Queue in HCM 7th vs. Micro Simulation
The objective of this article is to provide a brief overview of queue length calculations in Highway Capacity Manual 7th (HCM 7th) and micro simulation and to explain how to compare the two. This is important for using the queue length as a measure for calibration/validation of the simulation against the HCM or for reporting equivalent measures between the two. It should be noted that the results of the HCM are valid within the limitations of the methodologies stated in HCM.
Introduction
VISSIM and other traffic micro simulation software, output the following with respect to the queue upstream a point over each time interval:
QLenAvg: Average queue length (back of the queue distance) over the time interval (in unit of length)
QLenMax: Maximum queue length (back of the queue distance) reached in the time interval (in unit of length)
QStops: Total number of stops of vehicles that are in the queue (vehicles that meet queue definition) over the time interval
Note: Due to the stochasticity of simulation, usually the average of multiple simulation runs is reported as the reliable value of the outputs. In this article, this average value for any output “x” is called RunsAvg(x).
Highway Capacity Manual (HCM) methodologies output the Queue Length (average/mean queue length) for signalized intersections, and 95th Percentile Queue Length for both signalized and unsignalized intersections. The results are in vehicles (over a specific object, depending on the type of the intersection).
It should be noted that in the HCM calculations there is no time dimension. Therefore, the calculated queue represents the analysis time period or in other words is assumed to be fixed over the analysis time period (peak 15 min within the peak hour).
It is generally accepted that, under similar conditions in the field and for the same time period of the day, the length of queue follows a normal distribution due to the stochastic nature of traffic operation. In queue length discussions, the mean and 95th percentile refer to this normal distribution.
Besides, for the normal distribution the mean and 50th percentile (median) are equal. In some traffic analysis software, the average queue length is called 50th percentile while the HCM does not mention to 50th percentile and instead calls it either mean queue length or simply queue length.
Signalized Intersections
For signalized intersections, the HCM assumes that the maximum queue length in each signal cycle occurs during the green after the end of red. Exhibits 31-20 and 31-25 illustrate this assumption. As mentioned above, since there is no time dimension in the calculations, this value is assumed to represent the analysis time period or in other words to be constant for all cycles in the analysis time period.
Theoretically the HCM counts fully stopped vehicles as/in the queue. However practically, it considers 5 mph as the speed threshold for the fully stopped definition (page 31-67). It analyzes the simplified trajectory of the vehicles that arrive at the intersection and develops the relations. The three terms of Q (Eq 31-149) are explained on pages 31-64 to 31-66.
Note: In HCM Exhibits 31-21 to 31-24, the “v” should be on the vertical edge of the slope triangle.
With the explanations above for the mean queue length of the HCM, the most similar direct output from VISSIM 2025 is RunsAvg(QLenMax). Comparing the concepts behind the two, generally this VISSIM output over 15 min time intervals will be greater than the HCM result, because it is not averaged over the time interval and instead, it is the maximum during the time interval.
To clarify more, please note that the analysis time period of the HCM is the peak 15 min. If the same Evaluation Interval is used in VISSIM and assuming the signal cycle length is on average 90 seconds, there will be 10 cycles in the time interval or analysis time period. Apparently, there will be a difference between the average and maximum of the queue length for these 10 records.
To resolve the issue, the queue length can be collected over shorter evaluation time intervals (30 seconds matches with most practically used cycle lengths) and then the QLenMax become post-processed to obtain a better equivalent value to the HCM. To post-process, this collected data should be matched with cycle records to obtain one value for each cycle and then gets averaged over 15 min time intervals.
Any tricks to be applied to make the outputs of VISSIM more similar to the HCM, should be practically applicable to the scale of the model and should not cause any errors or long runtimes.
It should be noted that the queue of signalized intersections in the HCM is calculated for each lane group (please refer to the HCM for the definition). It is while, in general in VISSIM:
Output of the Evaluation Node (in Node Evaluation results) is for each Movement.
Output of the Queue Counter is over the cross-section of the Link. This will literally be the maximum of lane groups. As a simple trick, using a short dummy Link for each lane group on top of the actual Link, the lane group result can be output. “Consider adjacent lanes” option must be off for this trick and please note that this affects all queue results in VISSIM (both Queue Counters and Nodes together).
In addition, the HCM does not account for the length of the lanes (neither turning storage lanes, nor traveling lanes). As the result, the value of the queue of the lane group is not limited by the vehicle storage size of the lane group. This is actually why the HCM 95th percentile queue can be used to determine the required length of the associated storage lane(s). This is not the case in VISSIM.
Note: 95th percentile values are referenced in determining/designing the length of storage lanes. This is to keep the probability of overflow of the storage lane and resulting blockage of travel lanes to only 5% of the time. Just to mention, the HCM results are in vehicles for each lane group (that may have multiple lanes).
The HCM calculates the mean queue length (Eq 31-149) and then to come up with the 95th percentile of queue length, it provides an equation (Eq 31-150) which is literally the mean plus an approximate function of the standard deviation (SD) of queue length.
In general, the one-sided 95th percentile of a normal distribution is equal to Mean + 1.645 * SD (where SD is the Standard Deviation). Assuming the queue length follows a normal distribution, using this equation, the 95th percentile of the queue length can be calculated based on the mean and standard deviation of the normal distribution of queue length output by VISSIM (RunsAvg and RunsSD of QLenMax or its post-processed version mentioned before).
Additionally, the simplest method for determining the 95th percentile (which is the method used by VISSIM in determining the 95th percentile of the results, Runs95%(x)) is to arrange the records in ascending order and pick the item that 95% of the records are equal to (with inclusive definition of percentile) or less than that. For example, among 20 records, the 19th item (in ascending order) is the 95th percentile. Where the number of the records is less than 20, this will be equal to the maximum. So where the number of simulation runs is less than 20, simply the RunsMax(x) can be used as the 95th percentile of output “x”. For example, where the number of runs is less than 20, RunsMax(QLenMax) can be used as the 95th percentile queue of signalized intersections (apparently, the QLenMax can be the post-processed version explained before).
Unsignalized Intersections
For unsignalized intersections and roundabouts (RB), the paper that is referenced by the HCM (An approximation for the distribution of queue lengths at unsignalized intersections by Ning Wu in 1999) approximates the distribution of the queue length (averaged for/fixed over the analysis time period) based on assumptions on probabilities of the arrivals and simplifications. Then extracts the 95th percentile queue length from the distribution.
As mentioned, the distribution of the queue length above is more accurately the distribution of the average queue length of analysis time period (since there is no time dimension). So it can be concluded that RunsAvg(QLenAvg) from VISSIM is equivalent to the mean queue of this distribution. To calculate the equivalent value for the 95th percentile queue of the HCM, any of the methods mentioned in previous section can be used, for example RunsMax(QLenAvg) if the number of simulation runs is less than 20.
In the HCM methodologies, 95th percentile queue for TWSC is calculated for each movement. For AWSC and RB, it is on each lane.
Just to add, conceptually for unsignalized intersections and roundabouts, mean queue length can be calculated using the equation below. For TWSC this will be for each movement and for AWSC and RB it will be for each lane.
Mean queue length (veh) = AvgDelay (s) x Flow rate (veh/hr) /3600
Queue Length in Freeway Modeling
In simulating freeways (and highways), both RunsAvg(QLenAvg) and RunsAvg(QLenMax) have their own use cases and so both should be reported. Depending on the objectives of the model, RunsMax or other aggregation functions may additionally be useful.
