A stochastic two-dimensional intelligent driver car-following model with vehicular dynamics

The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models,especially the car-following(CF)models.These models of the movement of vehicles serve as the backbone of traffic flow analysis,simulation,autonomous vehicle development,etc.Two-dimensional(2D)vehicular movement is basically stochastic and is the result of interactions between a driver's behavior and a vehicle's characteristics.Current microscopic models either neglect 2D noise,or overlook vehicle dynamics.The modeling capabilities,thus,are limited,so that stochastic lateral movement cannot be reproduced.The present research extends an intelligent driver model(IDM)by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model,with vehicle dynamics based on the stochastic differential equation(SDE)theory.Control inputs from the vehicle include the steer rate and longitudinal acceleration,both of which are developed based on an idea from a traditional intelligent driver model.The stochastic stability condition is analyzed on the basis of Lyapunov theory.Numerical analysis is used to assess the two cases:(i)when a vehicle accelerates from a standstill and(ii)when a platoon of vehicles follow a leader with a stop-and-go speed profile,the formation of congestion and subsequent dispersion are simulated.The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement.The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.

Parameterized Solution to a Class of Sylvester Matrix Equations

A class of formulas for converting linear matrix mappings into conventional linear mappings are presented. Using them, an easily computable numerical method for complete parameterized solutions of the Sylvester matrix equation AX - EXF = BY and its dual equation XA - FXE = YC are provided. It is also shown that the results obtained can be used easily for observer design. The method proposed in this paper is universally applicable to linear matrix equations.

Analysis of delay variability at isolated signalized intersections

On urban arterials,travel time variability is largely dependent on the variability in the delays vehicles experience at signalized intersections.The interpretation of delay evolvement at intersections will give a comprehensive insight into arterial travel time variability and provide more possibilities for travel time estimation.Accordingly,an analytical model is proposed to study delay variability at isolated,fixed-time controlled intersections.Classic cumulative curves are utilized to derive average delay(per cycle) formulas by assuming a deterministic overflow queue.Then,an analogy with the Markov chain process is made to clarify the mechanism of stochastic delays and overflow queues at signalized intersections.It was found that,in undersaturated cases,the shape of the delay distribution changes very little over time,whereas for saturated and oversaturated cases the delay distribution is time-dependent and becomes flatter with an increasing number of cycles.The analysis of arrival distributions,e.g.,Poisson and binomial,produces the conclusion that the variability of arrivals has a significant effect on delay estimates in both undersaturated and oversaturated conditions.A larger variance of arrival flow results in a larger variance of delay distribution.All of these analyses can help road authorities to gain insights into arterial travel time variability.