Probabilistic Method/Model for Traffic Flow Context:  Given a network system or a traffic system with some value related to the system.
Question: Which probabilistic methods, model, distributions are used frequently to predict a event (for example, congestion of flow of traffic) of that system?
 A: This is going to be a "spherical cow shooting milk in all directions in a frictionless vacuum" approach. The basic idea is fine, but variations may make this model inaccurate. You can make every point where a person can choose to change his path a node in a directed graph. Each street at an intersection would be a node, an exit would be a node, an onramp would be a node, etc. If you can figure out the probability at each node of a person choosing each path from the node (e.g. at the road going north at a specific four-way intersection, 50% of people go forward, 25% go left, and 25% go right) at a specific time, you can construct a giant Markov matrix. You also need to know where everyone's starting position is. After that, you can treat the traffic like a Markov Process.

I drew up an example street graph, in which the dots indicate starting points and the arrows indicate which roads they can take. For instance, if someone starts at intersection A going left, he has a 100% chance of going South, as that is the only direction he can go. If he is at E going North (i.e. he is at the red dot), he has a 33% chance of turning left, a 50% chance of going straight, and a 17% chance of going left. A more complicated example would include parking, so someone could park at A and wouldn't have a 100% chance of going South or East.
