Some Moments for Circle Coverings.

by W. L. Doyle, I. S. Reed


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Some results on the random coverings of a circle by intervals. The first two moments of the uncovered circumference, and the expected number of segments comprising the uncovered portion of the circumference, are found. Results are applied to the case in which the distribution of intervals is uniform from zero to some length less than half the circumference. In terms of the coverage question for a communication system involving randomly available relay stations, these results amount to the mean and variance of outage times and the expected number of breaks during a basic period.

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