A Route Assignment Program Algorithm - algorithm

Question

What im trying to do, is create a program that will assign a route for a driving test. there will be three diffrent routes, linked together at certain points. Never should there be more than one student at a point of intersection.
Best way to solve this is to schedule these interection points by time.
This isnt my only problem, i will need routes to be equally distributed to examiners.
So route 1 will be given to examiner 1
route 2 - examiner 2
route 3- examiner 3...
The Real Baumann suggested this:
Calculate collision times from start.
Route 1 has 6 points. {A,B,C,D,E,F}
Route 2 has 5 points. {A,F,G,H,I}
Route 3 has 6 points. {A,H,K,L,M,N}
Possible Collisions at: {A,F,H}
So you need to calculate the following times:
Route 1: A->F, A->A
Route 2: A->F, A->H, A->A
Route 3: A->H, A->A
From here you can calculate time differences that create a collision.
If it takes you 20 minutes to go from route 1A to Route 1F and 5
minutes to get from Route 2A to Route 2F, then you know a collision
will occur if start an appointment on Route 2 exactly 15 minutes after
you began an appointment at Route 1.
Then you would have a set of non-working collisions:
Route 1 & 2 collide at: 15, 25, 40
Route 1 & 3 collide at: 25, 30
Route 2 & 3 collide at: 30, 40, 45
This i can understand to a point. But in terms of an algorithm i dont know where to start.
IF someone could help me with some pseudo code to work off, or something to make it clearer in my own mind. it would help a lot.

Answer 1

You should be able to calculate collision times from start.
Route 1 has 6 points. {A,B,C,D,E,F}
Route 2 has 5 points. {A,F,G,H,I}
Route 3 has 6 points. {A,H,K,L,M,N}
Possible Collisions at: {A,F,H}
So you need to calculate the following times:
Route 1: A->F, A->A
Route 2: A->F, A->H, A->A
Route 3: A->H, A->A
From here you can calculate time differences that create a collision.
If it takes you 20 minutes to go from route 1A to Route 1F and 5 minutes to get from Route 2A to Route 2F, then you know a collision will occur if start an appointment on Route 2 exactly 15 minutes after you began an appointment at Route 1.
Then you would have a set of non-working collisions:
Route 1 & 2 collide at: 15, 25, 40
Route 1 & 3 collide at: 25, 30
Route 2 & 3 collide at: 30, 40, 45
From here you should pretty easily be able to create your schedule without collisions.

Answer 2

I'm supposing you're not asking for tips on writing a super-duper algorithm that can resolve hundreds of paths with thousands of intersections simultaneously. It sounds like you need something simple and serviceable, so let's aim for that.
First off, let's simplify the problem. Looking at the map, what you're really saying is something like this: If a student starts route 1 at 8am, he'll be in intersection A sometime between 8:03 and 8:05, and then in intersection B sometime between 8:07 and 8:09.
To ensure that no other students are in the intersection, you can consider Intersection A "booked" from 8:03-8:05 by the first guy, and Intersection B "booked" similarly from 8:07-8:09.
Each intersection would have its own busy/free table.
Each time you schedule a route, you book the appropriate intersections during the time you believe the student will be in them.
When looking for the earliest available time for a route, you go through the routes and consider start time X "available" for that route if the of each intersections you'd pass through on the route are available at the time you'd pass through them.