Variable Response Time Lag Module for Car-Following Models: Development and Structuring with Fuzzy Set Theory

Abstract

The car-following process consists of a stimulus-response relationship between vehicles in which the driver of the following vehicle reacts to the actions of the lead vehicle after a time lag. Since the 1950s, the car-following phenomenon has been studied and analyzed, resulting in various models and algorithms. Throughout this period, driver response time lag has always been assumed to be a constant value for the driver at all times, regardless of the approach and level of detail of the model. The primary shortcoming of a constant time lag is that it introduces a number of strong assumptions that do not concur with human nature. To address the problems associated with constant time lag, an independent response time lag module was developed that can be used in any car-following model or algorithm without changing its fundamental mathematical structure. One of the most appealing aspects of this module is its flexible and transparent structure that can easily be adapted to and calibrated for any model or simulation algorithm. The development and structure of the module are described, including the fuzzy definitions of driving states, fuzzy rule extraction, and fuzzy time lag assignment. Statistical and graphical evaluations of the module performance are also included by integrating the module to a proportional car-following model. In the graphical evaluation, the module improved the model performance significantly by providing more precise timing for the driver response. Both Kolmogorov–Smirnov and root-mean-square error tests confirmed that the use of the module improves the car-following model performance.

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