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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 tcx 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 tcx 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.

t_{cx} = t_{cb} + _{tcHV} PHV + t_{cGG} − t_{c},T − t_{3},LT (30.1)

where, t_{cx} is the critical gap for movement “x”, tcb is the base critical gap from Table. 30:1 t_{cHV} is the adjustment factor for heavy vehicles P_{HV} is the proportion of heavy vehicles tcG 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 tfx 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. Followup 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. 30:1 and 30:2 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:

t_{fx} = t_{fb} + t_{fHV} P^{HV } (30.2)

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.

Conflicting volume

The traffic flow process at un-controlled intersection is complicated since there are many distinct vehicular movements to be accounted for. Most of this movements conflict with opposing vehicular volumes. These conflicts result in decreasing capacity, increasing delay, and increasing potentials for traffic accidents. Consider a typical four-legged intersection as shown in Fig. 30:5 The numbers of conflicts for competing through movements are 4, while competing right turn and through movements are 8. The conflicts between right turn traffics are 4, and between left turn and merging traffic are 4. The conflicts created by pedestrians will be 8 taking into account all the four approaches. Diverging traffic also produces about 4 conflicts. Therefore, a typical four legged intersection has about 32 different types of conflicts. Conflicts at an intersection are different for different types of intersection. The essence of the intersection control is to resolve these conflicts at the intersection for the safe and efficient movement of both vehicular traffic and pedestrians. The movements for determining conflict in four legged intersection are:

1. Major street left turns seek gaps through the opposing through movement, the opposing right turn movement and pedestrians crossing the far side of the minor street.

2. Minor street right turns seek to merge in to the right most lane of the major street, which contains through and right turning vehicles. Each right turn from the minor street must also cross the two pedestrians path shown.

3. Through movements from the minor street must cross all major street vehicular and pedestrians flows.

4. Minor street left turns must deal not only with all major street traffic flow but with two pedestrians flows and the opposing minor street through and right turn movements.

Figure 30:6: Three legged intersection conflicts volume determination for movement 7

Through this movements the conflict volume (V_{cx}) for the given movement x is can be computed. As an example the formula of conflict volume for movement 7 for three legged intersection shown in Fig. 30:6 computed as:

V^{c7} = 2V^{c4} + V_{c5} + V_{c2} + 0.5V_{3} + V_{13} + V_{15} (30.3)

**Potential Capacity **

Capacity is defined as the maximum number of vehicles, passengers, or the like, per unit time, which can be accommodated under given conditions with a reasonable expectation of occurrence. Potential capacity describes the capacity of a minor stream under ideal conditions assuming that it is unimpeded by other movements and has exclusive use of a separate lane. Once of the conflicting volume, critical gap and follow up time are known for a given movement its potential capacity can be estimated using gap acceptance models. The concept of potential capacity assumes that all available gaps are used by the subject movement i.e.; there are no higher priority vehicular or pedestrian movements and waiting to use some of the gaps it also assumes that each movement operates out of an exclusive lane. The potential capacity of can be computed using the formula:

where, c_{px} is the potential capacity of minor movement x (veh/h), v_{cx} is the conflicting flow rate for movement x (veh/h), t_{cx} is the critical gap for minor movement x, and t_{fx }is the follow-up time movement x.

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