5.1  Introduction

This chapter describes the processes of network preparation for freight demand modeling and associated freight assignment procedures and calibration.

5.2  Network Preparation

Network preparation is required to define and populate the attributes of the highway links that are necessary for freight assignment. These include travel impedance functions, free flow speeds, and link capacities. These attributes determine the capacity-related performance characteristics of each link.

5.2.1  Impedance Function

Travel time on a given link is estimated by dividing its length by the travel speed on that link. Therefore, travel time for a given link changes as the travel speed fluctuates. The speed of a given link can also be affected by roadway type or other conditions as indicated earlier. Consequently, this reduced speed would introduce a penalty to the initial link travel time. Thus the impedance function of a link can be mathematically expressed as:

          (5.1)

Where

T_j  = the link free flow travel time

L_j =  the length of link j in miles

S_j =  the free flow speed on link j in miles-per-hour

r_j   =  travel time adjustment factors, which is a function of the number of lanes, urban bypass, traffic restriction, truck route designation, tolls, and the link reliability

f_j   =  the penalty.

5.2.2  Free Flow Travel Speed

The free flow speed (FFS) of a link can be defined as the average speed of a vehicle on that link, measured under low-volume conditions when drivers tend to drive at their desired speed and are not constrained by control delay. The FFS for the FAF network link is determined by the following equations from the NCHRP Report 387, “Planning Techniques to Estimate Speeds and Service Volumes for Planning Applications”:

          (5.2)

          (5.3)

 

The link speed limit is obtained from HPMS data. The FAF network link with missing speed limit values are assumed based on the following four physical characteristics of highway segments:

1. Access control for the given highway segment
2. Median type
3. Quality of the roadway pavement (paved vs. unpaved)
4. Classification of the highway segment within or outside of an urban boundary.

Assumed speed limits for the combinations of these four characteristics are given in Table 5.1.

Table 5.1:  Speed Limits (mph) for Missing HPMS Speed Data

Functional Class	Pavement Type	Fully Controlled		Partially Controlled		Uncontrolled
		With Median	Without Median	With Median	Without Median	With Median	Without Median
Rural	Paved	65	60	65	55	65	55
	Unpaved	25	15	20	15	15	10
Urban	Paved	55	45	45	35	35	25
	Unpaved	15	10	10	10	10	10

 

5.2.3  Travel Impedance

The total impedance of a selected highway path (i.e., truck route), denoted as T, can be expressed mathematically as the sum of all link impedances (i.e., T_j ‘s). Assuming there are n links on the selected path, the impedance of the selected path is then equal to:

          (5.4)

The adjustment factors as denoted by r_j in equation 4.1 were estimated based on several road characteristics or criteria. The total adjustment factor, r, is a mathematical product of all adjustment factors that meet the following criteria:

Number of lanes:  When there are 4 or more lanes of traffic in both directions, the link travel time is reduced by 2 percent (r = 0.98).

Urban bypass:  When the given link is on an urban bypass, its travel time is increased by 4 percent (r = 1.04).

Truck restrictions:  When the link has known truck restrictions, the link travel time is increased by 60 percent (r = 1.6). For highway segments that prohibit trucks carrying hazardous materials, the travel time of the link is increased by 5 percent (r = 1.05).

Truck route designation:  If a link is on a federal or state designated truck route, the given link’s travel time is reduced by 1.5 percent (r = 0.985).

Tolls:  When the given link is a toll road or bridge, its travel time is increased by 2.5 percent (r =1.025).

Reliability:  This factor is based on the assumption that travel time on links with interstate designations are more predictable to the drivers than the other links. If the given link is on the rural interstate, then the travel time is reduced by 10 percent (r = 0.9). For an urban interstate, travel time is reduced by 5 percent (r = 0.95).

For example, assume that an FAF link is a multi-lane (4 or more) urban bypass with an urban interstate designation. The link is also part of a toll road and part of a federally designated truck route. The resultant adjustment factor of r for free flow travel time for this particular link can be estimated as:

          (5.5)

          (5.6)

The final adjustment of the travel impedance cost was done during the network calibration process under the FAF assignment. The network calibration was done by adjusting the link impedance cost, capacity, or both, so that the link flow was as close as possible to the baseline traffic. The baseline is the truck traffic data on the links that are derived from the state’s actual truck classification counts. The size of the network does not allow us to balance baseline truck flow with assigned truck trip (using the FAF O-D freight matrix) for each link. However, efforts were made to adjust the nation’s truck flow pattern for the major route.

Travel impedance cost is not a simple function of travel time only, and therefore caution must be taken to convert the travel cost to equivalent speed.

5.2.4  Link Capacity

The capacity of a given link can be defined as the a maximum sustainable flow rate at which vehicles or persons reasonably can be expected to traverse a point or uniform segment of a lane or roadway during a specified time period under given roadway, geometric, traffic, environmental, and control conditions; this capacity is usually expressed as vehicles per hour, passenger cars per hour, or persons per hour.

The link capacity of the FAF network is populated from 2002 HPMS data or estimated using the HPMS capacity estimation procedures. The general procedures for estimating highway capacity for 2-lane facilities, multilane facilities—divided and undivided and freeways by design are included in Appendix N of the HPMS Manual [11].

The capacity value reported in an HPMS sample section is for one direction on multilane facilities and for both directions on 2- or 3-lane facilities. Capacity is expressed as maximum service flow rate at Level of Service (LOS) E in passenger car per hour direction (one direction for multilane & both directions for 2 or 3 lane). The HPMS capacity is also called “practical capacity,” because the reported capacity has been reduced to account for the presence of heavy vehicles.

Since the FAF² truck assignment is based on average annual daily truck traffic (AADTT) O-D matrices, adjustment to capacity values were required to simulate the 24-hour equivalent capacity for a given link. This was done by expanding the capacity using the links D (directional) and K (traffic factor). This capacity is referred to as model capacity, to be used as freight assignment input. Typically an assignment model is carried out for an hourly trip that is estimated by multiplying the AADT by the D and K factors. To simulate the similar capacity constraint scenario, the FAF² AADTT O-D matrix was kept in terms of a daily average trip, the capacity was expanded by dividing the capacity (volume/hour/lane) by the D and K factors and the applicable numbers of lanes. The result (daily average capacity, expressed as volume/day/link) was then used as the model capacity for subsequent capacity constraint assignment.

5.3  Assignment Algorithm and Calibration

Traffic assignment models are used to estimate the flow of traffic on a network to establish the traffic flow patterns and analyze congestion points. Intra-zonal truck movements (local traffic) are not included in the assignment process. Even though the highway capacity analysis is focused on a detailed assessment of freight flows and impacts on the highway system, highway bottlenecks are highly dependent on the interaction of total truck and passenger car traffic. Therefore passenger traffic is a key consideration in the assignment process. In this regard, freight flows are assigned with passenger traffic and non-freight (local) trucks pre-loaded on the freight analysis network. Detailed demand analysis of passenger traffic was not performed as part of the study. Rather, current passenger traffic counts and future growth rates as included in the HPMS database are used. The assignment model and procedure applied to the FAF² freight demand modeling are described in the following sections.

5.3.1  Assignment Algorithm

The Stochastic User Equilibrium (SUE) traffic assignment procedure in TransCAD 4.8 with user defined volume delay function (VDF) is used. This assignment is constrained by the highway network’s current capacity. The SUE is a generalization of user equilibrium (a modified capacity constraint approach) that assumes travelers may not have perfect information concerning network congestion and delay and/or perceive travel costs in different ways; therefore, they may change the travel pattern by taking alternate routes as the network (or a specific link of a network) gets congested. The selected VDF for FAF² assignment is the Bureau of Public Roads (BPR) function. A detailed description of this function can be found in Chapter 9 of TransCAD user guide for Travel Demand Modeling with TransCAD. The general form of the BPR function is shown in equation 5.7.

          (5.7)

Where

t    =   Congested travel time

t_i    =   Free flow travel time on link i

C_i    =   Capacity of link i

x_i    =   Flow on link i

α_i    =   Calibration constant

β_i   =   Calibration constant.

Battelle has successfully used this procedure on FAF¹ and ongoing FHWA Strategic Multimodal Analysis (SMA) projects. This approach reasonably forecast the link traffic volumes on two parallel highways with same route distance but different degree of congestions. An example is US-99 in and I-5 in Los Angels County, California. The All or nothing (AON) or non-capacity traffic assignment without a passenger traffic pre-load will assign most of the truck traffic to I-5, but in reality, a large portion of truck traffic also uses US-99. Figure 5.1 illustrates the significant difference of these two methods of freight assignment.

 

Figure 5.1:  Comparison of AON and SUE Truck Traffic Assignment

 

5.3.2  Freight Assignment Calibration

The purpose of this step is to calibrate the 2002 base year demand flow so that the assigned truck trips reasonably match the HPMS truck volumes in the network as closely as possible. The calibration ensures that differences or discrepancies between the actual traffic flows and those estimated from freight O-D data are minimized. This is an iterative process that involves comparing assigned demand truck traffic flow with baseline flows. The output of this task is a calibrated baseline AADTT O-D matrix for the entire freight analysis network.

The challenge in calibrating network assignments is that the tonnage to truck freight data and the HPMS truck data, which form the baseline traffic, were derived from different sources. The baseline HPMS truck data were derived from states with varying quality and methods, and freight flow data were derived by converting the FAF² tonnage data using a set of tons to truck equivalent factors based on several assumptions and expert knowledge. Assumptions were made about the truck capacity and types of commodities carried. Reconciling these flows or minimizing the differences is a major challenge.

The calibration effort involves adjusting the link travel time or capacity or the calibration constant (αi and βi) of the network or both so that the assigned link flows are as close as possible to the baseline flows. In some instance, FAF² O-D matrices were adjusted to eliminate those long-distance trucks (200 miles or more) with commodities such as coal, gravel, sand, and grain. It is very unlikely that a truck trailer will haul a lower value commodity like coal or gravel a distance more than 200 miles. The size of the network makes it impossible to balance the flows link by link. However, efforts were made to balance the assigned flows to the baseline link flows as closely as possible for the major route (mostly interstate and principal arterials).
Table 5.2 summarizes the results of the calibration effort. The table shows a breakdown of the percent differences between the baseline (i.e., data from the HPMS) and assigned traffic volumes. Overall, 80 percent of the assigned FAF² flow is lower than the HPMS truck flow, and the remaining 20 percent is equal to the HPMS truck flow. Since FAF² flow includes only the inter-zonal flow and excludes the intra-zonal flow and local truck flow, the calibrated result should yield a flow that is less than or equal to the existing baseline ground truck flow (HPMS).

Table 5.2:  Results of Calibration

Change from Base HPMS Truck Traffic	Under	Over
No Change	20.66%	0
0 to <25%	4.82%	0
25% to <50%	11.01%	0
50% to <75%	12.92%	0
75% to <100%	50.59%	0

Once the network was calibrated, the forecast truck trip matrices for 2035 were assigned to the network. Figures 5.2, 5.3, and 5.4 illustrate the HPMS 2002 truck flow, FAF² base year 2002 flow, and FAF² 2035 flow respectfully.

The next major step was to determine the highway capacity-related performance measures resulting from the assigned freight traffic for 2002 and 2035. The outputs of the assignment process were used in the capacity analysis presented in Chapter 6.

Figure 5.2:  HPMS 2002 Truck Flow on FAF² Highway Network

 

Figure 5.3:  Base Year 2002 FAF² Truck Flow on FAF² Highway Network

 

Figure 5.4:  Year 2035 FAF² Truck Flow on FAF² Highway Network

 

 

previous | next