I am working on finding shortest disjoint path problem, When there are distinct origin destination pairs and there is a predefined time window (or length) associated with each object (which we want to move from one origin to its specific destination). This time window will tell us how long it will take for the object to pass a particular point on the network.
These objects should not encounter each other in any ways on the network, so it is a vertex-disjoint path problem with respect to time. For example if I have two objects A and B, and object A will pass node 1 from 10:00 a.m. to 12 p.m., during these time periods object B cannot cross this node, but any time after 12.00 and before 10 (as long as the time window of B allowed) B can pass through node 1.
I want to know if there is any application of this problem in computer science?