Graphical Optimization Method for Symmetrical Bidirectional Corridor Progression
Algorithm 3 Second round rotation transformation procedure.
Our third step is to optimize the common signal cycle and offsets, and the second round of the rotation transformation routine can be presented below.
Second Round Rotation Transformation Procedure
Step0. Determine the bottleneck intersections and the set SBm-1 and SEm-1.
According to Fp, V(2,m-1), C1, and λp, draw the beginning and end PTC lines in the time-space diagram. If Ip is the bottleneck intersection of the beginning PTC line, let and add Ip in set SBm-1, else . And if Ip is the bottleneck intersection of the end PTC line, let and add Ip in set SEm-1, else .
Step1. Make a judgment of whether the sets SBm-1 and SEm-1 meet any condition for stopping rotation.
If , or and , or and , then , finish the second round of rotation transformation. Otherwise, , proceed to Step 2.
Step2. Determine the rotation direction.
If , let , else if , let .
Step3. Determine the rotation angle.
If , connect points PEi and PFg (i + 1 ≤ ≤ n), points PBj and PSh (1 ≤ h ≤ j-1) in turn, calculate the corresponding VFg and VSh as shown in Equation (6), add the eligible VFg and VSh in set SVm, then select the maximum value in SVm as the updated adjusted speed V(2,m).
If , connect points PEi and PFg (1 ≤ ≤ i-1), points PBj and PSh (j + 1 ≤ h ≤ n) in turn, calculate the corresponding VFg and VSh as shown in Equation (6), add the eligible VFg and VSh in set SVm, then select the minimum value in SVm as the updated adjusted speed V(2,m).
