Module 3 : Microscopic Traffic Flow Modeling

Lecture 15 : Lane Changing Models

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	Desire to change the lane Decision to change the lane in discretionary lane change conditions may be taken due to a number of factors but basically what the driver has in mind should be higher utility in the target lane which may be for example higher speed. Here we use the equation suggested by Gipps (1986) to find if it is possible for the driver to attain his desired speed within the existing space difference between his vehicle and the preceding vehicle in the current lane. If required space difference is not available, the driver is assumed to decide lane change. The relation is given as: $$V_n(t+T)= b_n~T + \sqrt{b_n^2~T^2-b_n~(2D_x(t)~-V_n(t)~T-V_{n-1}(t)^2/b)}$$ (1) where, $V_n(t + T)$ is the maximum safe speed for vehicle $n$ with respect to the preceding vehicle at time (t+T), $V_n(t)$ is the velocity nth vehicle, $V_{n-1}(t)$ is the velocity n-1th vehicle, $b_n~(<0)$ is the most severe braking the driver is prepared to undertake, T is the time between consecutive calculations of speed and position, b is an estimate of $b_{n-1}$ employed by the driver of vehicle n, and $D_x(t)$ is the distance between front of subject vehicle and rear of leading vehicle at t. The driver is assumed to decide to change lane if $D_x$ is more than the existing space gap between the subject vehicle and preceding vehicle in current lane. Check for feasibility The lane change is said to be feasible if the chance that the subject vehicle would collide at the rear of preceding vehicle in the target lane and the chance that the lag vehicle in the target lane would collide at the rear of the subject vehicle is avoided. To check if the subject vehicle would collide at the rear of preceding vehicle in the target lane we consider the subject vehicle as n and preceding vehicle in the target lane as n-1.Then we substitute the values in the equation 1. If the maximum safe speed can be attained in the time T with a deceleration less than the maximum possible deceleration of the vehicle we say that the lane change is feasible. To check if the lag vehicle after sighting the subject vehicle in the target lane, would collide at the rear of subject vehicle in the target lane. For this we consider the lag vehicle as N and subject vehicle in the target lane as n-1. Also we have to consider that the space difference available will be changed as both the vehicles would have moved a distance during the lane change. Then we substitute the values in the equation 1. If the maximum safe speed can be attained in the time T by the lag vehicle with a deceleration less than the maximum possible deceleration of the vehicle we say that the lane change is feasible