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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 parti-
cles 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.
