On the Probabilistic and Physical Consistency of Traffic Random Variables and Models

Consideration of the existing relations among the different random variables involved in traffic problems is crucial in developing a consistent probability model. The consistency of stochastic traffic models from the points of view of probability and statistics and also from a dimensional analysis perspective are presented in this paper. The authors analyze and discuss the conditions for a model to be consistent from two different points of view: probabilistic and physical (dimensional analysis). Probabilistic leads to the concept of stability in general and reproductivity in particular because, for example, origin-destination (OD) and link flows are the sum of route flows and route travel times are the sum of link travel times. This implies stability with respect to sums (reproductivity). Normal models are justified because when the number of summands increases the averages approach the normal distribution. Similarly, stability with respect to minimum or maximum operations arises in practice. From the dimensional analysis point of view, some models are demonstrated not to be convenient. In particular, it is shown that some families of distributions are valid only for dimensionless variables. These problems are discussed and some proposed models in the literature are analyzed from these two points of view. When analytical consistency cannot be achieved, a possible alternative is the Monte Carlo simulation that permits satisfying the compatibilities easily.

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  • English

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  • Accession Number: 01536201
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Jul 25 2014 11:29AM