The Annals of Applied Statistics

Network tomography for integer-valued traffic

Martin L. Hazelton

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Abstract

A classic network tomography problem is estimation of properties of the distribution of route traffic volumes based on counts taken on the network links. We consider inference for a general class of models for integer-valued traffic. Model identifiability is examined. We investigate both maximum likelihood and Bayesian methods of estimation. In practice, these must be implemented using stochastic EM and MCMC approaches. This requires a methodology for sampling latent route flows conditional on the observed link counts. We show that existing algorithms for doing so can fail entirely, because inflexibility in the choice of sampling directions can leave the sampler trapped at a vertex of the convex polytope that describes the feasible set of route flows. We prove that so long as the network’s link-path incidence matrix is totally unimodular, it is always possible to select a coordinate system representation of the polytope for which sampling parallel to the axes is adequate. This motivates a modified sampler in which the representation of the polytope adapts to provide good mixing behavior. This methodology is applied to three road traffic data sets. We conclude with a discussion of the ramifications of the unimodularity requirements for the routing matrix.

Article information

Source
Ann. Appl. Stat., Volume 9, Number 1 (2015), 474-506.

Dates
First available in Project Euclid: 28 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1430226101

Digital Object Identifier
doi:10.1214/15-AOAS805

Mathematical Reviews number (MathSciNet)
MR3341124

Zentralblatt MATH identifier
06446577

Keywords
EM algorithm MCMC origin–destination polytope transport unimodular matrix

Citation

Hazelton, Martin L. Network tomography for integer-valued traffic. Ann. Appl. Stat. 9 (2015), no. 1, 474--506. doi:10.1214/15-AOAS805. https://projecteuclid.org/euclid.aoas/1430226101


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Supplemental materials

  • Supplement to "Network tomography for integer-valued traffic".: The supplementary materials, stored as a zip archive, include data and additional numerical results for the applications in Section 5. The data comprise link-path incidence matrices, observed traffic counts and prior pseudo counts for Bayesian analyses. The additional results include effective sample sizes for MCMC output, computing times and summaries of the slack for the route flow samplers considered.