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jinaicoeurvictp4ogwg
jinaicoeurvictp4ogwg
19.11.2019 • 
Mathematics

Network tomography. a network consists of n links, labeled 1; : : : ; n. a path through the network is a subset of the links. (the order of the links on a path does not matter here.) each link has a (positive) delay, which is the time it takes to traverse it. we let d denote the n-vector that gives the link delays. the total travel time of a path is the sum of the delays of the links on the path. our goal is to estimate the link delays (i.e., the vector d), from a large number of (noisy) measurements of the travel times along di erent paths. this data is given to you as an n n matrix p, where pij = 1 link j is on path i 0 otherwise, and an n-vector t whose entries are the (noisy) travel times along the n paths. you can assume that n > n. you will choose your estimate ^ d by minimizing the rms deviation between the measured travel times (t) and the travel times predicted by the sum of the link delays. explain how to do this, and give a matrix expression for ^ d. if your expression requires assumptions about the data p or t, state them explicitly. remark. this problem arises in several contexts. the network could be a computer network, and a path gives the sequence of communication links data packets traverse. the network could be a transportation system, with the links representing road segments.

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