. We mention that a lower bound of the following form can be found: IX. SUMMARY AND CONCLUSION (31) In this paper, we have proposed and established the consistency of a number of algorithms for inferr... |