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# Delay-Volume Relations for Travel Forecasting: Based on the 1985 Highway Capacity Manual

## Deficiencies in and Problems with the HCM from the Standpoint of Travel Forecasting

The 1985 Highway Capacity Manual is seriously incompatible with traditional travel forecasting models. The principal reason for this incompatibility is the complexity of many of the delay relations, particularly those relations which compute delay as a function of more than a single link volume or more than a single turning movement.

### Typical Limitations of Travel Forecasting Models

There are many travel forecasting packages; their capabilities vary greatly. The most popular packages have the following characteristics, which greatly limit users' ability to determine realistic estimates of delay.

• Delay on a link may be a function of volume only on that link. Models that can calculate delay for a turn do so by looking only at the volume for that single turn.
• The most preferred method of equilibrium traffic assignment, Frank-Wolfe decomposition, cannot handle delay as a function of many link volumes. Furthermore, the delay function must not contain discontinuities, must be monotonically increasing (i.e., strictly increasing with volume), and must be able to be analytically integrated.
• Many models permit only one functional form for delay and only one set of parameters for that function. This one functional form (typically the BPR function) is built into the model and cannot be easily user-modified; however most models permit all the parameters to be varied.
• Many models do not provide the ability to calculate turn penalties as a function of turning volumes.
• Traffic assignment algorithms tentatively estimate volumes greatly exceeding ultimate capacity (LOS E), particularly in early iterations of the calculation. Consequently, delay formulas must be capable of estimating delay for volume-to capacity ratios far beyond 1.0.
• It is very difficult to introduce user judgment during the assignment process. Delay formulas must be entirely self-contained.
• Some models recommend setting "capacity" on a link to the service flow at LOS C, sometimes referred to as the design capacity.
• Depending upon the nature of the path building algorithm, the existence of turn penalties or turning delay functions within a network can greatly increase computation times.

Relative to other parts of travel forecasting models, the calculation of delay is not particularly time consuming. If turn penalties can be avoided, additional complexity in delay relationships should not cause unreasonable increases in computation time.

### Data Limitations

Networks can have thousands of links and intersections, so there are severe limits to the amounts of data that can be economically provided for each. A typical model now requires only two pieces of information about each link for the purposes of delay calculations: capacity and free travel time. It is important not to burden the user with additional data requirements, unless the need has been firmly established through appropriate sensitivity tests of realistic delay relationships.

By their nature forecasts are done for future years; planners do not have very precise information about many of the important traffic characteristics affecting delay. For example, a planner doing a long-range forecast would have little knowledge about .the type of traffic control at any given intersection. The signal timing for signalized intersections would be essentially unknown, and there would be only vague information about the presence of pedestrians, bus operations, and parking maneuvers. Clearly, it would be inappropriate to construct delay relationships requiring data that cannot be obtained.

### How the HCM Violates Model Limitations

The following list of violations does not include assessments of the accuracy of the estimates of delay. It is likely that more realistic and more transferable models of delay can be devised, given sufficient time and resources.

Basic Freeway Sections and Multilane Highways

• The shapes of the speed/volume functions for basic freeway sections and multilane highways differ by facility type.

• Complete delay relations are not available for two-lane roads. Only a sketchy speed/volume function is presented. This speed/volume function differs significantly from those of other road types or from those of traffic flow theory. Approximate speeds are given for each level of service (HCM Table 8-1). These approximate speeds indicate that a different speed/volume function would be required for each category of percent-no-passing and for each category of terrain.
• The capacity of a two-lane road is a function of the directional split, which complicates the comparison of volume and capacity. A volume-to-capacity ratio could be calculated, but it requires knowledge of traffic volumes in both the subject and opposing directions.
• No mention is made about the applicability of the two-lane road procedures to lower-speed urban facilities, including road segments between traffic controlled intersections. The HCM does not discuss the effects of low-speed passing, turning at driveways, on-street parking, loading, etc. Better estimates of two-lane road capacity may be necessary on suburban arterials, especially where signal spacing is greater than 1 mile.

Weaving Sections

• Delay in a single weaving section is a function of up to four types of movements within the section.

All-Way Stop Controlled Intersections

• The 1985 HCM provides, at most, rough guidelines for the capacity of all-way stop controlled intersections. Delay relations are not presented. More complete all-way stop models have been developed (Richardson, 1987; Kyte, 1989) but have not yet been adopted.

Some-Way Stop Controlled Intersections

• The HCM provides procedures for calculating one-way and two-way stop capacity, but does not include delay relationships. Delay relations have been proposed (see Appendix A for an example).
• The relationship between potential capacity and conflicting traffic (Figure 10-3 in the HCM) does not span a sufficiently wide range of traffic conditions. No mathematical form or derivation is provided for this relationship.
• Capacity of any one approach is a function of turning and through volumes on all other approaches.
• No provision is made for traffic distribution across multilane approaches.
• The subprocedure for determining gaps in platooned traffic streams is not well integrated with other parts of the procedure.

Signalized Intersections

• The HCM provides conventional guidelines for setting cycle lengths and determining the lengths of green phases, but does not incorporate these principles into its delay procedures.
• The HCM provides only a sketchy discussion about the appropriateness of protected left turns; it does not indicate when a left turn should be protected, nor does it indicate how the protection should be accomplished.
• The HCM does not give a clear indication of how left-turning traffic should be split between protected and permitted phases for all possible cases. The Highway Capacity Software, for example, sometimes asks the user to determine this split.
• No guidance is given on how to allocate right turns to red phases.
• There are discontinuities in the estimates of delay; i.e., small increases in volume can cause abrupt increases or decreases in delay. A major discontinuity is introduced by the subprocedure for determining whether a shared left lane is operating as an exclusive left lane.
• Delay at an approach is affected by the amount of turning at this approach. Furthermore, delay at an approach is affected by the amount of left turns at the opposing approach.
• The delay function can become undefined for volume-to-capacity ratios only slightly greater than 1.0. This is due to the denominator of the d1 term (uniform delay), which can become negative for large values of g/C (ratio of green time to cycle length). This property of the HCM delay function is unlikely to cause problems for practicing traffic engineers, but it can cause computational difficulties in travel forecasting models.
• The time period for oversaturated flow has been set at 15 minutes (Akcelik, 1988); travel forecasting is typically done for a minimum time period of one hour. The HCM does not indicate how the time period may be changed for the purposes of travel forecasting.
• No explicit provision is made for acceleration and deceleration delays. These are included in the 1.3 factor between total and stopped delay. Consequently, acceleration delay is insensitive to the speed of traffic.
• Under some circumstances, the procedure gives separate delays for the left, through, and right moments. Under other circumstances, it does not.
• No mention is made of delay at freeway ramp meters.

General Issues

A more general problem concerns the definition of LOS C, often taken as the definition of "design capacity" in forecasting models. LOS C is largely subjective and is determined by different methods, depending upon the type of facility or type of traffic control. Thus, there no longer exists a simple method of relating LOS C to LOS E (ultimate capacity) that works across the full range of facilities or traffic controls.

For example, LOS C on freeways is determined by traffic density, while LOS on two lane roads is determined by percent time delay. The volume-to-capacity ratio for LOS C varies between 0.77 (freeway basic segment, 70 mph design speed) to 0.16 (two-lane road, mountainous terrain, 1 00% no passing).

### Minimum Requirements of Forecasting Models to Reasonably Approximate HCM Delay Procedures

As indicated in the preceding paragraphs serious incompatibilities exist between the HCM and existing travel forecasting models. The incompatibilities can be fully resolved only by extensive revisions to the forecasting models. The amount of effort necessary to make these revisions depends upon the structure of the existing computer code.

• The model must be capable of calculating intersection delay for each approach separately from delay on the link that includes the approach. For some models, this delay could easily be expressed as a turn penalty, but there would probably be a significant increase in computation time. A better but more complicated solution is to add the intersection delay, once calculated, to the delay for the approach link.
• At traffic-controlled intersections and at weaving sections, delay must be calculated considering all the movements. For example, delay for an approach at a four-way signalized intersection is related to all 12 possible movements at the intersection.
• Delay on two-lane roads must be calculated from both subject and opposing volumes.
• Different delay functions must be available for freeways at various design speeds, multilane highways at various design speeds, two-lane roads, and urban streets. If a sufficiently general functional form is available (for example, see Spiess, 1990), the differences between facility types could be accommodated with alternate sets of parameters.
• A method other than Frank-Wolfe decomposition must be available for calculating equilibrium traffic assignment.
Updated: 3/25/2014
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