In a chaotic traffic scenario, the only rule is to reach your destination as soon as possible by avoiding collisions with your nearest neighbours. It is a kind of directed random walk on the all possible available passages that change dynamically. Such a traffic situation is effective because it avoids collisions and everyone manages to reach his destination if the road doesn't become too crowded. So, it will be nice to see the simulations of the chaotic traffic. Have anyone ever seen such a traffic model?
Why bother with simulations when you can observe the real thing. What you are describing is the situation at any uncontrolled intersection in Vietnam. Maybe it is the same in Delhi however I have no experience. It is facinating to watch at least 500 scooters, cars the occasional truck entering an intersection of 5 roads with little traffic management where clearly the rule is reach destination via the most direct route and avoid collision. It is even more facinating to participate within an intersection on foot getting from one point to another!
Mind you it isn't all just random, there seems to be minor rules which revolve around "might is right pecking order".
Busses always have right of way and the loudest horn, everyone gives way to them and they travel the fasest, taxis like to think they give way to no one (because they are important) except busses, scooters being bigger than bicycles come next then it is the bicycles and pedestrians.
I don't think you can simulate it with simple random walk approach unless you constrained the random walks to maximum width paths and also also permit items to become stationary.
Working with DFA (Deterended Fluctuation Analysis) in pre-earthquake signals, I remember reading of application of DFA to traffic traces. The main concept of DFA is to delineate long-memory traces, if existing. A search of the classical work of Peng et al 1994 and later might help.
I have checked existing references. I found that the one referring to DFA in traffic traces is the following:
G. Dattatreya, 4th WSEAS international conference on
electronics, control and signal processing, 2005, 193–198.
I hope it helps
Lindsay Tremethick, You have understood the problem correctly. The reason I want to simulate it is to test the following: Chaotic traffic under certain condition (to be determined) can be quite efficient. One situation where chaotic traffic does not work is when the number of vehicles are too large. Also, a mix of ordered and chaotic traffic may lead to more traffic jams than the ordered or chaotic traffic alone. These are some hypothesis I want to test. As far as simulation algorithm is concerned, I am going to discretize the journey: it will be a kind of random walk on a two dimensional lattice with the rules I mentioned in the question.
Dimitrios Nikolopoulos, DFA is a method to time series data and I do not know how that relates with random walk or traffic simulation.
You have a interesting problem and I don't think that there is an off the shelf model that will suit your needs as all seem to assume some minor order or rule set is followed. However it seems here http://www.atrf.info/papers/2005/2005_Clement_Taylor_Rao_Mathew_Gundaliya.pdf
may well be onto something similar and it hints that typical models don't quite make the grade.
Thanks Lindsay Tremethick, the reference you have sent me is really helpful. It will be really helpful to view this problem as a case of cellular automata. Moreover, I was thinking of modelling this problem at constant velocity as a zeroth order approximation. The reference you send may show how to incorporate acceleration into the modelling. This seems quite interesting!
The DFA method produces normally two coefficients (alpha's). These are related to the Hurst exponent. Hurst exponent indicates if there is a so called "random walk" or there is a persistent or antipersistent regime. It also indicates if there is long-memory (chaotic behaviour) in the system under investigation. It is one of the marked methods regarding short signals as, I suppose, those of traffic. Therefore it can identify the randomness.
I have been pondering this and after a bit of reading and being pointed in a different direction it appears that pedestrian modelling may well be a reasonable analogue to explore and there is certainly a quantity of literature available online. Why we didn't think about this before escapes me but it make perfect sense that pedestrians in an urban environment generally are not constrained by road rules and make paths of least distance between points without colliding. There certainly is anything significantly different between how pedestrians move amongst one another than what I have seen in the traffic on a Vietnam intersection.
Look at this paper: https://www.researchgate.net/publication/257392971_Investigating_Traffic_Flow_in_The_Nagel-Schreckenberg_Model
The class of models is known as the ``Nagel-Schreckenberg'' model.
Article Investigating Traffic Flow in The Nagel-Schreckenberg Model
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