Despite somewhat unrealistic features on the level of individual
vehicles, these models describe aspects of the macroscopic behavior
correctly.
If we assume the values given above, i.e. a cell size of and a time step of
, then speeds are given in
multiples of
. More correctly,
average free speed is given by
. With
, one obtains the following possible average link
speeds:
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1 | 0.8 | 6.0 | 21.6 | 13.500 |
2 | 1.8 | 13.5 | 48.6 | 30.375 |
3 | 2.8 | 21.0 | 75.6 | 47.250 |
4 | 3.8 | 28.5 | 102.6 | 64.125 |
5 | 4.8 | 36.0 | 129.6 | 81.000 |
6 | 5.8 | 43.5 | 156.6 | 97.875 |
7 | 6.8 | 51.0 | 183.6 | 114.750 |
A typical measurement for real-world traffic is the flow-density fundamental diagram. For this, one measures flow and density at a fixed location over fixed periods of time, for example over 5 minutes. The resulting data is plotted with density on the x-axis and flow on the y-axis (see Fig. 17.1). There are some subtleties involved with measuring fundamental diagrams, which are discussed in Sec. 27.2. For the purposes of this section, let us assume that the two quantities are measured in the CA as follows:
The result is the density in ``number of vehicles per cell'',
corresponding to ``number of vehicles per 7.5 meters''. Multiplying
by converts this into ``number of vehicles per kilometer''.
Flow-density fundamental diagrams, as in Fig. 17.1,
start at zero flow when the density is zero (no cars on the road), and
eventually come back to zero flow when the jam density is reached. In
between, they show a roughly tri-angular shape as can be seen in
Fig. 17.1. Theoretical discussions will be
postponed until Chap. [[cha:traffic-flow-theory]], but it is
important to note that there is some value of maximum flow, about
in Fig. 17.1. For the STCA, this
value depends mostly on
: Larger
leads to
smaller maximum flows. These maximum flow values, also called
capacities, need to come out approximately correctly if one
wants a model that is useful for reality. 2000 vehicles per hour and
lane is a plausible value. Regional differences could be accomodated
by different values of
; this could even be made a function
of the link. One however has to note that changes in
also
change the average acceleration of vehicles, which will, for example,
change signal timing requirements or emissions. This is the reason
why the CA approach can only be seen as a first, relatively rough
starting point for a regional model. Once all other problems (such as
demand generation) are sufficiently solved, the CA driving logic
should be replaced by a model with continuous coordinates such as the
ones discussed in Chap. [[maps]].
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