The algorithms used in traffic assignment attempt to replicate the real-world process of choosing the best path between a given origin and destination. For the RIVCOM model, the algorithm used for assignment is the Frank-Wolfe algorithm. During the assignment process, the trip table is assigned to the highway network over multiple iterations. At the end of each iteration, link travel times are recalculated using the total link demand and compared to the link travel times of the previous iteration. The aggregate change of link travel times between the current iteration and the previous is compared against the convergence criteria. Thus, the number of iterations is determined by a user-defined closure parameter (set to 0.0001 for the RIVCOM model) or for a maximum number of iterations (set to 400 for the RIVCOM model). For a given iteration, the volume-delay function is used to update the link speeds based on the previous iteration’s vehicle demand and the link capacity. The state-of-the-practice Bureau of Public Roads (BPR) function is used for the RIVCOM model. Highway trip assignment is performed separately for the AM peak period, the PM peak period, and the Off-Peak period. At the end of the assignment procedure, the time-period assignments are summed to produce a daily traffic assignment.

The volume-delay function alpha and beta values used in the RIVCOM model are available here by area type and highway capacity manual (HCM) functional class: assignment/vol_delay_alpha

Static Validation

Static validation is an important part of the model development process. Static validation involves comparing model outputs to a data set not used during model estimation. In travel modeling, traffic counts collected in the base year of the model are most often used for this purpose. During static validation, it is important not to lose sight of the model’s actual purpose: to make reasonable predictions of the future. A model that perfectly replicates base year counts but is improperly sensitive to changes in the underlying input data is overfit and has failed.

It is also important to understand that traffic counts are themselves estimates and often come with a high degree of error. This is another reason why the goal of static validation should not be to perfectly match count data. Instead, the goal of validation is to ensure that an otherwise robust behavioral model can reasonably replicate current travel demand

There are several guidelines for comparing observed count to modeled volume. Three main criteria are often used:

  • maximum percent root mean square error (%RMSE) across all links,

  • correlation coefficient between model volume

  • % of links within the “maximum allowable deviation”.

Percent root mean square error (RMSE) – RMSE is the square root of the model volume minus the actual count squared divided by the number of counts. %RMSE is obtained by dividing RMSE by the average count value. Correlation coefficient – estimates the correlation (strength and direction of the linear relationship) between the actual traffic counts and the estimated traffic volumes from the model. “Percent of Links within Allowable Deviation” measures how many links of a certain functional class or volume group have modeled volumes that are within an acceptable tolerance of the count value. The maximum allowable deviation for a link type is based on the NCHRP Report 255 curve. The curve gives the acceptable amount of percentage deviation for an observed count. The acceptable deviations are higher for lower counts and decreases as the count increases. For RIVCOM, this criterion is checked for each link and then aggregated to the percentage of links that satisfy the criterion.

Maximum desirable error for link volumes

Maximum desirable error for link volumes

Overall Table

The table below shows the system-wide validation statistics for the three measures described above. The model %RMSE and the correlation coefficient are well within the accepted standards. The percentage of links within the maximum allowable deviation are less than our target value of 75%. This is mainly because most of the count data (300 out of 626 counts) used in validating the RIVCOM model is for minor arterial and below facility types, which generally tend to have lower volume and therefore small absolute change results in large percent change.

Overall Highway Validation Statistics
Statistic Model Threshold
% RMSE Overall 26.9% Below 40%
Correlation Coefficient 0.97 At Least 0.88
Percent of Links within Allowable Deviation 66.8% At least 75%

By Volume Group

The table below shows the validation statistics by different volume groups. %RMSE decreases for higher volume group, which is expected. In addition, the percentage of links within allowable deviation also increases for higher volume group category. These two metrics show that the RIVCOM model validates well at the principal arterial and above level and does a good job at levels below.

Volume Group Highway Validation Statistics
Count Volume Group Number of Links Mean Count Mean Model Volume Percent RMSE Percent Links Within Dev. Correlation Coefficient
<5000 65 3064 3648 109.82% 55.4 0.39
5000-24999 374 14195 14965 39.04% 63.9 0.66
25000-49999 80 32527 34343 27.34% 65.0 0.64
50000-99999 90 75309 73798 15.71% 82.2 0.78
>=100000 17 116484 113883 8.97% 100.0 0.81
Total 626 26946 27411 26.94% 66.8 0.97

By Facility Type

The validation by facility type is like the one for volume groups. % RMSE numbers are better for highways (general purpose) and major arterials than for minor arterials and collectors. HOV links have higher %RMSE than GP lanes, which is generally true for all transportation models.

Facility Type Highway Validation Statistics
Facility Name Number of Links Mean Count Mean Volume Percent RMSE Percent Links Within Dev. Correlation Coefficient
Freeways 122 73329 73458 15.53% 79.5 0.92
HOV 50 15994 15924 30.94% 68.0 0.59
Principal Arterial 154 21243 23669 33.57% 61.7 0.85
Minor Arterial 175 15615 15181 36% 63.4 0.84
Major Collector 121 9015 8845 51.02% 65.3 0.80
Minor Collector 4 6886 7330 39.55% 50.0 0.91

By Area Type

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Area Type Highway Validation Statistics
Area Type Number of Links Mean Count Mean Volume Percent RMSE Percent Links Within Dev. Correlation Coefficient
Rural 23 15736 17979 44.72% 60.9 0.91
Suburban 71 31559 30016 23.37% 70.4 0.97
Urban 532 26815 27471 27.05% 66.5 0.97


The table below shows the highway validations statistics for city groups. Count locations within Riverside County is grouped into seven city groups (or unincorporated) based on the geographic proximity. The mean volumes are very close for all the city groupings, showing that the model captures the regional traffic pattern well throughout the region. Percentage of links that are within the allowable deviation is best for Riverside/Corona, Moreno Valley and Coachella groups.

City Type Highway Validation Statistics
City Group Number of Links Mean Count Mean Volume Percent RMSE Percent Links Within Dev. Correlation Coefficient
BEAUMONT_BANNING 28 12795 10114 42.54% 53.6 0.96
COACHELLA_PALM SPRINGS 126 14133 15960 35.85% 60.3 0.86
CORONA_RIVERSIDE 162 26107 26957 25.78% 69.8 0.97
MORENO VALLEY_PERRIS 41 17817 17677 25.52% 75.6 0.96
San Bernardino County 131 46666 47467 23.2% 66.4 0.96
SAN JACINTO_HEMET 8 16817 16680 22.88% 87.5 0.88
TEMECULA_LAKE ELSINORE 82 24309 21624 24.25% 68.3 0.96
Unincorporated Riverside County 48 31839 34346 22.31% 68.8 0.99