Abstract
Given a network and the total flows into and out of each of the sink and source nodes, it is useful to select uniformly at random an origin-destination (O-D) matrix for which the total in and out flows at sinks and sources (column and row sums) matches the given data. We give an algorithm for small networks (less than 16 nodes) for sampling such O-D matrices with exactly the uniform distribution and apply it to traffic network analysis. This algorithm also can be applied to communication networks and used in the statistical analysis of contingency tables.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bezáková, I., Sinclair, A., Štefankovič, D., Vigoda, E.: Negative Examples for Sequential Importance Sampling of Binary Contingency Tables. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 136–147. Springer, Heidelberg (2006)
Chen, Y.: Conditional inference on tables with structural zeros. J. Comput. Graph. Statist. 16(2), 445–467 (2007)
Chen, Y., Diaconis, P., Holmes, S.P., Liu, J.S.: Sequential Monte Carlo methods for statistical analysis of tables. J. Amer. Statist. Assoc. 100, 109–120 (2005)
Diaconis, P., Efron, B.: Testing for independence in a two-way table: new interpretations of the chi-square statistic. Annals of Statistics 13(3), 845–874 (1985)
Dyer, M., Kannan, R., Mount, J.: Sampling contingency tables. Random Structures & Algorithms 10, 487–506 (1995)
Hogg, R.V., McKean, J.W., Craig, A.T.: Introduction to mathematical statistics. Pearson education international. Pearson Education (2005) ISBN 9780130085078, http://books.google.com/books?id=dX4pAQAAMAAJ
Holmes, R.B., Jones, L.K.: On uniform generation of two-way tables with fixed margins and the conditional volume test of diaconis and efron. Annals of Statistics 24(1), 64–68 (1996)
Jones, L.K., Deshpande, R., Gartner, N.H., Stamatiadis, C., Zou, F.: Robust controls for traffic networks: the near-bayes near-minimax strategy. Transportation Research Part C (in press, 2012)
Kannan, R., Lovász, L., Simonovits, M.: Random walks and an o(n5) volume algorithm for convex bodies. Random Structures & Algorithms 11(1), 1–50 (1997)
Liu, J.S.: Monte Carlo Strategies in Scientific Computing. Springer Series in Statistics. Springer (2008) ISBN 9780387763699, http://books.google.com/books?id=R8E-yHaKCGUC
Lovasz, L., Simonovits, M.: Random walks in a convex body and an improved volume algorithm. Random Structures & Algorithms 4(4), 359–412 (1993)
Xie, C., Kockelman, K.M., Waller, S.T.: Maximum entropy method for subnetwork origin-destination trip matrix estimation. Transportation Research Record: Journal of the Transportation Research Board 2196(4), 111–119 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Einstein, D.M., Jones, L.K. (2013). Uniformly Generating Origin Destination Tables. In: Aydinian, H., Cicalese, F., Deppe, C. (eds) Information Theory, Combinatorics, and Search Theory. Lecture Notes in Computer Science, vol 7777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36899-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-36899-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36898-1
Online ISBN: 978-3-642-36899-8
eBook Packages: Computer ScienceComputer Science (R0)