Fundamental
diagram for I-805 traffic
Freeway
traffic seems to come in two familiar "phases" - sparse
and fast, or dense and slow (i.e. jammed). Which is better?
First
of all, we should define what we mean by "better." Probably
the most sensible figure of merit in this regard is the total flow
rate, measured in vehicles per unit time which pass a particular
spot in the road. In this regard, fast is better than slow, but
dense is better than sparse.
A
particularly revealing way to analyze this is to plot total flow
rate (in vehicles per five minute interval) versus average
lane occupancy (low occupancy = sparse; high occupancy = dense).
This plot is what traffic scientists call the Fundamental Diagram.
Below, in the top panel, we plot the fundamental diagram obtained
from measurements on Interstate 805 (location: north of Governor
Drive) during the week of January 23-39, 2005. The results below
are rather typical of observed freeway data. At low occupancies,
the flow is linearly proportional to the occupancy. This is the
almost free flow regime, in which cars are traveling at their preferred
speeds (typically over the posted speed limit!); the slope is proportional
to the average speed. As the occupancy/density grows, so too does
the flow rate, until at some critical density this all breaks down,
and one starts to get dense, slow-as-molasses congestion. One can
see in the bottom panel, where average speed is plotted versus
occupancy (flow rate = speed x occupancy), how the average speed
is about 70 mph for sparse traffic, but decreases sharply after
the occupancy exceeds about 0.2. Interestingly, the flow rate is
approximately insensitive to occupancy in this congested phase.
So
the answer to the opening question (vis-a-vis total flow rate) is:
neither!
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