The expected length of a random line segment in a rectangle

Authors:
Eric Rosenberg
Affiliations:
AT&T Labs, Middletown, NJ 07748, USA
Venue:
Operations Research Letters
Year:
2004

Citing 2
Cited 0

On the distribution of routing computation in hierarchical ATM networks

IEEE/ACM Transactions on Networking (TON)
Optimization of hierarchical routing protocols

Performance Evaluation - Special issue: ATM networks: Performance modelling and analysis

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Abstract

We calculate the expected length of a random line segment in a rectangle, using a line making a random angle with the horizontal axis and having a random distance to a corner of the rectangle. Our result differs from previous calculations based upon two randomly placed points, and can be viewed as extending Bertrand's paradox to an important problem in geometric probability.