Modelling dual-carriageway traffic behaviour as a complex system: A proposal for discussion.
3. Complexity classes P and NPn
The association between the complexity classes P and NP remains an unresolved problem for computer science . The relation between the set of problems of related complexity P and NP is studied in the branch of theoretical computer science that deals with whether and how efficiently problems can be solved on a computer and dealing with the resources required during computation to solve a given problem. The most common resources are time (how many steps it takes to solve a problem) and space (how much memory it takes to solve a problem), how this applies to the problem outlined, is in relation to maximising the data gathered for a real-world road system with its maximum capacity of cars. The class P is the complexity class that consists of all those question with a yes-or-no answer that can be solved on a deterministic sequential machine with an expression that is constructed from one or more variables, constants and mathematical expressions; the class NP consists of all those decision problems whose solutions cannot be completely verified in a algorithm. When these distinct conditions are applied to our example it is very similar to the example of finding the composite number which becomes very resource dependent in terms of memory and time when the sample number is large.
Due to the large amount of steps in terms of time and space required to model accurately a modern motorway filled to capacity with a maximum number of cars, it is believed that this type of modeling would definitely fall into the classification of NP-hard problem.
4. Microscopic traffic system model
Traffic simulations can evaluate the improvements not only under normal circumstances, but also in hypothetical situations that would be difficult to create in the real-world. However, in this specific model novel strategies are being assigned to the individual drivers and the spread of these strategies is being compared to the global transit times for the model.
4.1 Traffic Regimes
In this model, each car may be in one of three distinct regimes (time headway windows), depending upon how close in time the car is to the car in front of it.
The characteristics that need to be generated at the entry to the micro model are divided into vehicle/driver attributes such as vehicle speed and time headway, and model variables. These micro characteristics are specific to each individual car with a good example being the cars assigned desired car velocity, which is the velocity the car will travel at if not interacting with any other cars. Attributes such as desired speed are generated independently based on the distribution of these characteristics in the general driver population got from an extensive study carried out and assigned to the micro model. Model variables, such as the vehicle’s speed and time headway to the vehicle in front need to be in accordance with the traffic situation upstream and downstream and, as such, are governed by the regimes outlines below. The variables that need to be assigned values at the entry of a vehicle into the micro models are usually: lane, time-headway to the vehicle in front and speed while this work is also looking at driver behaviour. The speed assigned to the vehicle is based on the following algorithm. see Regime 1, Regime 2, Regime 3
Where, th, the time headway is the time at which the car enters the model, V
is the desired speed (F1), F2 is the speed of vehicle directly in front of the car that is traveling along the motorway (F3) and F4 assigned desired speed (F3) of each car.
The above approach was proposed and tested with actual data by the Royal Institute of Technology, Sweden . Measurements of speeds and time headways on an urban freeway in Stockholm show high correlation of speeds between consecutive vehicles on the same lane, in the case of small headways (t1 = 0.5 seconds, t2 = 2.5 seconds). This correlation decreases with increased time headways, and remains at a constant low level beyond t3 = 7.5 seconds. In almost all micro models including this model, an initial acceleration rate of 0 m/s2 is assigned to the vehicles that enter the network.