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An implementation of Nagel-Schreckenberg vehicular traffic automaton
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NaSch.py 0.1 An implementation of Nagel-Schreckenberg vehicular traffic automaton. NaSch.py uses Cage software by Erik Max Francis (which you can download at http://www.alcyone.com/software/cage/) The basic requirements to run NaSch.py are: -cage (latest version, at time of realease it is 1.1.4) -PIL , python image library, which maybe you can install via the python setuptools -I have tested cage (and NaSch.py) with Python 2.5, 2.6 & 2.7 . It should run nice with Python 3, buth I'm not certain --- Installation & Running: -Copy nasch.py file in the same directory as cage software (as a matter of fact, you only need the cage.py file, the other files are nice CA players that come bundled with cage) -Run with python nasch.py --- NaSch.py and Cage Cage is a software for simulating cellular automata (CA). It consists of a main engine (cage.py) and several players, which according to certain rules, may be used to render the evolution of certain CA. NaSch.py consists of just some new rules used along with a NaschImagePlayer (extended from cage's ImagePlayer). More info, at the code... ;) --- Nagel-Schreckenberg vehicular traffic model: The Nagel-Schreckenberg (NaSch) model is a theoretical model for the simulation of freeway traffic. It was developed in the early 90s by the German physicists Kai Nagel and Michael Schreckenberg. Using algorithms it delivers predictions for roadway traffic, in particular concerning traffic density and traffic flow. The model was the first to explain how traffic congestions can emerge without external influence as a result of imperfect driving behavior. It is related to the fields of chaos theory and game theory. In the NaSch model, a road is represented by a single line or array of values, each of which represent an empty or an occupied cell. Each cell corresponds to the regular length of a vehicle. A cell with a vehicle is represented by a natural number, from 0 to max_speed (which in NaSch.py is 5, which again roughly corresponds to a maximum speed of something above 100 km/h or 62 mi/h - assuming that a cell correspond to something around 7 meters, which Nagel & Schreckenberg found as the mean longitude of a vehicle plus the space to the next one in a road). Each speed value corresponds too to the distance a vehicle will travel at each iteration. So a speed of 3 means the vehicle will be 3 cells in front of its current position at the next iteration. At each iteration of the CA, 4 rules are applied to each cell, to calculate if a vehicle will occupy it or not, and at which speed: 1) Acceleration: if vehicle hasn't reached max speed, accelerate by 1 2) Slowing down: in case the accelerated new speed would make the vehicle collide with the vehicle inmediatly in front of it, slow down the vehicle to the maximum speed between its new accelerated speed and the distance to the next vehicle, also, negative speeds aren't allowed 3) Randomnization: to simulate drivers' distractions, slow down by 1 the new accelerated-maybe-slowed-down speed of each vehicle with a probability of p (which in NaSch.py has been initialized to 30%, ie only 30% of the vehicles will be slowed down by this rule). Remember that no negative speeds are allowed 4) Motion: when all vehicles have their new speeds calculated, move them in the road at the calculated speed Of course, more things must be taken into account, such as the topology of the road (is it circular or open at the edges? if open, should new vehicles be injected at the front edge, and at what rate? if open, is it an 'infinite' topology? etc...) In NaSch.py, a circular road has been considered. At last, when a certain number of iterations has been run (in NaSch.py it is 500), you can inspect the 'image' of the different speeds of vehicles accross time. This is the final result NaSch.py will give. You will notice the presence of traffic waves, which are common in vehicular traffic, and which give the common sensation of boredom and desparation in any city ;-) (depending, of course, on the length of the traffic waves) For more information on Cellular Automata: http://en.wikipedia.org/wiki/Cellular_automaton Nagel & Schreckenberg model: http://en.wikipedia.org/wiki/Nagel-Schreckenberg_model Traffic waves: http://en.wikipedia.org/wiki/Traffic_wave At http://es.wikipedia.org/wiki/Modelo_Nagel-Schreckenberg you may find a list of some variants to the NaSch model --- COPYING: NaSch.py is licensed under the GPLv3 license (http://www.gnu.org/licenses/gpl.html) --- Contact: You may contact the author of NaSch.py at [email protected]
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