Investigating predictive effects on heterogeneous traffic through lattice modeling

With the continuous improvement and advancement in information technology (IT), drivers receive an appropriate assessment of the current state of real-time traffic in the next instant. This information (predictive effect) can impact the mixed traffic flow performance. In a mixed (heterogeneous) transportation system, various vehicles can be observed that differ in size or reaction time. Moreover, heterogeneous traffic more accurately reflects the actual features of vehicle flow. As a result, a novel lattice hydrodynamic model is put forth to examine the effects of predictive control on heterogeneous vehicular flow, encompassing both small and large automobiles. The presented model is examined theoretically through linear and nonlinear stability analyses. The reductive perturbation method is utilized to derive the ‘modified Korteweg-de Vries (mKdV)’ equation. Around the critical point, kink-antikink soliton solutions, which express density waves, are obtained. Observation of the results revealed that the stability of heterogeneous traffic increases when considering the predictive effect. Further, numerical simulations are conducted using the finite difference scheme through MATLAB software. Theoretical predictions are validated by numerical simulation, which shows that applying the predictive impact to a mixed traffic system can more effectively reduce traffic jams.