ITE Journal - January 2020 - 38

demand, as witnessed by queues that form and grow during the
congested period. If actual demand data are not obtained when
conditions are congested, the flow rate cannot exceed capacity
(by definition) and the analysis can significantly underestimate
delay and queues. Once demand exceeds capacity, the arrival rate
upstream of the stop line must be known in order to accurately
estimate the demand.
An illustrative example is provided in Table 2, where hypothetical volumes for an intersection lane group are shown. The lane
group capacity is 500 vehicles per 15-minute period. Stop line
departures are counted and totaled every 15 minutes. Counts for
time periods (TP) 1 and 2 are 300 and 400 vehicles, respectively,
which is less than capacity. Accordingly, there is no residual queue
at the end of these time periods.
At the end of Time Period 3, 500 vehicles have been observed
to cross the stop line and there is a queue of 25 vehicles. The queue
continues to grow over successive time periods until it reaches a
maximum (325 vehicles) at the end of TP 7. It remains for three
more time periods before finally disappearing at the end of TP 11.
To accurately compute the demand, the queued vehicles for the
period in question (t) must be added to the stop line count for the
same period, but the queued vehicles at the end of the previous
period (t-1) are subtracted, as they were the first vehicles to be
served in period t and are included in the stop line count.
The graph in Figure 2 shows the disparity between stop line count
and demand for this illustrative example. Beginning with TP 3 and
extending through TP 7, the actual demand exceeds the stop line
count, which results in underestimating the d3 term in the HCM delay
equation. Because delay increases exponentially when conditions are
oversaturated, the delay can be grossly underestimated.
When oversaturation is reached, stop line counts will be the
same (or very similar) for each time period and there will be
Table 2. Tabulation of Demand Over Multiple Time Periods.

38

J a n uar y 2020

i te j o u rn al

Figure 2. Comparison of Demand versus Capacity (Stop Line Departures).
residual queues. By counting the number of queued vehicles at the
end of each time period, the actual demand can be estimated using
the method provided in the example.

Application
Several commercial software tools implement the deterministic
HCM methods in their analysis of signalized intersections. To
accurately estimate delay when conditions are oversaturated, tools
should be capable of:
ƒ Performing multiple-period analyses when conditions are
oversaturated; and
ƒ Estimating unmet demand at the beginning of each
analysis period.
Before using any particular tool, it is the obligation of
the analyst to ensure the correct application of the tool when
conditions are oversaturated. Failing to do so undermines the
credibility of the tool, the analyst and the conclusions drawn from
the evaluation. In reporting the results, performance measures
(including delay) should be tabulated for each 15-minute time
interval within the study period. While this may expand the
reporting of results, it provides a more accurate picture of intersection operations within the entire peak period, regardless of its
length, and more importantly leads to better decision making in
mitigation efforts.
Some may choose to use microscopic simulation as an
alternative tool. Simulation tools compute delay differently than
the deterministic method documented in the HCM. However,
a properly calibrated simulation model should provide similar
results to the HCM method. Regardless of which approach is
taken, the temporal variation in demand over the analysis period
should be adequately reflected, whether in a multiple period
deterministic analysis or a microsimulation analysis.



ITE Journal - January 2020

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https://www.nxtbook.com/ygsreprints/ITE/ITE_December2019
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https://www.nxtbook.com/ygsreprints/ITE/G110110_ITE_October2019
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https://www.nxtbook.com/ygsreprints/ITE/G99495_ITE_October2018
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