Gap Acceptance

Main Page > Technical Documentation > Gap Acceptance ​

Gap Acceptance Logic ​

Gap acceptance models begin with the recognition that two-way-stop-controlled (TWSC) intersections give no positive indication or control to the driver on the minor street as to when it is appropriate to leave the stop line and enter the major street. The driver must determine when a gap on the major street is large enough to permit entry and when to enter on the basis of the relative priority of the competing movements. This decision-making process has been formalized analytically into what is commonly known as gap acceptance theory. Gap acceptance theory is the basis for operations of TWSC intersections and roundabouts.

This theory includes three elements: 1. Availability of Gaps 2. Usefulness of Gaps 3. Relative Proportions of Various Movements at the Intersection

1. The availability of gaps is the proportion of gaps of a particular size on the major major street offered to the driver entering from a minor movement, as well as the pattern of vehicle arrival times. The distribution of gaps between vehicles in the different streams has a major effect on the performance of the intersection 2. The second element pertains to how useful drivers find the size of gap when attempting to enter into intersection. It is generally assumed within gap acceptance that drivers are both consistent and homogeneous. However, studies have demonstrated that different drivers have different gap acceptance thresholds and even that the gap acceptance threshold of an individual driver often changes over time. 3. The third element in gap acceptance theory concerns the ranking of each movement in a priority hierarchy. Typically, gap acceptance processes assume drivers on the major street are unaffected by the minor movements. If this assumption is not the case at a given intersection, the gap acceptance process has to be modified. For TWSC methodology, priority hierarchy must be identified for each movement. Movements can be categorized by right-of-way priority as follows: Vehicular (solid arrows) and Pedestrian Movement (dashed arrows) at intersections- HCM 6th Edition'' ​ Headway times are used as measurement instead of gaps due to ease of calculation and requiring less information.
 * Movements of Rank 1 include through traffic on the major street, right-turning traffic from the major street, and pedestrian movements crossing the minor street.
 * Movements of Rank 2 include left turning and U-turning traffic from the major street, right turning traffic onto the major street, and pedestrian movements crossing the major street.
 * Movements of Rank 3 (subordinate to Ranks 1 and 2) include through traffic on the minor street (in the case of a four-leg intersection) and left-turning traffic from the minor street (in the case of a T-intersection).
 * Movements of Rank 4 (subordinate to all others) include left-turning traffic from the minor street. Rank 4 movements occur only at four-leg intersections.

Critical Headway and Followup Headway Critical headway tc is defined as the minimum time interval in the major-street traffic stream that allows intersection entry for one minor-street vehicle. Thus, the driver’s critical headway is the minimum headway that would be acceptable. A particular driver would reject headways less than the critical headway and would accept headways greater than or equal to the critical headway. Critical headway can be estimated on the basis of observations of the largest rejected and smallest accepted headway for a given intersection. The time between the departure of one vehicle from the minor street and the departure of the next vehicle using the same major-street headway, under a condition of continuous queuing on the minor street, is called the follow-up headway tf. Thus, tf is the headway that defines the saturation flow rate for the approach if there were no conflicting vehicles on movements of higher rank.

Computing Critical Headway and Followup Headway Critical Headway tc,x = tc,base+ tc,HVPHV + tc,GG-t3LT where, tc,x = critical headway for movement x (s), tc,base = base critical headway from "Base Critical Headways" (s) below, tc,HV = adjustment factor for heavy vehicles (1.0 for major streets with one lane in each direction; 2.0 for major streets with two or three lanes in each direction) (s), PHV = proportion of heavy vehicles for movement (expressed as a decimal; e.g., PHV = 0.02 for 2% heavy vehicles), tc,G = adjustment factor for grade for given movement (0.1 for Movements 9 and 12; 0.2 for Movements 7, 8, 10, and 11) (s), G = percentage grade (expressed as an integer; e.g., G = −2 for a 2% downhill grade), and t3,LT = adjustment factor for intersection geometry (0.7 for minor-street left-turn movement at three-leg intersections; 0.0 otherwise) (s).

HCM 6th Edition

Followup Headway tf,x = tf,base + tf,HV PHV

where, tf,x = follow-up headway for movement x (s), tf,base = base follow-up headway from "Follow-Up Headway" (s), tf,HV = adjustment factor for heavy vehicles (0.9 for major streets with one lane in each direction; 1.0 for major streets with two or three lanes in each direction), and PHV = proportion of heavy vehicles for movement (expressed as a decimal; e.g., PHV = 0.02 for 2% heavy vehicles).

HCM 6th Edition

Roundabouts The operation of roundabouts is similar to that of two-way STOP-controlled intersections. In roundabouts, however, entering drivers scan only one stream of traffic—the circulating stream—for an acceptable gap. The analysis procedure for roundabouts uses gap acceptance models and simple lane based regression for single-lane and double-lane roundabouts. Simple gap acceptance models alone may not capture all observed behavior.

SwashSim Implementation Within Swashim, it is imperative that the micro-simulation tools are consistent with the methodology from HCM, to adequately simulate real world situations. The headway times currently used for the Gap Acceptance in SwashSim are from CORSIM, an older simulation program, and correlate to driver type. The headway time by driver type is calculated based of the approaching target vehicle in the conflicting link of the designated downstream link of the subject vehicle. This headway time is then compared to the set headway times to determine if the gap is acceptable for the driver.

Test Networks The Gap Acceptance Logic has been used to create four-leg TWSC Swashsim Network for testing. This network has one lane in each direction on the minor streets and two lanes in each direction on the major street. This network has control points place on both minor roadways to determine the availability of gaps within the major street, giving control to the vehicles entering from the minor street. This network took into account movements of rank 2,3, and 4.

References