It was already pointed out in Sec. 17.3 that
important real world quantities for traffic are flow and density. A
third quantity is speed. In fact, there are two different ways to
measure traffic: space-averaged measurements, and point ( spot)
measurements. The space-averaged measurements are done at specific
points in time, and they correspond to what one is used to from, say,
fluid-dynamics. The point measurements are closer to what is measured
in reality: A sensor, e.g. an induction loop, usually covers only a
small amount of space. It is common use to average point measurements
over sometime
, for example
or
.27.1 These differences are not particularly intereresting, but they are
necessary to avoid some caveats.
The two measurements are:
![]() |
(27.1) |
![]() |
(27.2) |
Travel velocity is the more relevant quantity since
is the
time an average traveller needs for a distance
. It is also the
quantity which is relevant for fluid-dynamical relations, for example
.
(also throughput). This is traditionally the most important
quantity, since it is easy to measure (one just has to count the
number of passing vehicles at a fixed location), and it is important
for the performance of the transportation system as a whole. In order
to allow comparison, it is often useful to divide flow by the number
of lanes. Say that during time we have measured
vehicles.
Flow then is
![]() |
(27.4) |
Transportation science also uses the term volume. According to Gerlough and Huber (48), this should be reserved to hourly flows (i.e. measured over one hour and expressed in ``vehicles per hour''). Maximum flow is also called capacity.
There is no direct way to measure space-mean flow. However, sometimes
it is useful to use the relation . We then have
![]() |
(27.5) |
Space-averaged density
is the number of vehicles on a certain
stretch of road, divided by the length
of that stretch. In order
to allow comparison, it is useful to also divide by the number of
lanes:
![]() |
(27.6) |
Point density has no natural measurement. One can use
.
An alternative method for point density is the ``fraction of time that
a sensor is covered by a vehicle'', also called occupancy.
Unfortunately, this quantity is difficult to obtain from a
time-discrete simulation. Since the duration a sensor is covered by a
vehicle is , the correct measurement in a simulation would
be [[check]]
![]() |
(27.7) |