Office of Operations Freight Management and Operations

CHAPTER 5: CAPACITY AND PERFORMANCE ANALYSIS

5.1 Introduction

The next step of this project was to determine the capacity deficiencies of the freight transportation highway network based on the supply and demand of freight (truck traffic) flows. Given that truck travel patterns are different from commuter travel patterns, it is necessary to determine the effects of truck traffic on capacity requirements of the network for truck peak hour design flows.

5.2 Capacity Analysis

The highway capacity analysis was intended to provide information on a set of performance measures for each highway link. Highway capacity-related performance measures include traffic volume, travel time, link delay, congested speed, and service to flow ratio. These performance measures were estimated for the 2007 base year as well as the forecast year 2040. Differences in these performance measures between the base year and the forecast year are indications of changes in congestion and the ability of the highway system capacity to support freight transportation system demand in the future.

The capacity and performance results can be used to generate thematic maps that show highway links with capacity problems. The performance measures can also be aggregated to identify those congested highway links connecting border crossings, seaports, airports, and other gateways including intermodal transfer points. The performance measures resulting from the analysis can also be organized and aggregated to serve as inputs to other policy-related analyses.

This section explains the calculation of the performance measures for capacity analysis including

  • Traffic Volume
  • Design Hour Volume
  • Capacity
  • v/c (volume:capacity) ratios
  • Travel times, Speed, and Delay.

5.2.1 Traffic Volume

The traffic volume on any link on the network, for a particular forecast year x, is the sum of passenger vehicles, freight trucks, and non-freight trucks as expressed in Equation 5-1.

Vx = Nx + FAFx + Px      (5-1)

where

Vx = The total AADT volume in a segment of the network
Nx = The total non-FAF trucks on the segment
FAFx = The total freight trucks on the segment
Px = The passenger cars on the segment.

The freight truck volumes on each highway link for 2007 and 2040 are outputs of the assignment process. This relationship holds true for both years. However, the calculation of non-freight and passenger volumes varies from 2007 to 2040. The non-FAF truck volume in 2007 was calculated as follows:

The term begin uppercase N end uppercase begin subscript 2007 end subscript is equal to the logical expression AADTT minus operator FAF begin subscript 2007 end subscript if AADTT is greater than or equal to FAF, is equal to zero otherwise. (5-2)

where AADTT = baseline HPMS truck volume for 2007.

The passenger car volume is the difference between the AADT and the AADTTs available for each segment.

P2007 = AADT2007AADTT2007 (5-3)

where AADT = baseline total traffic volumes for 2007.

In order to obtain the corresponding passenger and non-FAF truck traffic volumes for 2040, growth factors were applied. The growth factors were derived using the county-specific HPMS growth factor using HPMS vehicle miles traveled (VMT, for sample sections only) over the next 20 years from the base year 2007. A straight-line projection was used to estimate the 2040 growth rate. The volumes of passenger cars and non-freight trucks for 2040 is given by equations 6.4 and 6.5 as follows.

P2040 = P2007 (1 + Gp)33 (5-4)

N2040 = N2007 (1 + Gt)33 (5-5)

Where
Gp= HPMS growth rate for passenger cars per year
Gt = HPMS growth rate for trucks per year
P2007 = passenger car traffic volume for 2007
P2040 = passenger car traffic volume for 2040
N2007 = non-FAF truck traffic volume for 2007
N2040 = non-FAF truck traffic volume for 2040.

5.2.2 Design Hour Volume

While daily volumes are useful for planning purposes, they cannot be used alone for design or operational analysis. Volume varies considerably during the course of the day and by direction. The peak hour volumes are often used as the basis for highway design and for many types of operational analysis. One way of estimating peak hourly volumes is to use the daily volume projections and the K factor, using the following relationship.

DHVx = Vx x K-Factor (5-6)

where
DHVx = Design hour volume on the link for forecast year x (vph)
Vx = Daily volume on the link for forecast year x (vpd)
K-Factor = Proportion of daily traffic occurring during the peak hour, expressed as a decimal. For design purposes, this represents the proportion of AADT occurring during the 30th highest peak hour of the year.

The AADT volumes for 2007 and 2040 were converted using the above relationships to obtain design hour volumes.

5.2.3 Capacity

The capacity of a segment is assumed as the service volume at LOS E. The general procedures for estimating highway capacity for 2-lane facilities, multilane facilities—divided and undivided, freeways by design are included in Appendix N of the HPMS Manual and utilize Highway Capacity Manual (HCM) 2000 procedures.

5.2.4 V/C Ratios

A critical factor in any capacity analysis is the proportion of the facility’s capacity being utilized by current or projected traffic. This ratio is often used as a measure of sufficiency of existing or proposed capacity. In forecasting situations, a volume to capacity (v/c) ratio above 1.00 predicts that the facility will fail, i.e., be unable to discharge the demand arriving at the section, leading to excessive delays and queues. The v/c ratios for each segment are calculated by dividing the design hour volume by the capacity calculated in the previous section. These ratios are then classified into three groups: <0.75, 0.75 to 95.0, and >0.95 for different groupings like functional classes, rural/urban, etc. The v/c ratios can also be combined with the network and plotted thematically, allowing visual inspection of congested segments of the roadway.

5.2.5 Travel Time, Speed, and Delay

The congested travel time and link speed for the FAF network was estimated using the HCM 2000 area wide planning level procedure listed in Chapter 30 of the HCM 2000. The vehicle speed for the FAF link was computed using Equation 5-7:

The term begin uppercase S end uppercase is equal to the expression begin fraction begin numerator begin uppercase L end uppercase end numerator over begin denominator begin uppercase R end uppercase plus operator begin fraction begin numerator begin uppercase D end uppercase end numerator over begin denominator begin numeral 3600 end numeral end denominator end fraction end denominator end fraction end expression. (5-7)

Where
S= link speed
L=link length
R=link transversal time (h)
D = Node delay and assumed zero for this exercise.

The link traversal time was calculated using Equation 5-8:

The term begin uppercase R end uppercase is equal to the expression begin uppercase R end uppercase begin subscript 0 end subscript plus operator begin uppercase D end uppercase begin subscript 0 end subscript plus operator 0.25 begin uppercase T end uppercase open square bracket open parenthesis begin uppercase X end uppercase minus operator 1 close parenthesis plus operator begin square root open parenthesis begin uppercase X end uppercase minus operator 1 close parenthesis begin superscript 2 end superscript plus operator begin fraction begin numerator 16 begin uppercase J end uppercase multiplication operator begin uppercase X end uppercase multiplication operator begin uppercase L end uppercase begin superscript 2 end superscript end numerator over begin denominator begin uppercase T end uppercase begin superscript 2 end superscript end denominator end fraction end square root close square bracket. (5-8)

Where
R = link transversal time (h)
R0 = link transversal time at link FFS (h)
D0 = zero-flow control delay at signalized intersection (h)
T = expected duration of demand (typically 1h) (h)
X = link demand to capacity ratio
J = calibration parameter
L = link length (mi).

The link transversal time for free-flow condition (R0) was computed from the FFS, using Equation 5-9:

The tern begin uppercase R end uppercase begin subscript 0 end subscript is equal to the fraction begin numerator begin uppercase L end uppercase end numerator over begin denominator begin uppercase S end uppercase begin subscript 0 end subscript end denominator end fraction. (5-9)

Where
R0 = link transversal time at link FFS (h)
L = link length (mi)
S0 = link FFS (mi/h).

The calibration parameter J was selected so that the transversal time equation will predict the mean speed of the traffic when demand is equal to capacity. Substituting x = 1.00 in the transversal time equation and solving for J yields the equation:

The term begin uppercase J end uppercase is equal to the fraction begin numerator open parenthesis begin uppercase R end uppercase begin subscript begin uppercase C end uppercase end subscript minus operator begin uppercase R end uppercase begin subscript 0 end subscript close parenthesis begin superscript 2 end superscript end numerator over begin denominator begin uppercase L end uppercase begin superscript 2 end superscript end denominator end fraction. (5-10)

Where
J = calibration parameter
R0 = link transversal time at link FFS (h)
R0 = link transversal time when demand equals capacity (h)
L = link length (mi).

The assumed values of parameter J for freeway, multilane, and urban links are listed in Table 5-1 and are derived from HCM Exhibit 30-4. Table 5-2 lists the J values for urban links. Since FAF used the BPR vehicle delay function for freight assignment, these values are more appropriate for estimating link transversal times.

Table 5-1. J Values for Multilane, Freeway, and Rural FAF Highway Links
RoadType MinSpeed MaxSpeed J
1 0 55 3.31E-06
1 56 60 8.65E-06
1 61 65 0.0000148
1 66 70 0.000021
1 71 85 0.0000269
2 0 45 2.52E-06
2 46 50 1.63E-06
2 51 55 2.03E-06
2 56 80 0.0000023
3 0 44 0.000929
3 45 50 0.0004
3 51 56 0.000202
3 57 63 0.000114
3 64 80 0.0000691

Table 5-2. J Values for Urban FAF Highway Links
RoadType FClass J
4 14 0.000468
4 16 0.000502
4 17 0.00455
4 19 0.0137

5.3 Highway Capacity Impacts

A summary of highway capacity impacts due to 2007 and 2040 freight truck traffic volumes was also estimated, using the service v/c ratio value. The impact on highway capacity is expressed as the miles of highway that fall into one of three categories based on the following v/c ratios:

  1. Below capacity – v/c less than 0.75
  2. Approaching capacity – v/c ratio 0.75 to 0.95
  3. Exceeding capacity – v/c ratio greater than 0.95.

Figure 5-1 and Figure 5-2 illustrate highway congestion for 2007 and 2040.

Peak-Period Congestion on the National Highway System: 2007
An outline map of the fifty states shows the extent and size of peak period congestion. Highest congestion is indicated for the major metropolitan areas along the east coast, around the Great Lakes, in the south in Louisiana and Texas, and in California.
Note: Highly congested segments are stop-and-go conditions with volume/service flow ratios greater than 0.95. Congested segments have reduced traffic speeds wiht volume/ratios between 0.75 and 0.95.
Source: U.S. Department of Transportation, Federal Highway Administration, Office of Highway Policy Information, Highway Performance Monitoring System, and Office of Freight Management and Operations, Freight Analysis Framework, version 3.1, 2010.

Figure 5-1. NHS Highway Network Congestion for Year 2007


Peak-Period Congestion on the National Highway System: 2040
An outline map of the fifty states shows the extent and size of peak period congestion. Highest congestion is indicated for the major metropolitan areas along the east coast, across the Midwestern and southern states, in Texas, and up the west coast.
Note: Highly congested segments are stop-and-go conditions with volume/service flow ratios greater than 0.95. Congested segments have reduced traffic speeds wiht volume/ratios between 0.75 and 0.95. The volume/service flow ratio is estimated using the procedures outlined in the HPMS Field Manual, Appendix N
Source: U.S. Department of Transportation, Federal Highway Administration, Office of Freight Management and Operations, Freight Analysis Framework, version 3.1, 2010.

Figure 5-2. NHS Highway Network Congestion for Year 2035

The capacity analysis results for the scenario analysis are summarized in Table 5-3, which shows the highway miles in the three categories of capacity as defined by the v/c ratios by functional highway class. Highway miles in each v/c category are also expressed as percentages of the total highway miles in that functional class and state.

Table 5-3. Summary Statistics of Capacity Analysis
Miles of Highway by V/C Ratio Category Miles of Highway by V/C Ratio Category Miles of Highway by V/C Ratio Category 2007 2007 2040 2040
NHS,IS (miles) Urban <= 0.75 8,565 51.96% 2,785 16.90%
NHS,IS (miles) Urban 0.75 - < 0.95 4,558 27.65% 2,299 13.95%
NHS,IS (miles) Urban > 0.95 3,361 20.39% 11,399 69.16%
NHS,IS (miles) Rural <= 0.75 27,361 90.65% 15,640 51.82%
NHS,IS (miles) Rural 0.75 - < 0.95 2,239 7.42% 5,279 17.49%
NHS,IS (miles) Rural > 0.95 583 1.93% 9,265 30.70%
NHS, Non-IS (miles) Urban <= 0.75 27,495 82.57% 16,283 48.90%
NHS, Non-IS (miles) Urban 0.75 - < 0.95 3,406 10.23% 6,095 18.30%
NHS, Non-IS (miles) Urban > 0.95 2,397 7.20% 10,920 32.79%
NHS, Non-IS (miles) Rural <= 0.75 82,207 97.74% 70,053 83.29%
NHS, Non-IS (miles) Rural 0.75 - < 0.95 1,416 1.68% 6,486 7.71%
NHS, Non-IS (miles) Rural > 0.95 483 0.57% 7,568 9.00%
All NHS (miles) All NHS (miles) <= 0.75 145,628 88.76% 104,761 63.85%
All NHS (miles) All NHS (miles) 0.75 - < 0.95 11,619 7.08% 20,159 12.29%
All NHS (miles) All NHS (miles) > 0.95 6,824 4.16% 39,152 23.86%
Non-NHS (miles) Urban <= 0.75 55,795 93.14% 37,747 63.01%
Non-NHS (miles) Urban 0.75 - < 0.95 2,463 4.11% 9,595 16.02%
Non-NHS (miles) Urban . 0.95 1,647 2.75% 12,562 20.97%
Non-NHS (miles) Rural <= 0.75 217,698 99.09% 200,035 91.05%
Non-NHS (miles) Rural 0.75 - < 0.95 1,283 0.58% 9,550 4.35%
Non-NHS (miles) Rural > 0.95 714 0.32% 10,110 4.60%
All FAF network (miles) All FAF network (miles) <= 0.75 419,121 94.47% 342,543 77.21%
All FAF network (miles) All FAF network (miles) 0.75 - < 0.95 15,365 3.46% 39,304 8.86%
All FAF network (miles) All FAF network (miles) > 0.95 9,185 2.07% 61,824 13.93%

NOTE: The analysis excludes ferry and roadway through Canada.

Figure 5-3 shows the number of interstate and non-interstate highway miles that exceed capacity in the years 2007 and 2040. Figure 5-4 shows the percentage of miles exceeding the capacity in the year 2007 and 2040.

  • In all, 4.16 percent of NHS miles exceeded the capacity in 2007, and this will increase to 23.86 percent in 2040.
  • In 2007, 483 miles of rural interstate exceeded the capacity, and the miles with heavy congestion will increase to 9,265 miles in 2040, which represents 30.70 percent of the total rural interstate miles.
  • About 3,361 miles of urban interstate were heavily congested in 2007, accounting for 20.39 percent of the total NHS urban interstate miles. This percentage increases considerably to 69.16 percent in 2040, corresponding to 11,399 miles of urban interstate that will exceed the capacity.
A vertical bar chart plots miles of highway for four categories of highway for the years 2007 and 2040. The value plotted for the year 2007 for urban interstate is 3,361, for rural interstate is 583, for urban non-interstate is 2,397, and for rural non-interstate is 483. The value plotted for the year 2040 for urban interstate is 11,399, for rural interstate is 9,265, for urban non-interstate is 10,920, and for rural non-interstate is 7,568.

Figure 5-3. NHS Highway Miles Exceeding Capacity


A vertical bar chart plots percent of total in each class for four categories of highway for the years 2007 and 2040. The value plotted for the year 2007 for urban interstate is 20.39%, for rural interstate is 1.93%, for urban non-interstate is 7.20%, and for rural non-interstate is 0.57%. The value plotted for the year 2040 for urban interstate is 69.16%, for rural interstate is 30.70%, for urban non-interstate is 32.79%, and for rural non-interstate is 9.00%.

Figure 5-4. Percentage of NHS Highway Miles Exceeding Capacity

Figure 5-5 shows miles of NHS interstate for the year 2007 and 2040 by volume to capacity ratio.

A vertical bar chart plots miles of interstate for three ranges of capacity for the years 2007 and 2040. The value plotted for the range less than or equal to 0.75 is 35,926 for the year 2007 and 18,425 for the year 2040. The value plotted for the range 0.75 to 0.95 is 6,797 for the year 2007 and 7,578 for the year 2040. The value plotted for the range greater than 0.95 is 3,944 for the year 2007 and 20,664 for the year 2040.

Figure 5-5. NHS Interstate Highway Miles by Capacity Categories

5.4 Highway Impact on Truck Traffic

The summary statistics for the years 2007 and 2040 are shown in Table 5-4 based on the truck traffic for various highway functional classes. The table represents the highway miles based on the functional class and AADTT volume groups. The three truck volume groups used are:

  1. Light Truck Traffic – 0 – 5,000 AADTT
  2. Moderate Truck Traffic – 5,000 to 10,000 AADTT
  3. Heavy Truck Traffic – greater than 10,000 AADTT.

Figures 5-6 to 5-8 show the interstate, NHS non-interstate, and non-NHS miles by truck volume groups.

  • In all, 80.38 percent and 65.10 percent of the NHS miles in the years 2007 and 2040 respectively carry less than 5,000 AADTT.
  • In 2007, 6,360 (38.63 percent) miles of urban NHS interstate and 3,479 miles (11.53 percent) of rural NHS interstate carry more than 10,000 trucks per day. The miles with heavy truck traffic will increase more than twofold in 2040 to 12,615 miles (76.52 percent) of urban NHS interstate and 19,261 miles (63.81 percent) of rural NHS interstate.
  • Out of the total 163,852 NHS miles, only 10,879 miles (6.64 percent) in 2007 and 36,045 miles (21.97 percent) in 2040 experience heavy truck traffic.
  • The table shows that 0 percent to 2 percent of non-NHS miles carry daily truck traffic of more than 10,000 AADTT in 2007 and 2040. The percentage of non-NHS miles with heavy truck traffic is comparatively lower than rest of the highways in the NHS network.
Table 5-4. Miles of Highway by Truck Volume Groups
Miles of Highway AADTT Volume Groups Miles of Highway AADTT Volume Groups Miles of Highway AADTT Volume Groups 2007 2007 2040 2040
NHS,IS (miles) Urban 0-5,000 3,536 21.48% 1,145 6.94%
NHS,IS (miles) Urban 5,000-10,000 6,568 39.90% 2,726 16.53%
NHS,IS (miles) Urban > 10,000 6,360 38.63% 12,615 76.52%
NHS,IS (miles) Rural 0-5,000 15,571 51.59% 4,320 14.31%
NHS,IS (miles) Rural 5,000-10,000 11,135 36.89% 6,604 21.88%
NHS,IS (miles) Rural > 10,000 3,479 11.53% 19,261 63.81%
NHS, Non-IS (miles) Urban 0-5,000 29,589 89.18% 24,535 73.64%
NHS, Non-IS (miles) Urban 5,000-10,000 2,688 8.10% 5,850 17.56%
NHS, Non-IS (miles) Urban > 10,000 902 2.72% 2,932 8.80%
NHS, Non-IS (miles) Rural 0-5,000 83,014 98.80% 76,827 91.34%
NHS, Non-IS (miles) Rural 5,000-10,000 872 1.04% 6,044 7.19%
NHS, Non-IS (miles) Rural > 10,000 138 0.16% 1,237 1.47%
All NHS (miles) All NHS (miles) 0-5,000 131,710 80.38% 106,826 65.10%
All NHS (miles) All NHS (miles) 5,000-10,000 21,263 12.98% 21,224 12.93%
All NHS (miles) All NHS (miles) > 10,000 10,879 6.64% 36,045 21.97%
Non-NHS (miles) Urban 0-5,000 59,255 99.08% 56,425 94.19%
Non-NHS (miles) Urban 5,000-10,000 519 0.87% 2,865 4.78%
Non-NHS (miles) Urban > 10,000 30 0.05% 617 1.03%
Non-NHS (miles) Rural 0-5,000 219,508 99.98% 218,262 99.35%
Non-NHS (miles) Rural 5,000-10,000 32 0.01% 1,357 0.62%
Non-NHS (miles) Rural > 10,000 2 0.00% 77 0.04%
All FAF network (miles) All FAF network (miles) 0-5,000 410,474 92.62% 381,513 85.98%
All FAF network (miles) All FAF network (miles) 5,000-10,000 21,814 4.92% 25,446 5.74%
All FAF network (miles) All FAF network (miles) > 10,000 10,911 2.46% 36,740 8.28%

NOTE: The analysis excludes ferry and roadway through Canada.

 A vertical bar chart plots miles of highway for three ranges for the years 2007 and 2040. The value plotted for the range 0 to 5,000 is 131,710 for the year 2007 and 106,826 for the year 2040. The value plotted for the range 5,000 to 10,000 is 21,263 for the year 2007 and 21,224 for the year 2040. The value plotted for the range greater than 10,000 is 10,879 for the year 2007 and 36,045 for the year 2040.

Figure 5-6. NHS Miles of Roadway by Truck Traffic (AADTT) Groups

A vertical bar chart plots miles of highway for three ranges for the years 2007 and 2040. The value plotted for the range 0 to 5,000 is 19,107 for the year 2007 and 5,464 for the year 2040. The value plotted for the range 5,000 to 10,000 is 17,703 for the year 2007 and 9,330 for the year 2040. The value plotted for the range greater than 10,000 is 9,893 for the year 2007 and 31,876 for the year 2040.

Figure 5-7. Interstate Miles of Roadway by Truck Traffic (AADTT) Groups

A vertical bar chart plots miles of highway for three ranges for the years 2007 and 2040. The value plotted for the range 0 to 5,000 is 112,604 for the year 2007 and 101,362 for the year 2040. The value plotted for the range 5,000 to 10,000 is 3,560 for the year 2007 and 11,894 for the year 2040. The value plotted for the range greater than 10,000 is 1,040 for the year 2007 and 4,169 for the year 2040.

Figure 5-8. NHS Non-Interstate Miles of Roadway by Truck Traffic (AADTT) Groups

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