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

### Nature of a Generalized Intersection

An adaptive intersection is one in which the capacity of all approaches can be adjusted to provide better or fairer traffic flow. In reality, all signalized intersections are somewhat adaptive, because signal timing can at least be manually adjusted to better serve existing volumes.

At very low volumes, a signalized intersection would impose greater delays than a stop-controlled intersection or an uncontrolled intersection. Therefore, if the assignment is completely adaptive, it also should be able to change the nature of the traffic control (such as adding or removing signals and signs, changing to four-way flash, etc.) Such a highly adaptive assignment algorithm would design the traffic controls as it loads traffic to the network. Although it would be significantly slower, this type of algorithm would not be particularly difficult to accomplish. The computer code written for the tests in the above paragraphs could be easily so modified. The question of whether a highly adaptive assignment is desirable cannot yet be completely answered.

Estimating the Effects of Adaptation. Planners, however, may choose to modify the nature of the traffic control after they see the assigned volumes - in essence adapting their networks. To do this properly, they would need information about delays at stop-controlled intersections. Figure 6 shows the relationship between volume and delay at a two-way stop-controlled intersection, a four-way stop-controlled intersection, and a signalized intersection. The lane geometry and volumes were the same in all three cases. In this figure, the subject and opposing volumes were varied together, while the conflicting volumes were held constant. The delays at each approach are shown in Appendix D.

Figure 6 shows that the three types of traffic control perform almost equally well at a volume of 400 vph on the subject and opposing approaches. Below 400 vph the two-way stop is superior; above 400 vph the signal is superior. Other tests show that the point at which all controls are equally effective varies with the amount of conflicting volume. This point is at about 100 vph when the conflicting volume is a 600 vph; it is at about 200 vph when the conflicting volume is 400 vph. In no circumstances did the four-way stop outperform the combination of the signal and the two-way stop, suggesting that the four-way stop need not be considered any further. Rules, similar to the signal warrants in the Manual on Uniform Traffic Control Devices, could be used to select the type of traffic control.

In a highly adaptive network, low volumes on one or more approaches might indicate a need for a two-way stop. The effect on the delay/volume curve depends upon whether the subject approach is signed or unsigned. At very low volumes, a vehicle at a signed approach experiences a delay consisting of about 2 to 4 seconds plus any time lost to acceleration (typically 4 to 7 seconds; see Equation A.1 in Appendix A). Vehicles at unsigned approaches experience almost no delay.

The concept of a generalized intersection implies that the delay values in Appendix C for signalized intersections are excessively large for very low volumes on the subject approach. Planners need to be aware of this possibility while calibrating their networks and performing forecasts.

Figure 6: Total Delay on All Approaches for a Four-Way Stop, a Two-Way Stop and a Signal (Opposing Volume Same as Subject Volume, Conflicting Volumes at 200 vph, 25% Right Turns, 25% Left Turns, One Lane at All Approaches, 20 MPH Speed)

Planners need to seriously consider the appropriate amount of adaptation for their networks. Even if their assignment algorithm is not formally adaptive, planners indirectly introduce adaptation as they calibrate their networks or choose their assignment algorithms. Although the Highway Capacity Manual does not discuss adaptive assignment, it does indicate how adaptation can occur. The following levels of adaptation could be invoked, to various degrees, for any given network.

Level 0. No adaptation. Capacity is rigidly fixed on all streets and intersection approaches.

Level 1. Low cost traffic engineering improvements for isolated intersections without changing the type of traffic control. Capacity varies with the amount and nature of conflicting and opposing traffic. (Examples: signal timing; conversion of a through lane to an exclusive lane.)

Level 2. Major traffic engineering improvements for isolated intersections. Capacity varies with the amount of and nature of conflicting, opposing, and subject approach traffic. (Examples: installation of signals, rearrangement of signs, relocation of bus stops.)

Level 3. Traffic engineering improvements involving a system of intersections. Capacity and delay vary with the nature of traffic at surrounding intersections.

(Example: signal coordination.)

Level 4: Geometric changes at isolated intersections. Capacity varies principally with volume on the subject approach. (Examples: adding exclusive lanes, removal of on-street parking, increasing curb radii.)

Only Level 1 has been tested here (see the previous discussion of the UTOWN network). Any combination of the levels of adaptation could be mixed in a single assignment.

Levels 1, 2, and 3 are now included in forecasts through the process of network calibration. Because these levels reallocate resources between facilities, inclusion of one or more of them can result in multiple equilibrium solutions.

Level 4 is now included in forecasts by proposing alternative projects. If all levels of adaptation are included in the forecast, the assignment would be constrained only by cost or operational limitations.

All long term forecasting should be adaptive to the extent that obvious design flaws in the highway system are eliminated. A good working assumption is that continuing efforts will be made to eliminate bottlenecks due to poor geometry or operations, especially those with low-cost solutions. An important implication of adaptation is that planners may be able to ignore many small and isolated reductions in capacity when building and calibrating their future year networks.

Updated: 3/25/2014
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