This paper considers the problem of finding shortest-path probability distributions in graphs whose branches are weighted with random lengths, examines the consequences of various assumptions concerning the nature of the available statistical information, and gives an exact method for computing the probability distribution, as well as methods based on hypothesis testing and statistical estimation. It presents Monte Carlo results and, based on these results, it develops an efficient method of hypothesis testing. Finally, it discusses briefly the pairwise comparison of paths.

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The traffic demands at the stations of a communication network are usually not deterministic. Optimum loca tions found using deterministic techniques are poor when the random nature of the network traffic is con sidered. The concepts of absolute centers and medians are generalized to maximum probability absolute cen ters and medians. Minimum variance points are also considered. Techniques to locate these optimum points are discussed.

ABSTRACT. ties. There are two interpretations of the situation. A natural disaster such as an earthquake or hurricane can cause the elements to fail. One can then ask for the expected nwnber of node pairs which can communicate i f this event should occur. Alternatively, one might seek the probability the net will fail (i.e., become disconnected) as a result of the event. The Thus, with this criterion a This paper considers networks with randomly faiting links In P a r t I, nodes are assumed t o be perfectly r e t i -We assume that links and nodes fail with known probabiliNetworks, 1: 279-290