Explaining Freeway Breakdown with Geometric Brownian Motion Model
Publication: Journal of Transportation Engineering, Part A: Systems
Volume 145, Issue 9
Abstract
A traffic volume which can trigger a breakdown event at one point in time may not trigger it at another time. The critical question is why a roadway under the same loading is stable in one instance and unstable in another. This paper explains this behavior by using a linear first-order stochastic differential equation (SDE) model, a geometric Brownian motion (gBm) model. This simple stochastic (time-dependent) model of diffusion treats traffic volume, the load on the roadway system, as a random process. The model response variables are (1) the breakdown probability, which is the transition from a free-flow to a congested state for a given traffic loading; and (2) traffic delay. There are two major challenges. The first is formulating an approach, i.e., a mathematical model, that can reliably forecast traffic breakdown at a data collection site located upstream of a bottleneck where no data are collected. The second is selecting and calibrating an appropriate gBm model with extremely volatile data. The approach was assessed by performing match tests, assessing the field data summaries against model forecasts of traffic volume, breakdown probability, and delay. The potential for using the gBm modeling approach as an operational analysis tool was discussed.
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Published In
Journal of Transportation Engineering, Part A: Systems
Volume 145 • Issue 9 • September 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jan 28, 2017
Accepted: Jan 11, 2019
Published online: Jun 21, 2019
Published in print: Sep 1, 2019
Discussion open until: Nov 21, 2019
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