Limits of the CA technology and relations to other methods

More realistic representations

A standard problem with CA methods is that they may be difficult to calibrate against realistic values. Take for example the STCA as described above in Sec. 2. The length of a cell is straightforward: this needs to be the space a vehicle occupies in a jam in the average. The time step is traditionally taken as 1 sec, which is justified by reaction time arguments [27]. This implies that speeds come in increments of 7.5 m/s; 5 cells per second $=$ 37.5 m/s $=$ 135 km/h is a convenient maximum speed. The remaining free parameter, $p_{noise}$, is now selected such that the maximum flow comes out at 2000 veh/sec; this results in $p_{noise} = 0.2$. Lane changing rules can be calibrated similarly, and can even reproduce the density inversion which happens on German freeways when they are close to capacity [28].

So far so good. The problems start if for some reason the above is not good enough. For example, the existing speed classes are not fine enough to resolve a difference between a 55mph and a 50mph speed limit, a common occurence in the U.S. Similarly, although the fundamental diagram comes out plausibly, acceleration of vehicles turns out to be too high, which is a problem for emissions calculations.

And it is difficult to resolve those problems via a clever choice of the probability $p_{noise}$. For example, increasing $p_{noise}$ leads to lower acceleration (which is desired), but also to lower throughput (which is not desired). A possible way out is to have $p_{noise}$ dependent on the velocity: A small $p_{noise}$ at low velocities together with a large $p_{noise}$ at high velocities leaves the fundamental diagram nearly unchanged while leading to a much lower average acceleration. However, unfortunately such measures also change the fluctuations of the system - for example, such a reduced acceleration will lead to a much wider spread of the times that vehicles need to accelerate from 0 to full speed. Also note that in slow-to-start models, the modifications of $p_{noise}$ are exactly the other way round.

As an alternative, it would be possible to make the resolution of the cells finer, for example to introduce cells of length 3.75 m and make vehicles occupy two cells. It is unclear if this would be worthwhile; it would certainly be slower than the standard method because twice the number of cells needs to be treated.

A possible method that seems to work well in many cases in practice are hybrid simulations. Here, one leaves the cellular structure intact, but allows for offsets of particles against the cellular structure. For directional traffic, it seems that one can ultimately completely dispense with the grid and work with a method that still has a 1 sec time resolution but a continuous resolution in space [27]. The reason why this works for traffic is that it is computationally relatively cheap to keep track of neighbors since a link is essentially one-dimensional. For higher-dimensional simulations, keeping some cellular structure is normally advantagous for that task alone - see for example the parallel code for molecular dynamics which turned out to also handle the problem of neighbor finding very efficiently.

(Even) less realistic representations

Another problem with microscopic simulations often is that the necessary input data is not available. For example, for a CA-based traffic microsimulation one would need at least the number of lanes and some idea about the signal schedules. Most transportation network databases, in particular if they were put together for transportation planning, only contain each link's capacity. It is difficult to construct CA links so that they match a given capacity. The only way seems to be a heuristic approach, by selecting the right number of links and then to restrict the flow on the link for example by a (fake) traffic light. Still, this leaves many questions open. For example, signals phases need to be coordinated so that not two important incoming links try to feed into the same outgoing link at the same time. Furthermore, from the above it is not clear which incoming lane feeds into which outgoing lane (lane connectivities).

In consequence, there are situations where a CA representation is still too realistic, and a simpler representation is useful. A possibility to do this is the queue model. This is essentially a queuing model with added queue spillback. Links are characterized by free speed travel time, flow capacity, and storage capacity. Vehicles can enter links only when the storage capacity is not exhausted. Vehicles which enter a link need the free speed travel time to arrive at the other end of the link, where they will be added to a queue. Vehicles in that queue are moved accross the intersection according to the capacity constraint, and according to availability of space on the next link.

This describes only the most essential ingredients; care needs to be taken to obtain fair intersections and for parallelization [29]. Also, there are clearly unrealistic aspects of the queue model, such as the fact that openings at the downstream end of the link are immediately transmitted to the upstream end. This has for example the consequence that queue resolution looks somewhat unrealistic: queues break up along their whole length simultaneously, instead of from the downstream end. Nevertheless, the queue simulation is an excellent starting point for large scale transportation simulations.