The Mobility Simulation

As said above, the mobility simulation refers to the simulation of the physical transportation system. It computes what happens to the agents' strategies when they are confronted with (a synthetic version of) the real physical world. That synthetic version of the real world specifically includes the interaction between agents, which is responsible for congestion. This implies that a mobility simulation that fits into our framework needs to be capable of executing the strategies (plans) of all agents simultaneously.

As also said above, the mobility simulation needs to return information about the agents' performances to the strategy generation modules. In our implementation, this is achieved by so-called events which are output every time they are triggered. The format of events is ''(time, agent ID, event type)''; examples of events are ``agent XY left from/arrived at activity location'' or ``agent XY entered/left link''. Clearly, it is possible that also ITS devices write event information to file. Our events format has the advantage that it is very easy to implement; it should therefore be possible to implement it into any existing micro-simulation. It also has the advantage that the aggregation of the data is completely left to the strategy generation modules. These can aggregate information according to their own preferences; for example, a router will aggregate information according to link IDs, while the agent database (see below) will aggregate information according to agent IDs.

There are several methods for designing such a mobility simulation. They will be introduced in the following. Only a subset of them is useful for ITS.

The field of traffic operations has a long history of microscopic simulation. Microscopic means that each vehicle is individually resolved, and it is modeled with many aspects of its driving dynamics. There are many different methods for the microscopic simulation of traffic, including coupled differential equations (4,43,30), coupled maps ($=$ models with continuous space and velocity but coarse-grained discrete time; 58,36), and the so-called cellular automata approach (41,18,26).

Alternatives to microscopic models are fluid-dynamical models. Maybe the easiest way to understand them is to cut the road into segments with, say, a length of 1 km, and then to formulate the mass conservation equations for these segments. First,

$$N_{t+\Delta t}(x) = N_t(x) + \Delta t \, \Big( Q_{t}(x-\frac{\Delta x}{2}) - Q_{t}(x+\frac{\Delta x}{2}) + S_t(x) \Big) \ ,$$

which just states that the number of vehicles in segment $x$ is increased by inflow upstream, reduced by outflow downstream, and changed by source/sink terms. The crucial step is to couple the flow terms $Q_t(x)$ to the number of vehicles in the cells. Standard fluid-dynamical partial differential equations are recovered in the limit of $\Delta t \to 0$, $\Delta x \to 0$. A recent example of such an approach to traffic flow is NETCELL (14). Fluid-dynamical models per se do not track individual particles/vehicles, and are therefore unsuitable for ITS (but see further down).

Even more aggregated (called macroscopic) approaches are the volume-based cost function of static assignment, or the gravity model often used in trip distribution (e.g. 44). Those do not have any temporal dynamics and are therefore even less suitable for ITS.

As said above, in traffic a pure fluid-dynamical method is often not very useful, since it does not allow one to track individual particles/vehicles. In such cases, hybrid methods, corresponding to the smoothed particle hydrodynamics method (27), are useful: They keep individual particles, but move them according to fluid-dynamical equations. Examples from the traffic simulation area are DYNEMO (51), DYNAMIT (20), and DYNASMART (21).

In order to push the limits of computational feasibility, it makes sense to search for very fast microscopic (or mesoscopic) models. A good example of this is the so-called queue model (25). It has similarities to queuing theory and queueing models (e.g. 53), because it decomposes a street network into queues. Vehicles are discharged from a queue according to the flow capacity. They then enter the next link, along which they travel with free flow speed. Once they have reached the end of the link, they are added to the queue and they are discharged once it is their turn. So far, this is indeed a standard queuing model. The important distinction is that in the queue model of traffic, the number of vehicles on a link (moving plus waiting) is limited. Once the link is full, no vehicle can enter, and this constraint is propagated upstream, so that in addition to the flow capacity constraint of the link itself also the storage constraint of the downstream link can limit outflow from a link. A critical issue here is the allocation of empty spaces. One possibility is to do this proportional to the capacity of the incoming links (15).

This model, by definition, models free speeds and flow capacities realistically. It has some shortcomings in terms of the speed of the backpropagating kinematic wave, and is limited in its representation of dynamics that go beyond the queuing paradigm, such as lane changing, faster cars passing slower cars, complicated intersection dynamics, etc. Nevertheless, rather realistic results can be achieved with this model, as will be shown in Sec. 5.

Sometimes, the term mesoscopic models is used. By definition, they lie between microsopic and macroscopic models. Yet, the definition is not totally clearcut of what is included and what not.