Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

INTEGRATION Framework for Modeling Tolls Considering Different Subpopulations with Different Values of Time

Version 1 : Received: 14 April 2021 / Approved: 15 April 2021 / Online: 15 April 2021 (16:52:34 CEST)

How to cite: Rakha, H. INTEGRATION Framework for Modeling Tolls Considering Different Subpopulations with Different Values of Time. Preprints 2021, 2021040425 (doi: 10.20944/preprints202104.0425.v1). Rakha, H. INTEGRATION Framework for Modeling Tolls Considering Different Subpopulations with Different Values of Time. Preprints 2021, 2021040425 (doi: 10.20944/preprints202104.0425.v1).

Abstract

Unique analytical challenges arise when drivers, who face a route choice between a toll lane and a set of free lanes, have different values of time. The most complex situation is one in which multiple sub-populations of drivers exist, each with their own unique mean and coefficient of variation of value of time. This situation, when imbedded within a larger network cannot be tackled using existing planning models, and consequently is usually only approximated. This paper examines these different approximations, the resulting numerical solutions and the implications of these approximations on the estimate of the number of expected toll lane users. The paper also shows how this problem can be solved using a combined traffic assignment/simulation model. The first part of this paper develops an analytical formulation for solving the toll lane scenario using the “value of time” representations range from the simplest to the most complex. It is shown that one of the most critical issues is a determination of who the marginal users are of the toll lane, at each level of usage, as the perceived disutility of the last marginal toll lane user depends dynamically upon that driver’s value of time. Analytical formulations based on these different approximations are then solved numerically in the second part of the paper. These numerical solutions show that significant different lane use estimates result, depending upon the representation of value of time. Consequently, it is clear that solving this problem with the fewest approximations is both of theoretical and practical importance. The third part of the paper illustrates the solution to the toll lane problem, with each level of approximation, using a combined traffic assignment/simulation model. The simulated resulting estimates of the toll lane usage for each case matches both the relative and absolute trends found in analytical solutions. However, the solution using the assignment/simulation model is not only much faster and simpler to obtain, but is also scalable both in size and complexity. The additional complexities, that are associated with a less approximate representation of value of time, should therefore be incorporated in all future assessments of toll lane facilities, be they analyzed analytically or through simulation.

Subject Areas

Tolls; INTEGRATION software; microscopic traffic simulation; traveler value of time

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