HERS-ST Highway Economic Requirements System - State Version: Technical Report - Chapter 2: An Outline of the Model Structure
A separate document, the HERS-ST Overview (September 2002), provides a conceptual description of the HERS "engine" (the analytic core of HERS-ST) for those interested in gaining an overall understanding of how the model works. The Overview is recommended to analysts who may have topics of particular concern (e.g., pavement wear) but want to know the context in which these topics relate to the rest of the model. The technical report in hand provides details of equations, parameters, and the sequence of processing.
While not a substitute for the Overview, this section provides enough description of the structure of the HERS system to indicate generally how the model components are interrelated and the time and other dimensions over which it operates.
The basic function of the HERS model is to conduct project evaluations using benefit-cost methods. Given a set of highway sections as input, HERS looks at each section in turn and decides whether an improvement is warranted and, if so, what type of improvement. These choices may be constrained by user-specified improvement types or by funding caps or performance requirements. After projects have been selected for a given time period or funding period, the model moves on to the next period.
HERS-ST can be run under several "scenarios." One of these selects all sections for improvement for which at least one alternative passes the benefit-cost threshold, and picks the improvement with the highest benefit-cost ratio (BCR) for that section. In this scenario, the evaluation of each project is independent of the evaluation of other sections. At a very general level, this process is illustrated in Figure 2-1.
The user may choose to constrain the scenario by limiting funds, or by imposing minimum performance requirements. HERS reacts to the constraints by making tradeoffs between one section and another among worthwhile (those that pass the minimum BCR threshold) improvements.
The scope of project evaluation in HERS encompasses three general steps, shown in Figure 2-2:
Design of Alternatives. HERS can look for deficiencies and suggest improvements to correct the deficiencies, or the user can, in various ways, mandate that a particular improvement be made.
Impacts. The model estimates the conditions (traffic, pavement wear, accidents, emissions, etc.) that will occur under each alternative that is evaluated.
Evaluation. Differences in travel time, accidents, vehicle operating costs, and agency (maintenance) costs between the improvement and the base alternative are valued in present worth terms and compared to the cost of the improvement.
The structure of this technical report proceeds through these three steps.
The HERS model has many routines (components or submodels) that perform specialized functions for the model as a whole. Some of these routines are simple calculations, using input data or the results from other routines, and some are complex procedures that may call other procedures. The procedures that are most important for estimating the impacts of project alternatives (base and improvement) on section conditions can be grouped into "models" (i.e., submodels of the HERS model) for explanatory purposes. These and their interrelationships are shown in Figure 2-3.
The dashed line represents the effect of costs to the user (the "price" of travel) on travel forecasts due to demand elasticity. The capacity calculation is invoked only after implementing an improvement.
For each funding period, for each sample section, for each of the logical sequences, the program performs the same set of predictions:
- predicts future traffic volume
- predicts future pavement conditions
- predicts current and future speeds
- predicts section capacity after improvement.
These predicted conditions are then used to calculate costs:
- costs to users of the highway system:
- operating costs
- travel time costs
- safety costs
- agency costs:
- capital improvement costs
- maintenance costs
- costs associated with vehicle emissions.
The information generated by the prediction and calculation models is used within the logic structure to evaluate and select improvements. The prediction and calculation models are discussed in detail in Chapter 5, "Estimation of Impacts."
HERS distinguishes three kinds of costs:
- Resources consumed that constitute costs to society and also costs to users, in that users pay for them (e.g., travel time and vehicle operating costs).
- Resources consumed that constitute costs to society but are not paid by users (or as a consequence of usage) and are therefore external costs or externalities (e.g., damage from pollution).
- Transfers that are not costs to society but are regarded as costs by users (e.g., user taxes).
Costs of either of the first two kinds that are affected by an improvement are counted as benefits of the improvement. Transfers, the third kind of cost, amount to a gain by some persons and a loss by others, but no resources are consumed in the process (ignoring transaction costs). Tolls are paid by users and received by the owner of the road.
The distinctions are important not only for enumerating and quantifying benefits, but also for predicting the behavior of users, especially in response to a highway improvement. Users can be viewed as participants in a market, in which the volume of travel is affected by its price. In HERS, the price is the "generalized" cost of travel to the user, which includes travel time, other user costs, as well as user taxes and tolls.
An improvement that reduces the travel time between geographically dispersed locations is reducing the price of travel. If demand is not perfectly inelastic, more travel will ensue if the price is lower than if it is higher. The magnitude of this response is the travel demand elasticity, which may vary with the location, time of day, and whether the adjustment takes place in the short run or the long run, among many factors. Empirically, the elasticity of demand for highway travel is neither perfectly elastic (travel volume changes infinitely for even a miniscule change in price) nor perfectly inelastic (volume is the same no matter what the price). Elasticity concepts as applied in HERS allow for induced demand to occur in both the short and long run (See Appendix B, "Induced Traffic and Induced Demand" for an explanation of the elasticity concepts, Appendix C, "Demand Elasticities for Highway Travel" for ranges of empirical values, and section 5.6.2 "Applying Elasticity to Travel Volume Forecasts" on page 5-53 for the supply-demand algorithms).
The scope of costs and benefits can be summarized in the form of a table, shown in Table 2-1. Changes in costs that constitute benefits are stated as cost reduction being a positive benefit, but the costs could also increase as a consequence of an improvement, resulting in negative benefits or disbenefits. Travel time might go down, for example, while accidents and emissions go up. Incremental consumer surplus is a representation of the user cost savings resulting from a change in the volume of travel as a result of non-zero elasticity. If the price goes down and travel increases, incremental consumer surplus is a positive contribution to benefits (see section 7.8.1 "Consumer Surplus" on page 7-8 for a description of the computations).
|cost to user (price)||cost to society (benefit)|
|travel time cost savings||X||X|
|vehicle operating cost savings||X||X|
|accident cost savings||X||X|
|incremental consumer surplus||X||X|
|highway maintenance cost savings||X|
|residual value of facility||X|
|fuel excise taxes and tolls||X|
Any change in resource consumption that occurs as a consequence of an improvement is counted in the benefit category, except for the initial capital cost; this classification (cost or benefit) is important only for calculation of benefit-cost ratios. The goal is to maximize net benefits, and for this purpose it is only important to get the arithmetic sign correct (as well as, of course, the magnitude). Residual value might be regarded as a reduction in the capital cost of the improvement, but HERS treats it as a (discounted) benefit.
Hence items with an "X" in the cost-to-society column count as benefits, those with an "X" in the price column affect travel behavior through demand elasticity, and those items marked in both columns are both real social costs and also user costs. Those with an "X" only in the cost-to-society column are externalities, and those with an "X" only in the price column are transfers.
In any given run, HERS is designed to perform one of three types of analysis as specified in the user input field "Objective." The user-specified objective may be in any of three possible forms:
- Maximize the net present value of all benefits of highway improvements subject to specified constraints on funds available during the period;
- Minimize the cost of improvements necessary to achieve a specified goal for the performance of the highway system at the end of the funding period; or
- Implement all improvements with a benefit-cost ratio (BCR) greater than some specified threshold value.
The three forms are also referred to as Constrained Fund, Performance Constrained, and Minimum BCR, respectively.
When Objective is set to "1", HERS will solve for highway conditions and performance when improvements are constrained by available funds (referred to as a "constrained fund" run). When Objective is set to "2", HERS will solve for the funding levels required to bring the system to a specified level of performance (referred to as a "performance constrained" run). When Objective is set to "3", HERS will solve for both the required funding level and the resultant performance levels when improvements are constrained to return a minimum ratio of benefits relative to their cost (a "minimum benefit-cost ratio (BCR)" run). The model recognizes two special cases. The first is an "engineering needs" run (sometimes referred to as "full needs"), which is a minimum BCR run with the minimum BCR set to a very low negative number so that all sections with deficiencies are selected for improvement. The second is a "maintain current conditions" run in which the model first determines the level of system performance at the beginning of the run based on user-specified parameters (for example, current highway-user costs), and selects the least costly mix of improvements to maintain that level of performance. Each of the special cases can be selected via a dedicated input field. Finally, while a minimum BCR run where the minimum BCR is set to 1.0 is referred to as an "economic efficiency" run, this is not a different type of analysis, but a specific and often used Objective 3 scenario, and was used as the Maximum Economic Investment scenario in the 2002 C&P Report.
Objective 2 scenarios, such as the Maintain User Costs scenario of the 1997 C&P Report, can be specified as a goal for a single type of highway-user cost or highway agency cost per vehicle-mile (e.g., number of fatalities per vehicle-mile); or it can be specified as a dollar-valued composite of all net user and agency costs estimated by HERS (travel time costs, operating costs, fatality costs, injury costs, property damage, and maintenance costs). The dollar-valued composite can be obtained as a simple sum of the component costs or as the sum of two or more components with different weights. (The run specification file provides one set of weights used in balancing components of the incremental benefit-cost ratio, and another set for balancing components of the performance goal.) In the latter event, it is recommended (but not required) that the components of the IBCR be given weights that are consistent with the specified goal; e.g., the goal might be that the sum of user costs plus two times agency costs should not exceed $0.50 per vehicle-mile, in which case it is recommended that agency costs be weighted twice as heavily as user costs in the IBCR as well.
The basic process is agreeably straightforward: forecast section condition; identify deficiencies and potential improvements; evaluate and select improvements; and implement improvements (or, for unimproved sections, implement the unimproved condition forecast for the end of the period). Output statistics are accumulated, and the process is repeated for each subsequent funding period. However, the model has two features (alternative improvement selection procedures, and mandatory correction of unacceptable conditions) which complicate the structure. Each feature offers a pair of alternatives, which, selected independently, define four distinct logical structures.
The first feature is that the model supports two improvement selection procedures. Both procedures use benefit-cost analysis to choose between potential improvements, but one procedure chooses among improvement options for a single section at a time, while the other selects from all potential improvements to all sections in the system.
The "minimum BCR" alternative (Objective = 3) instructs the model to implement, for each deficient section, the most ambitious improvement which meets a minimum benefit-cost ratio. Under this option, all deficient sections with an "economically justifiable" candidate improvement are improved. An improvement is considered "economically justifiable" if its benefit-cost ratio is greater than or equal to the user-specified minimum. (For the "Economic Efficiency" scenario, the minimum BCR is set to 1.0.) Benefit-cost analysis is used first to determine if a section will be improved, and second to identify the most attractive of the potential improvements. (The improvement with the greatest BCR is considered more attractive.) The model is under no budget or performance constraints, but will implement the most attractive improvement for each qualifying section.
The "constrained" alternative (Objective = 1 or 2) effectively compels the model to rank all potential improvements, for all sections, in order of economic desirability (that is, ranked by BCR). The model then selects improvements in order of decreasing BCR until a specific constraint (available funds or system performance level) has been reached. While not all economically attractive improvements may be selected, those selected will all be more economically attractive than those not selected for implementation. When the constraint is available funds, the program selects the set of improvements which return the maximum benefit for the capital expenditure. When the program is constrained to attain a specific level of performance for the highway system, it selects the set of improvements which will achieve those goals at the lowest cost.
Figure 2-4 shows flow diagrams for these two selection procedures. In the minimum BCR version, the model selects a section's improvement immediately after evaluating the possible improvements. In the constrained run, the model "pre-selects" a section's most attractive improvement and places it on a list of potential improvements. After all sections have been evaluated, the model initiates a second selection procedure which selects improvements from the potential list (which is ordered by BCR) until the constraint, whether a budget limit or a performance goal, has been met.
The processes for identifying potential improvements are presented in Chapter 4, "Design of Improvement Alternatives."
The second feature which can complicate the HERS selection process is the provision of a "safety-net" to force the model to improve unacceptably deficient sections without regard for the economic desirability of the improvement. If this option is selected, HERS will make a special pass through all sections prior to the normal evaluation to identify low-cost improvements to correct unacceptable conditions. Improvements selected on this basis are referred to as "mandatory improvements." For most purposes, such as preparation of data for the Conditions and Performance Report, the model is run without selecting this option, so no mandatory improvements are implemented.
The processing flow after the identification of mandatory improvements varies depending upon the analytical objective. The simplest case is illustrated in Figure 2-5. In this case, after identifying mandatory improvements for sections with unacceptable conditions, the program re-examines each section to identify economically attractive improvements. On a section for which a mandatory improvement has been identified, the model will implement either the mandatory improvement or an economically attractive improvement which also corrects all unacceptable conditions. On sections without mandatory improvements, the economically most attractive improvements will be implemented.
The processing flow for a performance constrained run with mandatory improvements is shown in Figure 2-6. In this type of run, the program forecasts the unimproved condition of the system at the end of the funding period, then implements improvements until the level of system performance reaches the specified goal. If implementing the mandatory improvements alone achieves the performance goal, no additional improvements are considered during this funding period. If the goal has yet to be achieved, the program loops through the sections again to identify economically attractive improvements, which are ordered by BCR and selected until the goal is attained.
Figure 2-7 shows the processing flow for a constrained fund run with mandatory improvements. For this scenario, the analyst specifies two funding levels: the total amount of funds to be expended per funding period, and the amount of the total funds which are to be used for more aggressive (that is, non-mandatory) improvements. For example, the analyst might specify that 100 million dollars be allocated for the first funding period, of which 70 million dollars is reserved for non-mandatory improvements. After identifying mandatory improvements for all sections, the program checks whether the cost of all mandatory improvements exceeds the 30 million dollars allocated for mandatory improvements.
If the mandatory improvements cost more than the funds allocated for them, the program selects from the mandatory improvements in order of their BCRs until it has expended all the available funds on the economically most attractive improvements. It then checks whether additional funds have been reserved for more aggressive (nonmandatory) improvements. If not, it implements the selected improvements and advances to the next funding period.
However, if funds were reserved for non-mandatory improvements, or if the mandatory improvements cost less than the funds allocated for them, the program loops through all the sections again to identify more aggressive improvements for implementation with the remaining funds. These improvements are selected in BCR order.
Note that in all cases, it is possible for the model to identify a mandatory improvement for a section, and subsequently replace it with an economically more attractive improvement which corrects all the unacceptable conditions which existed on the section.
The identification of potential improvements to correct sections in unacceptable condition is discussed in section 184.108.40.206 "Addressing Unacceptable Conditions: the Optional First Pass" on page 4-15. The process of selecting mandatory improvements, or of replacing a mandatory improvement with a more aggressive improvement, is presented in paragraph section 7.12 "Selecting Mandatory Improvements" on page 7- 19.
The condition of each section is maintained in a set of data items which are originally populated from the HPMS database. While many of these items are not changed during analysis (for example, section identification and location), others (such as traffic volume and pavement condition) can be expected to change with each passing funding period. Improvements are implemented through changes to applicable data items (notably pavement condition and number of lanes).
At the beginning of each funding period, the model forecasts the condition of each section at the end of the funding period. This basic forecast consists of predicting future traffic volume, then calculating the effect of this traffic on the pavement condition. For sections which are unimproved during the funding period, this becomes the condition of the section at the beginning of the subsequent funding period. Because HERS treats improved sections as receiving their improvements at the midpoint of the funding period, determining the end of period condition of an improved section consists of upgrading the section's condition to reflect the improvement and then forecasting its condition at the end of the period.
At this point, the program accumulates the statistics which will be used to generate the output pages. See Chapter 8, "Model Output" for more details.
The HERS program operates over a set of time frames known as funding periods (FPs), as shown in Figure 2-8. These funding periods are equal in length, and combine to form the overall analysis (OA) period. The set of all funding periods form a sequence, with the first one beginning at the start of the OA period, and each succeeding funding period starting at the end of the preceding one. HERS defines additional funding periods which start after the end of the OA period. These "post analysis period" funding periods are the same length as the funding periods within the OA period, and extend far enough beyond the end of the OA period to permit benefit-cost (B/C) analyses to be performed on all improvements that might be implemented during the OA period. Figure 2-8 depicts an overall analysis period consisting of four five-year funding periods.
HERS performs B/C analyses on all improvements that might be implemented during the OA period, but not on improvements that might be implemented after the OA period. For purposes of the B/C analyses, HERS treats all improvements as if they were implemented at the midpoint of the funding period. Accordingly, every benefit-cost analysis period (BCAP) extends from the midpoint of a funding period to the midpoint of a subsequent funding period (which can extend beyond the end of the OA period). Additionally, because of the impact of an improvement upon the price to the user of the section, the time-frame for the elasticity calculations (shown in the exhibit as ELAS) also run from funding period midpoint to funding period midpoint.
The HERS program recognizes nine functional classes of highways, including all of the urban arterial and collector classes, and all of the rural arterial and major collector classes. Rural minor collectors and roads functionally classified as local are not recognized by HERS.
A large number of HERS parameters can be specified by the user with different values for each of the nine functional classes. Some of these items are:
- Deficiency Levels
- Serious Deficiency Levels
- Unacceptability Levels
- Minimum Tolerable Conditions
- Design Standards
- Improvement Costs
- Truck Growth Factors
- Cost of Non-Fatal Injuries
- Property Damage Cost per Crash
- Funds Available for Improvements (Fund Constrained Run)
- Highway Performance Goals (Performance Constrained Run)
- Weights for Highway Performance Goals
- Weights for Benefit-Cost Ratio Calculation.
The Fleet Composition model also relies on functional class. (See section 2.11 "The Fleet Composition Model" on page 2-15)
When performing a constrained fund run or a performance constrained run, HERS allows the user the options of setting separate budget constraints or performance goals for each functional class, or for certain combinations of functional classes. These combinations are shown in Table 2-2. The user can set targets for:
- 1 group (for all functional systems combined);
- 2 groups (for the urban system and for the rural system);
- 2 groups (for the principal arterials and for the minor arterials and collectors);
- 4 groups (for urban principal arterials, for rural principal arterials, for urban minor arterials and collectors, and for rural minor arterials and collectors); or
- 9 groups (for each of the nine functional classes distinguished by HERS).
The flow charts in Figure 2-4 through Figure 2-7 are based upon the standard case where the set of sample sections is treated as a single system (one group). However, if the user elects to use multiple functional class groups in setting performance goals or budget constraints, then during initialization, HERS takes the additional step of separating the sample sections into the component groups, and maintains a separate section file for each group. During processing, the model processes each group in turn in a loop nested between the loops for funding periods and sections. The structure then becomes:
Loop through each funding period...
Loop through each functional class group...
Loop through all sections in the class group...
Process a section (forecast conditions, identify potential improvements, pre-select an improvement)
End loop (all sections)
Select improvements until constraint is satisfied for the class group
Implement selected improvements for the class group
End loop (functional class group)
End loop (funding period)
|Single System||Rural and Urban||Princ. Art. & Other||Princ. Art. & Other by Rural/Urban||By Functional Class|
|Number of Groups||1||2||2||4||9|
|01||Principal Arterial - Interstate||1||1||1||1||1|
|02||Other Principal Arterial||1||1||1||1||2|
|11||Principal Arterial - Interstate||1||2||1||3||5|
|12||Principal Arterial - Other Freeways and Expressways||1||2||1||3||6|
|14||Other Principal Arterials||1||2||1||3||7|
HERS is not designed to handle rural minor collectors or sections on the two local functional systems. To allow states to analyze sections on these three systems, HERS-ST treats all sections on these systems as if they were rural major collectors or urban collectors, as appropriate. Accordingly, statistics printed by HERS-ST for rural major collectors actually include information for any rural minor collectors and rural local roads analyzed; and statistics for urban collectors similarly include information for any urban streets analyzed.
HERS decomposes the vehicle fleet into three vehicle categories which include a total of seven vehicle types. These data on fleet composition are used by HERS when estimating speed, operating costs, travel-time costs, section capacity, and pavement deterioration. The progression from the entire fleet to the seven vehicle types is shown (proceeding from left to right) in Table 2-3
|Fleet||Weighing Factor||Vehicle Category||Weighting Factor||Vehicle Type|
|All Vehicles||Section data item: Percent Combination Trucks||Combination Trucks||Prorated from HPMS Vehicle Classification Study||Five or More Axle Combination Trucks|
|Three/Four Axle Combination Trucks|
|Section data item: Percent Single Unit Trucks||Single Unit Trucks||Prorated from HPMS Vehicle Classification Study||Three or More Axle Single Unit Trucks|
|100% less percent of Single Unit and Combination Trucks||Four Tire Vehicles||Prorated from HPMS Vehicle Classification Study||Pickups & Vans|
The fleet is divided into vehicle categories based upon section-specific percentages of the two truck classifications. These are reported in the HPMS input data record for each section. The four wheel category consists of the percentage of total traffic which is not part of either truck category. For the disaggregation of vehicle categories to vehicle types, HERS uses factors derived from the 1982 HPMS Vehicle Classification Case Study1. As shown in Table 2-4, these functional class dependent factors have been prorated to total 100 percent for each of the three categories.
|Functional Classes||Four Tire Vehicles||Single Unit Trucks||Combination Trucks|
|Small Autos||Med/Lg Autos||Pickups & Vans||Six Tire Trucks||3+Axle SUTs||3 4 Axle Combos||5+ Axle Combos|
|Rural Minor Arterial||.2081||.4762||.3156||.6404||.3596||.1675||.8325|
|Rural Major Collector||.1536||.4882||.3582||.6180||.3820||.2518||.7482|
|Urban Other Freeway/Expressway||.2521||.5583||.1896||.7000||.3000||.1253||.8747|
|Urban Minor Arterial||.1976||.5998||.2027||.6590||.3410||.1765||.8235|
The HERS parameter file has entries for specifying the annual growth rate of the percentage of truck traffic for each functional class. This is applied to the section-specific percentages for the two truck categories to derive the new percentages for each category. For the 1997 Conditions and Performance Report the truck growth factors were set to 1.0 (i.e., no growth).
As an example of the weighted summation process used by HERS, let VCATA, VCATSU, and VCATCM designate the three vehicle categories (four-tire vehicles, single unit trucks, and combination trucks), VT1 through VT7 correspond to the seven vehicle types, and FAF1 through FAF7 to the fleet disaggregation factors for each of the respective vehicle types (as shown in Table 2-4). After determining the quantity for each vehicle type (for example, travel time cost per 1000 vehicle miles), HERS calculates the quantity for each vehicle category weighted by vehicle type:
|VCATA = VT1 × FAF1fc + VT2 × FAF2fc + VT3 × FAF3fc|
|VCATSU = VT4 × FAF4fc + VT5 × FAF5fc|
|VCATCM = VT6 × FAF6fc + VT7 × FAF7fc|
Note that the fleet disaggregation factors are indexed by functional class. HERS next determines the percentages of single unit and combination trucks at the time of interest (t, in years) by applying the user-specified truck growth factor (TRKFAC) for the section's functional class to the percentages of average single unit (PCAVSU) and combination trucks (PCAVCM) reported in the section's HPMS data record:
|PCSU = PCAVSU × TRKFACfct|
|PCCM = PCAVCM × TRKFACfct|
where PCSU and PCCM are the percentages at the time of interest. Finally, HERS produces a total weighted sum (TWS) combining the weighted values of the three vehicle categories:
|TWS = VCATA × (1 ∠ PCSU ∠ PCCM) + VCATSU × PCSU + VCATCM × PCCM|
Although HERS is primarily oriented toward evaluation of investment in highway improvement projects, the model can also estimate the impacts of several policy alternatives.
Limited funds for capital investment is a necessary condition for investment decisions, and HERS allows for funding caps by funding period and by functional class groupings. Constrained funding can also be modeled by adjusting the minimum BCR threshold until the HERS-recommended spending meets the budget constraint; this method then reveals the level by which worthwhile projects are not implemented. For additional information see section 2.10.1 "HERS Functional Class Groups" on page 2-14, section 2.7.1 "The Improvement Selection Procedures" on page 2-7, and section 7.11.2 "Constrained Analysis" on page 7-15.
The price of fuel (gasoline and diesel) is entered exclusive of federal and state excise taxes or local sales taxes. Separately, a value for fuel taxes in dollars per gallon is entered. This value is included in the price of travel to the user (therefore affects traffic volume through the demand elasticity) but is not included in benefits (from society's viewpoint, the tax is a transfer).
As a policy option, the user can specify the maximum number of lanes permitted on sections of each functional class. If the existing number of lanes exceeds this maximum, lanes will not be removed to meet the cap, but HERS will not add lanes in excess of the limit. The cap might be interpreted in some circumstances to represent corridor capacity, such as with parallel freeways.
The user may also specify, by functional class, an override value applied to each section's widening feasibility code. Where the section data indicate that widening is not feasible, this override can be applied to allow adding lanes at a higher cost. The cost can be specified by the user. This option might allow for double-decking or parallel facilities. For details, see section 4.2.4 "Effects of HERS Improvements" on page 4-20 and section 4.3 "The Widening Feasibility Model" on page 4-26.
The user can also specify the maximum number of normal cost lanes permitted on sections of each functional class. Any lanes added on a section in excess of this limit are added at high cost without regard to the section's widening feasibility code.