Splitting lines at multiple points in ArcGIS

I have two shapefiles:

1. First shapefile consists of lines features (approx 1500); it represents the public transport lines
2. Second shapefile consists of point features (approx 3000); it represents the public transport stops on the lines

Now, I want to do a analysis on it and I want to split each line feature into half according to the points. For example I have one line with starting point A and ending point B and 3 point features (lets say a,b,c) on it. I want to split the line and calculate the distance as follows:

1. Split the line in two parts one is from A-a and a-B
2. Split the same line two part one is from A-b and b-B
3. Split the same line two part one is from A-c and c-B

This is what I want to do for the entire network but doing it manually will take a lot of time. How can I identify the tool which can do it fast and without any error?