The Four step process and Static assignment

For people with a Complex Systems background it is clear what to do here: Program a version of the real-world spatial substrate, consisting of roads and intersections, and then populate it with agents which follow increasingly sophisticated rules. And in fact, this is what we will describe in the next section. Before we do this, we will however glance at the traditional approach to the problem. This is instructive since it many similarities to a steady-state solution in physics and an equilibrium in economics.

The traditional method of traffic prediction for transportation planning is based on the four step process [2]:

1. Trip generation: This module generates, for each traffic zone, the number of trips starting there and the number of trips ending there. This can be done for arbitrary time slices, but is often done for a typical 24-hour weekday.

2. Trip distribution: Trip generation results in sources and sinks, but not how they are connected. This is done in the trip distribution module. The result is an origin-destination matrix, which has, at row $i$ and column $j$, the number of trips going from zone $i$ to zone $j$.

3. Modal choice: In this module, the trips are split between the modes of transportation.

4. Route assignment: For each trip, a path is found through the network so that no other path is faster. Congestion is taken into account via the link travel time being a function of the trips using that link.

Route assignment has traditionally achieved a lot of attention as a mathematical programming problem. In fact, it can be shown that the solution to a certain version of the above route assignment problem can also be obtained as the solution of a certain non-linear minimization problem. For that reason, many standard methods for non-linear minimization can be used, although certain simplifications are possible because of the structure of the problem [2].

The problem is in fact very similar to a non-linear static network flow problem in physics, where the link ``cost'' (voltage differential) is given via $U = R I$ with a non-constant $R(I)$, and where sources and sinks are given via the result of the trip generation. The only (but important) difference is that in assignment ``particles know where they go'', meaning that one cannot in general exchange particles as one can, in electrical networks, do with electrons.

Static assignment has many shortcomings. Most importantly, it does not correctly represent dynamic effects such as queue build-up, and it does not have enough microscopic information to do, for example, emission calculations. It also de-couples decisions from individual actors. For example, the only decision available for modal choice is the origin and the destination of the trips; important aspects such as income, car ownership, additional trips during the day, etc. are not used. These latter aspects could however be overcome by a different software design. What cannot be overcome are the shortcomings in the representation of dynamic effects - or, differently stated: when reformulating the dynamics so that it becomes more realistic, most if not all the known mathematical results become invalid, meaning that one loses all the mathematical guidance which has made static route assignment so attractive.