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3.4 Methodologies for Estimating Speed in Areas with a TDF Model
The use of a TDF model requires development of a computerized roadway network, typically representing all major roadway links in a region. The model then estimates traffic volumes on these represented links, for a base year and forecast years. Thus, areas that use a TDF model have volume and capacity information for all major roadway links, and can use this information to estimate speeds for the purpose of estimating emissions.
This section discusses methods for estimating speeds for links covered by the TDF model, as well as methods for estimating speeds for links outside of the TDF model coverage (i.e., donut areas beyond the MPO modeling area).
3.4.1 Methodologies to Estimate Speeds in Model Area
A TDF model estimates traffic speed on each link as part of the network assignment process. The assignment process typically determines the route between an origin node and a destination node that results in the shortest travel time. The assignment process is iterative - all trips are first routed based on free-flow travel times, then link travel times are recalculated based on congestion delay, then trips are re-routed based on the new link travel times, and so on until the process reaches equilibrium.
TDF models are typically calibrated so that they closely match observed traffic volumes, but not traffic speeds. Because TDF models must quickly calculate speeds for thousands of links, they use relatively simple equations, such as the BPR formula, and generally do not account for detailed facility or traffic characteristics in the speed calculation. TDF models calculate speeds only for the purposes of facilitating the traffic assignment process, not for the purpose of emissions estimation or other planning practices. Thus, the TDF model speeds may or may not accurately reflect current and future speeds.
Some regions use TDF model speeds directly for developing emission factors (Method 1). Other regions perform adjustments of TDF model speeds to improve accuracy (Method 2), or use a post-processor to estimate speeds rather than use TDF model speeds (Method 3). Use of a post-processor typically relies on methods such as the BPR formula described in Section 3.3.
Estimating Speed with a TDF Model: Analysis in Area Covered by Model
Method 1: Use TDF Model Outputs

- Description
- This methodology makes use of TDF model outputs to develop the speed inputs for the MOBILE model. TDF models estimate traffic speeds on each link for the purposes of assigning trips to the network. These traffic speeds can be used to develop emission factors, either by estimating a VMT distribution by speed or by estimating average speeds by facility type.
- Method Applicability
- This method is applicable for areas that have a validated TDF model, but do not have observed traffic speed data for the purposes of modifying inaccurate model speeds and do not have the resources for more detailed and accurate speed estimation methods.
- Data Sources and Procedures
-
If the TDF model speeds are determined to be acceptable, link-level speeds can be processed for developing emissions factors in the MOBILE6 model. The best option is to determine the distribution of VMT by speed bin for each facility type. Link volumes are multiplied by link length to calculate link VMT. For each facility type, link VMT is then allocated to speed bins, and the distribution of this VMT become a MOBILE6 input.
Alternatively, links can be grouped by facility type, and an average speed (weighted by VMT) calculated for each facility type. The same process is applied for base year speeds and forecast year speeds.
- Advantages
-
- For regions with a calibrated TDF model, this method requires little additional resources or effort.
- Accounts for future changes in traffic volumes and congestion.
- Limitations
-
- TDF models are not designed to accurately calculate speeds. Actual speeds may differ significantly from modeled speeds.
- Example Location
-
Butte County, California used this method to develop emission factors for NOx, VOC, and CO. Madera County, California used this method to develop emission factors for NOx, VOC, and PM-10. Both counties used TDF model output to group link VMT by speed for the purposes of estimating a VMT distribution by speed bin.
Bannock County, Idaho used this method to estimate average speeds by facility type for the purposes of developing PM-10 emission factors in MOBILE6.2.
Resources:
Butte County Association of Governments, "Draft Air Quality Conformity Determination for the 2001 Regional Transportation Plan And Adopting Resolution", Adopted April 26, 2001.
Earth Matters, "San Joaquin Valley Air Quality Modeling Procedures - 2001 RTPs and TIPs," 2001.
Estimating Speed with a TDF Model: Analysis in Area Covered by Model
Method 2: Use TDF Model Outputs with Adjustments where Model Values Appear Unreliable

- Description
- This method relies on TDF model speeds where they appear accurate and makes adjustments to the model speeds where they appear inaccurate when compared against a sample of observed traffic data.
- Method Applicability
- This method is applicable for areas that have a validated TDF model and have some observed traffic speed data for the purposes of modifying inaccurate model speeds.
- Data Sources and Procedures
-
This method first requires a review of TDF model output speeds to assess their accuracy. Data on observed traffic speeds should be organized by link, and then compared to the modeled speeds on those links. Modeled speeds may be unacceptable for all facility types, or may be unacceptable for only selected facility types (e.g., arterials) or for selected area types (e.g., CBD).
In the case of facility/area types for which model speeds appear accurate, these speeds are used as described in Method 1. The best option is to determine the distribution of VMT by speed bin for each facility type. Alternatively, links can be grouped by facility type, and an average speed (weighted by VMT) calculated for each facility type. The same process is applied for base year speeds and forecast year speeds.
In the case of facility/area types for which model speeds are inaccurate, a variety of approaches can be taken. In some cases, modeled speeds may simply be scaled up or down to better reflect observed speeds. Speeds can also be estimated by applying a formula or look-up table based on the V/C ratio (see Method 3 below). The same process is applied for base year speeds and forecast year speeds.
- Advantages
-
- For regions with a calibrated TDF model, this method requires little additional resources or effort.
- This method makes use of TDF model speeds where they appear accurate, which can save time and resources as compared Method 3 (below).
- Limitations
-
- Modeled speeds may accurately reflect base year observed speeds, but may not accurately estimate future year speeds.
- If modeled speeds are adjusted up or down to match base year observed speeds without consideration of V/C ratio, the method may be inaccurate for estimating future speeds.
- Example Location
-
A variation of this method was used to estimate NOx and VOC emissions in Parkersburg, West Virginia (Wood County). A review of TDF model speeds revealed that the model was overestimating speeds on local roads. For urban local roads, the MOBILE6 local road default speed was used. For rural local roads, an average of the model speed and the MOBILE6 default speed was used.
References:
Wilbur Smith Associates, "Appendix F - Air Quality Conformity Analysis" from the Wood-Washington 20 Year Multimodal Transportation Plan, January 2004.
Estimating Speed with a TDF Model: Analysis in Area Covered by Model
Method 3: Use Formula and/or Lookup Tables to Estimate Speed Based on Modeled V/C Ratio

- Description
- This method makes use of the link-level volume and capacity information from the TDF model to estimate speeds, typically using some form of the BPR formula. The TDF model speeds are not used. This is the method employed by most large urban areas when estimating emissions. (For detailed information on this method, refer to NCHRP Report 387, Planning Techniques to Estimate Speeds and Service Volumes for Planning Applications and Travel Model Speed Estimation and Post Processing Methods for Air Quality Analysis, Federal Highway Administration, 1997; see Resources information for web links).
- Method Applicability
- This method is applicable for areas that have a validated TDF model, have observed traffic speed data, and have sufficient resources to apply more detailed and accurate speed estimation methods.
- Data Sources and Procedures
-
The method estimates speed using some form of the BPR formula, which is based on the volume/capacity (V/C) ratio and the free-flow speed. BPR-type formulas require three inputs: free-flow speed, roadway capacity, and traffic volume. The accuracy of this method is highly dependent on the accuracy of the capacity and free-flow speed inputs. The development of these inputs is discussed under Method 4 in Section 3.3 and in the Appendix of this report. It also is reviewed below.
Because most TDF models are run for a 24-hour period or for peak and off-peak periods, this method can be used to estimate hourly speeds if this level of detail is desired for MOBILE6 input. To do this, link-level volumes are distributed by hour of day, based on distribution fractions typically developed from local traffic count data. The hourly VMT on each link is calculated by multiplying link volume by link length. Link speeds are estimated based on the
V/C ratio, using the BPR formula, look-up tables, or other methods. A VMT distribution by speed bin then can be calculated for each hour of the day, by facility type.Free-flow speed estimation
NCHRP Report 387 recommends estimating free-flow speed by link using separate equations for unsignalized and signalized facilities. These equations are presented in the Appendix.
Many regions estimate free-flow speeds based on look-up tables developed from default values in the Highway Capacity Manual, NCHRP Report 387, or other sources.
Some regions estimate free-flow speed by facility type using simplistic methods based on the posted speed limit, such as adding or subtracting a fixed amount to/from the speed limit. For example, one region used the speed limit plus 5 mph for highways based on typical observed speeds. Another region multiplied the speed limit for each functional classification by a fixed percentage (e.g., 62% of speed limit for collectors) developed from observed speeds. When using these rules for estimating free-flow speeds, the equations often differ based on area type (e.g., CBD, rural).
Other regions estimate free-flow speeds by facility type using observed off-peak speeds.
Roadway capacity estimation
NCHRP Report 387 recommends a set of equations for estimating capacity that are based on the 1994 Highway Capacity Manual. There are separate equations for freeways, 2-lane unsignalized roads, and signalized arterials. These equations are presented in the Appendix to this report.
Many regions estimate roadway capacity based on look-up tables developed from default values in the Highway Capacity Manual, NCHRP Report 387, or other sources.
Computing average speed
A variety of equations are used to estimate speeds. The most common is the BPR formula. The updated BPR formula is as follows:
![s = s<sub>f</sub>/[1 + a(v/c)<sup>b</sup>]](formula12.gif)
where: s = predicted mean speed
sf= free-flow speed
v = volume
c = practical capacity
a = 0.05 for facilities with signals spaced 2 mi apart or less
= 0.20 for all other facilities
b = 10
Many regions have modified the parameters a and b so that the formula calculates speeds that more closely reflect observed local speeds. The original BPR formula uses a = 0.15 and b = 4. Other regions have used values of a as high as 1.0 and values of b as high as 11.
- Advantages
-
- Can produce highly accurate speed estimates if applied properly.
- Accounts for future congestion impacts on speed.
- Limitations
-
- In order to produce accurate speed results, requires accurate local information on capacity and free-flow speed. Use of default look-up tables for these values can lead to inaccurate speed estimates.
- To apply this method for individual links, requires detailed information regarding signalization characteristics, traffic characteristics, etc.
- Example Location
-
Ohio DOT uses this method to estimate speeds for small urban areas with TDF models. The TDF model output is used to determine a V/C ratio for each link. Speeds are then estimated using look-up tables taken from the Highway Capacity Manual.
Website: http://www.dot.state.oh.us/urban/index.htm
(Speed forecasting procedures described under "documents" section)
References:
"Technical Memorandum: Clinton County 2000-2003 STIP/TIP Emissions Estimate," Ohio DOT, May 25, 1999.
Statewide Travel Time Study, Gregory T. Giaimo, Ohio DOT, May, 2001.
3.4.2 Methodologies to Estimate Speeds in Donut Areas not covered by TDF Model
In metropolitan areas that have a TDF model, there may be "donut" areas that are not covered by the model. These areas often lack detailed information on the roadway network and associated traffic volumes. Therefore, to estimate speeds in these areas, the methods presented in Section 3.3 (areas without a TDF model) can be used. Similar to Section 3.3, average speeds by functional class often must be estimated based on a subset of roadway segments. In some case of donut areas, however, output from a nearby area with a TDF model may be available to provide region-specific speed data to help estimate donut area speeds.
Following are the methods that have been identified in practice to estimate speeds in donut areas not covered by a TDF model, which rely to some extent on data from the TDF model:
- Method 1: Using Speeds from Modeled Area by Functional Class
- Method 2: Using a Mix of Speeds data from Statewide Model and from MPO Model
In addition, methods the are applicable to areas without a TDF model (see Section 3.3) can also be applied in donut areas, such as use of observed speeds and/or speed limits, or use of a formula and/or lookup tables.
Estimating Speed with a TDF Model: Analysis in Area Not Covered by Model
Method 1: Use Speeds from Modeled Area by Functional Class

- Description
- This method assumes that TDF model speeds apply to the non-modeled donut areas.
- Method Applicability
- This method is most applicable if little or no roadway traffic volume and capacity information is available for the donut area.
- Data Sources and Procedures
- To apply this method, the speeds generated from the TDF model are used for the donut area. If the region uses the TDF model to estimate average speeds by functional class, then these average speeds are used for the VMT by functional class in the donut area. If the region uses the TDF model to develop a VMT distribution by speed bin, this distribution can be applied to the VMT in the donut areas.
- Advantages
-
- For regions with a calibrated TDF model, this method requires little additional effort and no new data collection.
- This method it likely to be more accurate than using MOBILE default speeds.
- Limitations
-
- TDF models are not designed to accurately calculate speeds. Actual speeds may differ significantly from modeled speeds.
- Travel speeds in donut areas (often predominantly rural) may differ significantly from travel speeds in the area covered by the TDF model (which are predominantly urban).
- Example Location
-
The Kentucky Transportation Cabinet (KYTC) has used this method to estimate emissions in several donut areas. Average speeds by functional class from the TDF model were assumed to apply to the entire nonattainment or maintenance area, including the donut area.
References: M.L. Barrett, R.C. Graves, D.L. Allen, J.G. Pigman, G. Abu-Lebdeh, L. Aultman-Hall, S.T. Bowling, Analysis of Traffic Growth Rates, University of Kentucky Transportation Center, August 2001.
Estimating Speed with a TDF Model: Analysis in Area Not Covered by Model
Method 2: Use Mix of Speeds from Statewide Model and from MPO Model

- Description
- This method involves combining speed results from both a statewide travel model and the MPO's TDF model. A statewide model generally provides broad geographic coverage (including coverage of the donut area) but relatively sparse network detail. The MPO TDF model provides more extensive network detail, but does not cover the donut area.
- Method Applicability
- This method is applicable for a county (or other geographic area) that contains both a donut area covered by a statewide travel model and an urbanized area covered by a TDF model.
- Data Sources and Procedures
-
To apply this method, the statewide model is used to determine speeds by link for the donut area. The metropolitan area TDF model is used to determine speeds by link for the modeled areas within the same county (i.e., for the links contained within both TDF models, speeds are based on the metropolitan area TDF model). Speeds from the two models are then combined, weighted by VMT, and averaged by functional class. The resulting average speeds by functional class are used for the entire county (both modeled and non-modeled areas).
Local roads are not covered by statewide models. To estimate speeds for local roads in the donut area, an average local road speed is calculated for the area covered by the TDF model.
- Advantages
-
- If an area has both a statewide model and an MPO TDF model, this method makes use of both models, which can improve accuracy as compared to using only one model.
- Requires little additional effort and little or no new data collection.
- Accounts for future congestion impacts on speed.
- Limitations
-
- TDF models are not designed to accurately calculate speeds. Actual speeds may differ significantly from modeled speeds.
- Travel speeds in donut areas (often predominantly rural) may differ significantly from travel speeds in the area covered by the TDF model (which are predominantly urban). Therefore, using a single average speed by functional class for a county that contains both modeled area and donut area may introduce inaccuracies.
- Example Location
-
Michigan Department of Transportation (DOT) applied this method to estimate emissions in Allegan County. Michigan DOT maintains a statewide TDF model that includes 2,300 zones and a subset of roadway links. The MPO TDF model covers portions of Allegan County (City of Holland and three townships).
References:
Michigan DOT. "Allegan County Air Quality Conformity." Undated.
Michigan DOT, Travel Demand Analysis Section. "Technical Documentation of the Procedures Used to Develop VMT and Speed Estimates for Michigan Non-Attainment Counties Containing a Modeled Urban Area." 1995.