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Random coverage of a circle with applications to a shadowing problem

Published online by Cambridge University Press:  14 July 2016

M. Yadin and
S. Zacks
M. Yadin*
Affiliation:
Technion — Israel Institute of Technology
S. Zacks*
Affiliation:
State University of New York at Binghampton
*
∗ Postal address: Faculty of Industrial and Management Engineering, Technion — Israel Institute of Technology, Haifa, Israel.
∗∗ Postal address: Department of Mathematical Sciences, State University of New York, Binghampton, NY 13901, U.S.A.
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Abstract

The coverage problem on the circle is considered from the shadowing process point of view. A random number of shadow arcs are distributed on a circle. The length of each arc is a random variable which depends on the random diameter of a shadowing disk and its random location. Formulae are derived for the numerical determination of the moments of the measure of vacancy of arcs on the circle, for a special example. An approximation to the distribution of the measure of vacancy is also provided.

Keywords

RANDOM ARCSVACANCY PROBABILITIESCOVERAGEPOISSON FIELDSSHADOWING PROCESSES

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982, pp. 562 - 577
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Partially supported by ONR Contract N00014-80-C-0325 (NR 042–276) at Virginia Polytechnic Institute and State University; and Contract ONR N00014-81-K-0407 (NR 042–276) at State University of New York at Binghamton.

References

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