Module 6 : Traffic Intersection Control
Lecture 30 : Uncontrolled Intersection
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Gap acceptance and follow-up time

Gap acceptance is one of the most important components in microscopic traffic characteristic. The gap acceptance theory commonly used in the analysis of uncontrolled intersections based on the concept of defining the extent drivers will be able to utilize a gap of particular size or duration. A driver entering into or going across a traffic stream must evaluate the space between a potentially conflicting vehicle and decide whether to cross or enter or not. One of the most important aspects of traffic operation is the interaction of vehicles with in a single stream of traffic or the interaction of two separate traffic streams. This interaction takes place when a driver changes lanes merging in to a traffic stream or crosses a traffic stream. Inherent in the traffic interaction associated with these basic maneuvers is concept of gap acceptance.

Basic Terminologies

  1. Gap means the time and space that a subject vehicle needs to merge adequately safely between two vehicles. Gap acceptance is the minimum gap required to finish lane changing safely. Therefore, a gap acceptance model can help describe how a driver judges whether to accept or not.
  2. Gap acceptance: The process by which a minor stream vehicle accepts an available gap to maneuver.
  3. Critical gap: The minimum major-stream headway during which a minor-street vehicle can make a maneuver.
  4. Lag: Time interval between the arrival of a yielding vehicle and the passage of the next priority stream vehicle (Forward waiting time).
  5. Headway: The time interval between the arrivals of two successive vehicles. Headway differs from gap because it is measured from the front bumper of the front vehicle to the front bumper of the next vehicle.
  6. Minimum Headway: The minimum gap maintained by a vehicle in the major traffic stream.
  7. Follow-up time: Time between the departure of one vehicle from the minor street and the departure of the next vehicle using the same gap under a condition of continuous queuing.
  8. Delay: The additional travel time experienced by a driver, passenger or pedestrian.
  9. Conflicting movements: The traffic streams in conflict at an intersection.
  10. Capacity: The maximum hourly rate at which persons or vehicles can reasonably be expected to traverse a point or uniform section of a lane or a roadway during a given time period under prevailing roadway, traffic, and control conditions.

Critical Gap

The critical gap $ t_{cx}$ for movement x is defined as the minimum average acceptable gap that allows intersection entry for one minor street or major street. The term average acceptable means that the average driver would accept or choose to utilize a gap of this size. The gap is measured as the clear time in the traffic stream defined by all conflicting movements. Thus, the model assumes that all gaps shorter than $ t_{cx}$ are rejected or unused, while all gaps equal to or larger than $ t_{cx}$ would be accepted or used. The adjusted critical gap $ t_{cx}$ computed as follows.

$\displaystyle t_{cx} = t_{cb} + t_{cHV} PHV + t_{cG} G - t_{c,T} - t_{3,LT}$ (1)

where, $ t_{cx}$ is the critical gap for movement ``$ x$'', $ t_{cb}$ is the base critical gap from Table. 1 $ t_{cHV}$ is the adjustment factor for heavy vehicles $ P_{HV}$ is the proportion of heavy vehicles $ t_{cG}$ is the adjustment factor for grade $ G$ is the percent grade divided by 100, $ t_{cT}$ is the adjustment factor for each part of a two-stage gap acceptance process, and $ t_{3LT}$ is the critical gap adjustment factor for intersection geometry.

Follow-up time

The follow up time $ t_{fx}$ for movement ``$ x$'' is the minimum average acceptable time for a second queued minor street vehicle to use a gap large enough admit two or more vehicles. Follow-up times were measured directly by observing traffic flow. Resulting follow-up times were analyzed to determine their dependence on different parameters such as intersection layout. This measurement is similar to the saturation flow rate at signalized intersection. Table. 1 and 2 shows base or unadjusted values of the critical gap and follow up time for various movements. Base critical gaps and follow up times can be adjusted to account for a number of conditions, including heavy - vehicle presence grade, and the existence of two stage gap acceptance. Adjusted Follow up Time computed as:

$\displaystyle t_{fx} = t_{fb} + t_{fHV} P_{HV}$ (2)

where, $ t_{fx}$ is the follow-up time for minor movement $ x$ $ t_{fb}$ is the base follow-up time from table 1 $ t_{fHV}$ is the adjustment factor for heavy vehicles, and $ P_{HV}$ is the proportion of heavy vehicles for minor movement.
Table 1: Base critical gap and follow up times
  Base Critical Gap,$ t_c$,base (s) Base Follow-up
Vehicle Movement Two-Lane Four-Lane Time
  Major Street Major Street $ t_{f,base}$ (s)
Left turn from major 4.1 4.1 2.2
Right turn from minor 6.2 6.9 3.3
Through traffic on minor 6.5 6.5 4.0
Left turn from minor 7.1 7.5 3.5


Table 2: Adjustments to base critical gap and follow up times
Adjustment Values(s)
Factor  
$ t_{cHV}$ 1.0 Two-lane major streets
  2.0 Four-lane major streets
$ t_{cG}$ 0.1 Movements 9 and 12
  0.2 Movements 7,8,10 and 11
  1.0 Otherwise
$ t_{cT}$ 1.0 First or second stage of two-stage process
  0.0 For one-stage process
$ T_{3LT}$ 0.7 Minor-street LT at T-intersection
  0.0 Otherwise
$ t_{fHV}$ 0.9 Two-lane major streets
  1.0 Four-lane major streets