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Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Jung-Han Kimu


Deterministic traffic ow models are able to capture important physical phenomenon of traffic; however, these models are typically dependent on an assumed ow-density relationship which admit large variations from historical data. Stochastic models have been developed to account for large deviations in ow-density relationships. Recently, Jabari and Liu proposed a Gaussian approximation of a stochastic model in the Gaussian approximation is a deterministic model as a result of the limiting stochastic process, with a variance computed from the deviance between the stochastic and deterministic models. We are interested in the claims that the deterministic model produces a range of density estimates which avoid non-negative densities, that the model is accurate, and can be performed in a reasonable amount of time. To test this, we implement the model for a case study in which we wish to describe traffic conditions downstream on a homogeneous road with no lane changes from knowledge of conditions upstream. This is the most basic of all cases of estimating traffic conditions and would be represented by asking if a point source detector upstream can predict traffic ow downstream assuming no lane changes. The model is shown capable of producing accurate queue length estimates in a viable amount of time for cycle-by-cycle traffic estimation on an arterial road. Unfortunately, accurate results come at the cost of large enough confidence intervals such that non-negative densities are not guaranteed. Mean densities are implicitly guaranteed to be non-negative.

Library of Congress Subject Headings

Traffic flow -- Mathematical models
Gaussian processes


Includes bibliographical references (pages 40-42)



Number of Pages



South Dakota State University


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