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This paper generalizes an approach for enhancing a standard
input-output diagram to represent graphically the time and
distance that
vehicles spend in a queue upstream of a bottleneck. The
approach requires
the construction of a curve depicting the cumulative number of
vehicles to
have reached the back of the queue as a function of time. The
original
technique, described in a previous paper, is reviewed for
bottlenecks
with constant capacity, and for those where capacity changes
once. The
paper then generalizes the approach to allow multiple changes
in
bottleneck capacity, and relaxes the original assumption of a
triangular
flow-density (q-k) relation to one which is piecewise-linear
concave.
Although it is consistent with the kinematic wave theory of
traffic
flow, the proposed approach is simpler to apply to complex
problems
because it avoids the laborious construction of a time-space
diagram.
It allows the estimation of several measures required in the
evaluation
of the impacts of bottlenecks, including the (accurate) number
of
vehicles in queue and the physical extents of queues at any
time, and
the total time spent by vehicles in different traffic states.
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