Chapter 6: Capacity and Performance Analysis

6.1 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.

6.2 Capacity Analysis

The highway capacity analysis is 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 are estimated for the 2002 base year as well as the forecast year 2035. 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

6.2.1 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 6.1.

(6.1)

where

V_x = The total AADT volume in a segment of the network

N_x = The total non-FAF trucks on the segment

FAF_x = The total freight trucks on the segment

P_x = The passenger cars on the segment.

The freight truck volumes on each highway link for 2002 and 2035 are outputs of the assignment process. This relationship holds true for both years. However, the calculation of non-freight and passenger volumes varies from 2002 to 2035. The non-FAF truck volume in 1998 was calculated as follows:

Equation 6.2. N subscript 2000 equals AADTT minus FAF subscript 2002 if ADDTT is greater than or equal to FAFF subscript 2002. Otherwise N subscript 2002 equals zero. (6.2)

where AADTT = baseline HPMS truck volume for 2002.

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

(6.3)

where AADT = baseline total traffic volumes for 2002.

In order to obtain the corresponding passenger and non-FAF truck traffic volumes for 2035, growth factors were applied. The growth factors were derived using the county-specific HPMS growth factor using HPMS VMT (for sample sections only) over the next 20 years from the base year 2002. A straight-line projection was used to estimate the 2035 growth rate. The volumes of passenger cars and non-freight trucks for 2035 is given by equations 6.4 and 6.5 as follows.

(6.4)

(6.5)

Where

G_p = HPMS growth rate for passenger cars per year

G_t = HPMS growth rate for trucks per year

P₂₀₀₂ = passenger car traffic volume for 2002

P₂₀₃₅ = passenger car traffic volume for 2035

N₂₀₀₂ = non-FAF truck traffic volume for 2002

N₂₀₃₅ = non-FAF truck traffic volume for 2035.

6.2.2 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 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.

(6.6)

where

DHV_x = Design hour volume on the link for forecast year x (vph)

V_x = 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 2002 and 2035 are converted using the above relationships to obtain design hour volumes.

6.2.3 Capacity

The capacity of a segment is assumed as the service volume at level of service (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 HCM 2000 procedures.

6.2.4 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 1.0, and >1 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.

6.2.5 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 Highway Capacity Manual 2000. The vehicle speed for the FAF link was computed using equation 6.7:

Equation 6.7. S equals L divided by the sum of R plus the quotient D divided by 3600. (6.7)

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 is calculated using equation 6.8:

Equation 6.8. R equals R subscript zero plus D subscript zero plus the product 0.25 T times the following quantity: X minus 1 plus the square root of the difference X minus 1, that difference squared, plus the quotient sixteen times J times X times L squared divided by T squared, end square root, end quantity. (6.8)

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) is computed from the FFS, using equation 6.9:

Equation 6.9. R subscript zero equals L divided by S subscript zero. (6.9)

Where

R₀ = link transversal time at link FFS (h)

L = link length (mi)

S₀ = link FFS (mi/h).

The calibration parameter J is 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:

Equation 6.10. J equals the difference R subscript C minus R subscript zero, that difference squared and divided by L squared. (6.10)

Where

J = calibration parameter

R₀ = link transversal time at link FFS (h)

R_c = 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 6.1 and are derived from HCM Exhibit 30-4. Table 6.2 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 6.1: J Value 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 6.2: 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

6.3 Highway Capacity Impacts

A summary of highway capacity impacts due to 2002 and 2035 freight truck traffic was also estimated using the volume to capacity ratio value. The impact on highway capacity is expressed as the miles of highway that fall into one of the three categories based on the v/c ratios:

Below capacity – v/c less than 0.75
Approaching capacity – v/c ratio 0.75 to 1.0
Exceeding capacity – v/c ratio greater than 1.0.

Figures 6.1 and 6.2 illustrate highway congestion for 2002 and 2035.

Figure 6.1. Map of the USA illustrating estimated NHS Highway Network Congestion for Year 2002 by indicating roads which are: below capacity, approaching capacity, and exceeding capacity.

Figure 6.1: NHS Highway Network Congestion for Year 2002

Figure 6.2. Map of the USA illustrating estimated NHS Highway Network Congestion for Year 2035 by indicating roads which are: below capacity, approaching capacity, and exceeding capacity.

Figure 6.2: NHS Highway Network Congestion for Year 2035

The capacity analysis results for the scenario analysis are summarized in Table 6.3, 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 6.3: Summary Statistics of Capacity Analysis
Miles of Highway by V/C Ratio Category			2002		2035
NHS, IS (miles)	Urban	<=0.75	8,614	52.37%	2,416	14.69%
		0.75 - < 1	4,931	29.98%	2,498	15.19%
		>1	2,904	17.65%	11,534	70.12%
	Rural	<=0.75	27,713	91.81%	15,038	49.82%
		0.75 - < 1	2,153	7.13%	5,707	18.91%
		>1	320	1.06%	9,442	31.28%
NHS, Non-IS (miles)	Urban	<=0.75	27,541	83.35%	13,712	41.50%
		0.75 - < 1	3,647	11.04%	6,900	20.88%
		>1	1,855	5.62%	12,432	37.62%
	Rural	<=0.75	80,973	98.17%	66,143	80.19%
		0.75 - < 1	1,158	1.40%	8,221	9.97%
		>1	355	0.43%	8,123	9.85%
All NHS (miles)		<=0.75	144,841	89.32%	97,308	60.01%
		0.75 - < 1	11,888	7.33%	23,326	14.38%
		>1	5,435	3.35%	41,530	25.61%
Non - NHS (miles)	Urban	<=0.75	56,864	93.55%	31,827	52.36%
		0.75 - < 1	2,672	4.40%	11,486	18.90%
		>1	1,246	2.05%	17,468	28.74%
	Rural	<=0.75	219,180	99.23%	198,429	89.83%
		0.75 - < 1	1,428	0.65%	12,777	5.78%
		>1	282	0.13%	9,685	4.38%
All FAF network (miles)		<=0.75	420,874	94.83%	327,592	73.81%
		0.75 - < 1	15,988	3.60%	47,588	10.72%
		>1	6,975	1.57%	68,658	15.47%

NOTE: The analysis excludes ferry and roadway through Canada.

Figure 6.3 shows the number of interstate and non-interstate highway miles that exceed capacity in the years 2002 and 2035. Figure 6.4 shows the percentage of miles exceeding the capacity in the year 2002 and 2035.

In all, 3.35 percent of NHS miles exceeded the capacity in 2002, and this will increase to 25.6 percent in 2035.
In 2002, 320 miles of rural interstate exceeded the capacity, and the miles with heavy congestion will increase to 9442 miles in 2035, which represents 30 percent of the total rural interstate miles.
About 2904 miles of urban interstate were heavily congested in 2002, accounting for 17.96 percent of the total NHS urban interstate miles. This percentage increases considerably to 70.12 percent in 2035, corresponding to 11,534 miles of urban interstate that will exceed the capacity.

Figure 6.3. Bar chart comparing year 2002 and year 2035 NHS highway miles which exceed capacity grouped by these four highway functional classes: urban interstate, rural interstate, urban non-interstate, and rural non-instate.

Figure 6.3: NHS Highway Miles Exceeding Capacity

Figure 6.4. Bar chart comparing the percent of year 2002 and year 2035 NHS highway miles which exceed capacity grouped by these four highway functional classes: urban interstate, rural interstate, urban non-interstate, and rural non-instate.

Figure 6.4: Percentage of NHS Highway Miles Exceeding Capacity

Figure 6.5 shows miles of NHS interstate for the year 2002 and 2035 by volume to capacity ratio. About 15 percent of the NHS interstate highways were approaching capacity while 7 percent of the interstate were operating above the capacity in the year 2002. By the year 2035, 20,976 miles, i.e., 45 percent of the total interstate miles, will exceed the capacity.

Figure 6.5. Bar chart comparing the volume to capacity ratio of year 2002 and year 2035 NHS highway miles for less than capacity, approaching capacity, and exceeding capacity.

Figure 6.5: NHS interstate Highway Miles by Capacity Categories

6.4 Highway Impact on Truck Traffic

The summary statistics for the year 2002 and 2035 are shown in Table 6.4 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:

Light Truck Traffic – 0 – 5,000 Average Annual Daily Truck Traffic (AADTT).
Moderate Truck Traffic – 5,000 to 10,000 AADTT.
Heavy Truck Traffic – greater than 10,000 AADTT.

Figures 6.6 to 6.8 show the Interstate, NHS non-interstate, and non-NHS miles by truck volume groups.

In all, 81.52 percent and 65.59 percent of the NHS miles in the years 2002 and 2035 respectively carry less than 5,000 AADTT.
In 2002, 5,882 (35.76 percent) miles of urban NHS interstate and 3,448 miles
(11.42 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 2035 to 11,855 miles (72.07 percent) of urban NHS interstate and 15,353 miles (50.86 percent) of rural NHS interstate.
Out of the total 162,164 NHS miles, only 10,444 miles (6.44 percent) in 2002 and 32,896 miles (20.29 percent) in 2035 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 2002 and 2035. The percentage of non-NHS miles with heavy truck traffic is comparatively lower than rest of the highways in the NHS network.

Table 6.4: Miles of Highway by Truck Volume Groups
Miles of Highway by AADTT Volume Groups			2002		2035
NHS, IS (miles)	Urban	0 - 5,000	4,480	27.24%	1,691	10.28%
		5,000 - 10,000	6,087	37.01%	2,903	17.65%
		>10,000	5,882	35.76%	11,855	72.07%
	Rural	0 - 5,000	16,784	55.60%	6,971	23.09%
		5,000 - 10,000	9,954	32.98%	7,862	26.05%
		>10,000	3,448	11.42%	15,353	50.86%
NHS, Non-IS (miles)	Urban	0 - 5,000	29,533	89.38%	23,019	69.66%
		5,000 - 10,000	2,541	7.69%	6,132	18.56%
		>10,000	969	2.93%	3,893	11.78%
	Rural	0 - 5,000	81,394	98.68%	74,678	90.53%
		5,000 - 10,000	946	1.15%	6,015	7.29%
		>10,000	146	0.18%	1,794	2.18%
All NHS (miles)		0 - 5,000	132,190	81.52%	106,356	65.59%
		5,000 - 10,000	19,530	12.04%	22,912	14.13%
		>10,000	10,444	6.44%	32,896	20.29%
Non - NHS (miles)	Urban	0 - 5,000	60,680	99.83%	54,341	89.40%
		5,000 - 10,000	102	0.17%	5,311	8.74%
		>10,000	0	0.00%	1,131	1.86%
	Rural	0 - 5,000	220,798	99.96%	219,253	99.26%
		5,000 - 10,000	93	0.04%	1,429	0.65%
		>10,000	0	0.00%	209	0.09%
All FAF network (miles)		0 - 5,000	413,127	93.08%	380,251	85.67%
		5,000 - 10,000	20,207	4.55%	29,351	6.61%
		>10,000	10,503	2.37%	34,236	7.71%

NOTE: The analysis excludes ferry and roadway through Canada.

Figure 6.6. Bar chart comparing year 2002 and year 2035 NHS Miles of Roadway by Truck Traffic (AADTT) Groups for volumes 0 to 5,000, 5,000 to 10,000, and greater than 10,000.

Figure 6.6: NHS Miles of Roadway by Truck Traffic (AADTT) Groups

Figure 6.7. Bar chart comparing year 2002 and year 2035 Interstate Miles of Roadway by Truck Traffic (AADTT) Groups for volumes 0 to 5,000, 5,000 to 10,000, and greater than 10,000.

Figure 6.7: Interstate Miles of Roadway by Truck Traffic (AADTT) Groups

Figure 6.8. Bar chart comparing year 2002 and year 2035 NHS Non-Interstate Miles of Roadway by Truck Traffic (AADTT) Groups for volumes 0 to 5,000, 5,000 to 10,000, and greater than 10,000.

Figure 6.8: NHS Non-Interstate Miles of Roadway by Truck Traffic (AADTT) Groups

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