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Distribution of Minimal Path Lengths when Edge Lengths are Independent Heterogeneous Exponential Random Variables

Part of: Combinatorial probability Graph theory

Published online by Cambridge University Press:  04 February 2016

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗ Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu
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Abstract

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We find the joint distribution of the lengths of the shortest paths from a specified node to all other nodes in a network in which the edge lengths are assumed to be independent heterogeneous exponential random variables. We also give an efficient way to simulate these lengths that requires only one generated exponential per node, as well as efficient procedures to use the simulated data to estimate quantities of the joint distribution.

Keywords

Shortest pathexponential edge lengthjoint distributionsimulation

MSC classification

Primary: 05C80: Random graphs 60C05: Combinatorial probability
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 895 - 900
Copyright
© Applied Probability Trust 

Footnotes

This material is based upon work supported by, or in part by, the US Army Research Laboratory and the US Army Research Office under contract\grant number W911NF-11-1-0115.

References

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