Link-Based Signalized Arterial Progression Optimization with Practical Travel Speed

Table 1

Calculation of upper/lower interference for link bandwidth.

Common situation	Upper interference	Lower interference
𝐺OBT,𝑖≤𝐺OBT,𝑖+1𝐺IBT,𝑖+1>𝐺IBT,𝑖	UI𝛽𝑖,𝛽𝑖+1=𝐺𝐼𝐵𝑇,𝑖−(−RO𝑖,𝛽𝑖+𝑇𝑖,𝑖+1+RO𝑖+1,𝛽𝑖+1+𝐺IBT,𝑖+1+𝑇𝑖+1,𝑖)mod𝐶	LI𝛽𝑖,𝛽𝑖+1=(−RO𝑖,𝛽𝑖+𝑇𝑖,𝑖+1−𝑂𝑠𝑖+1,𝑖+RO𝑖+1,𝛽𝑖+1+𝑇𝑖+1,𝑖)mod𝐶
𝐺OBT,𝑖>𝐺OBT,𝑖+1𝐺IBT,𝑖+1>𝐺IBT,𝑖+1	UI𝛽𝑖,𝛽𝑖+1=(𝐺IBT,𝑖−(−RO𝑖,𝛽𝑖+𝐺OBT,𝑖−𝐺OBT,𝑖+1+𝑇𝑖,𝑖+1+RO𝑖+1,𝛽𝑖+1+𝐺IBT,𝑖+1+𝑇𝑖+1,𝑖)mod𝐶)mod𝐶	LI𝛽𝑖,𝛽𝑖+1=(−RO𝑖,𝛽𝑖+𝑇𝑖,𝑖+1−𝑂𝑠𝑖+1,𝑖+RO𝑖+1,𝛽𝑖+1+𝑇𝑖+1,𝑖)mod𝐶
𝐺OBT,𝑖+1≤𝐺OBT,𝑖𝐺IBT,𝑖+1≤𝐺IBT,𝑖	UI𝛽𝑖,𝛽𝑖+1=(𝐺IBT,𝑖+1−(−RO𝑖+1,𝛽𝑖+1−𝑇𝑖,𝑖+1+RO𝑖,𝛽𝑖+𝐺IBT,𝑖−𝑇𝑖,𝑖+1)mod𝐶)mod𝐶	LI𝛽𝑖,𝛽𝑖+1=(−RO𝑖+1,𝛽𝑖+1−𝑇𝑖,𝑖+1−𝑂𝑠𝑖,𝑖+1+RO𝑖,𝛽𝑖−𝑇𝑖+1,𝑖)mod𝐶
𝐺OBT,𝑖+1>𝐺OBT,𝑖𝐺OBT,𝑖+1≤𝐺OBT,𝑖	UI𝛽𝑖,𝛽𝑖+1=(𝐺IBT,𝑖+1−(−𝑅𝑂𝑖+1,𝛽𝑖+1+𝐺OBT,𝑖+1−𝐺𝑂𝐵𝑇,𝑖−𝑇𝑖,𝑖+1+RO𝑖,𝛽𝑖+𝐺IBT,𝑖−𝑇𝑖+1,𝑖)mod𝐶)mod𝐶	LI𝛽𝑖,𝛽𝑖+1=(−RO𝑖+1,𝛽𝑖+1−𝑇𝑖,𝑖+1−𝑂𝑠𝑖,𝑖+1+RO𝑖,𝛽𝑖−𝑇𝑖+1,𝑖)mod𝐶
Special situation	Upper/lower interfence	Interference adjustment
𝐼𝑠𝑖,𝑖+1<0	𝐶+𝐼𝑠𝑖,𝑖+1≤LI𝛽𝑖,𝛽𝑖+1≤𝐶	LI𝛽𝑖,𝛽𝑖+1=LI𝛽𝑖,𝛽𝑖+1−𝐶
LI𝛽𝑖,𝛽𝑖+1<0	𝐶+LI𝛽𝑖,𝛽𝑖+1≤min{GIBT,i,𝐺IBT,𝑖+1}	LI𝛽𝑖,𝛽𝑖+1=LI𝛽𝑖,𝛽𝑖+1+𝐶
𝐼𝑠𝑖,𝑖+1<0	𝐶+𝐼𝑠𝑖,𝑖+1≤UI𝛽𝑖,𝛽𝑖+1≤𝐶	UI𝛽𝑖,𝛽𝑖+1=UI𝛽𝑖,𝛽𝑖+1−𝐶
UI𝛽𝑖,𝛽𝑖+1<0	𝐶+UI𝛽𝑖,𝛽𝑖+1≤min{𝐺IBT,𝑖,𝐺IBT,𝑖+1}	UI𝛽𝑖,𝛽𝑖+1=UI𝛽𝑖,𝛽𝑖+1+𝐶