**Lecture notes in Traffic Engineering And Management**

*Date:* February 19, 2014

- Introduction
- Gap acceptance and follow-up time
- Potential Capacity
- Movement capacity and impedance effects
- Determining control delay
- Conclusion
- References
- Acknowledgments

All the road junctions designated for the vehicles to turn to different directions to reach their desired destinations. Traffic intersections are complex locations on any highway. This is because vehicles moving in different direction want to occupy same space at the same time. In addition, the pedestrians also seek same space for crossing. Drivers have to make split second decision at an intersection by considering his route, intersection geometry, speed and direction of other vehicles etc. A small error in judgment can cause severe accidents. It causes delay and it depends on type, geometry, and type of control. Overall traffic flow depends on the performance of the intersections. It also affects the capacity of the road. Therefore, both from the accident perspective and the capacity perspective, the study of intersections are very important by the traffic engineers. Intersection design can vary widely in terms of size, shape, number of travel lanes, and number of turn lanes. Basically, there are four types of intersections, determined by the number of road segments and priority usage.

**Priority Intersection:**Occur where one of the intersecting roads is given definite priority over the other. The minor road will usually be controlled by some form of sing marking, such as stop or yield sign; thus ensuring that priority vehicles travailing on the main street will incur virtually no delay.**Space sharing intersection:**Are intended to permit fully equally priority and to permit continuous movement for all intersecting vehicle flows; example would be rotaries and other weaving areas.**Time Sharing Intersection:**Are those at which alternative flows are given the right of way at different point in time. This type of intersection is controlled by traffic signal or by police officer.**Uncontrolled intersection:**are the most common type of intersection usually occurs where the intersecting roads are relatively equal importance and found in areas where there is not much traffic shown in Fig. 1.

At uncontrolled intersection the arrival rate and individuals drivers
generally determine the manner of operation, while the resulting performance
characteristics are derived from joint consideration of flow conditions and
driver judgment and behavior patterns.
In simplest terms, an intersection, one flow of traffic *seeks gaps* in the
opposing flow of traffic.

At priority intersections, since one flow is given priority over the right
of way it is clear that the secondary or minor flow is usually the one *seeking
gaps*.
By contrast at uncontrolled intersection, each flow must seek gaps in the other
opposing flow.
When flows are very light, which is the case on most urban and rural roads large
gaps exist in the flows and thus few situation arise when vehicles arrive at
uncontrolled intersection less than 10 second apart or at interval close enough
to cause conflicts.
However when vehicles arrive at uncontrolled intersection only a few second
apart potential conflicts exist and driver must judge their relative time
relationships and adjusts accordingly.

Generally one or both vehicles most adjust their speeds i.e. delayed
somewhat with the closer vehicle most often taking the right of way; in a sense,
of course, the earlier arriving vehicle has *priority* and in this instance
when two vehicles arrive simultaneous, the rule of the road usually indicate
*priority* for the driver on the right.
The possibility of judgmental in these, informal priority situation for
uncontrolled intersection is obvious.
At an Uncontrolled intersection: Service discipline is typically controlled by
signs (stop or yield signs) using two rules two way stop controlled intersection
(TWSC) and all way stop controlled intersection (AWSC).

- The major street through and right-turning movements are the highest-priority movements at a TWSC intersection. This movements shown Fig. 3 are 2, 3, 5, 6, 15 and 16.
- Vehicles turning left from the major street onto the minor street yield only to conflicting major street through and right-turning vehicles. All other conflicting movements yield to these major street left-turning movements. The movements on this rank are 1, 4, 13, 14, 9 and 12.
- Minor Street through vehicles yield to all conflicting major street through, right-turning, and left-turning movements. The movements on this rank are 8 and 11.
- Minor Street left-turning vehicles yield to all conflicting major street through, right-turning, and left-turning vehicles and to all conflicting minor street through and right-turning vehicles. The movements on this rank are 7 and 10.

The analysis of AWSC intersection is easier because all users must stop. In this type of intersection the critical entity of the capacity is the average intersection departure head way. Secondary parameters are the number of cross lanes, turning percentages, and the distribution volume on each approach. The first step for the analysis of capacity is select approach called subject approach the approach opposite to subject approach is opposing approach, and the approach on the side of the subject approach is are called conflicting approach.

**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.**Gap acceptance:**The process by which a minor stream vehicle accepts an available gap to maneuver.**Critical gap:**The minimum major-stream headway during which a minor-street vehicle can make a maneuver.**Lag:**Time interval between the arrival of a yielding vehicle and the passage of the next priority stream vehicle (Forward waiting time).**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.**Minimum Headway:**The minimum gap maintained by a vehicle in the major traffic stream.**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.**Delay:**The additional travel time experienced by a driver, passenger or pedestrian.**Conflicting movements:**The traffic streams in conflict at an intersection.**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.

where, is the critical gap for movement ``'', is the base critical gap from Table. 1 is the adjustment factor for heavy vehicles is the proportion of heavy vehicles is the adjustment factor for grade is the percent grade divided by 100, is the adjustment factor for each part of a two-stage gap acceptance process, and is the critical gap adjustment factor for intersection geometry.

where, is the follow-up time for minor movement is the base follow-up time from table 1 is the adjustment factor for heavy vehicles, and is the proportion of heavy vehicles for minor movement.

Base Critical Gap,,base (s) | Base Follow-up | ||

Vehicle Movement | Two-Lane | Four-Lane | Time |

Major Street | Major Street | (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 |

Adjustment | Values(s) | |

Factor | ||

1.0 | Two-lane major streets | |

2.0 | Four-lane major streets | |

0.1 | Movements 9 and 12 | |

0.2 | Movements 7,8,10 and 11 | |

1.0 | Otherwise | |

1.0 | First or second stage of two-stage process | |

0.0 | For one-stage process | |

0.7 | Minor-street LT at T-intersection | |

0.0 | Otherwise | |

0.9 | Two-lane major streets | |

1.0 | Four-lane major streets |

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

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, is the potential capacity of minor movement (veh/h), is the conflicting flow rate for movement (veh/h), is the critical gap for minor movement , and is the follow-up time movement .

The movement capacity is found by multiplying the potential capacity by an adjustment factor. The adjustment factor is the product of the probability that each impeding movement will be blocking a subject vehicle. That is

where, is the movement capacity in vph, is the potential capacity movement x in vph, is the probability that impeding vehicular movement is not blocking the subject flow; (also referred to as the vehicular impedance factor for movement , is the probability that impeding pedestrian movement is not blocking the subject flow; also referred to us the pedestrian impedance factor for the movement .

where, is the demand flow for impeding movement , and is the movement capacity for impeding movement vph. Pedestrian impedance factors are computed as:

where, is the pedestrian impedance factor for impeding pedestrian movement , is the pedestrian flow rate, impeding movement in peds/hr, is the lane width in m, and is the pedestrian walking speed in m/s.

Vehicle Stream | Must Yield to | Impedance Factor for |

Pedestrian Stream | Pedestrians, | |

where, is the shared lane capacity in veh/hr, is the flow rate, movement sharing lane with other minor street flow, and is the movement capacity of movement sharing lane with other minor street.

where, is the average control delay per vehicle for movement in s/veh, is the capacity of movement or shared lane in veh/hr, is the analysis period h (15 min=0.25 h), and is the demand flow rate, movement or shared lane in veh/hr.

For AWSC intersections, the average control delay (in seconds per vehicle) is used as the primary measure of performance. Control delay is the increased time of travel for a vehicle approaching and passing through an AWSC intersection, compared with a free flow vehicle if it were not required to slow or stop at the intersection. According to the performance measure of the TWSC intersection, LOS of the minor-street left turn operates at level of service C approaches to B.

Level of Service | Control delays(s/veh) |

A | 0-10 |

B | 10-15 |

C | 15-25 |

D | 25-35 |

E | 35-50 |

F | 50 |

- The speed of the pedestrians is 1.2m/s
- All flows contains 10% trucks
- The percentage of the grade is 0.00
- Ignore moments coming from south bound
- The analysis period is 15 min. (T=0.25)

- Compute the critical gap and follow up time:
- Critical gap . From table. 1 and table. 2 we have = 7.1 s , = 0.2, = 0.0, = 0.0. Then at movement 7 computed as: = 7.1 + 1.0 0.1+0.2 0.0 - 0.0 - 0.0 = 6.50 sec
- To compute the Follow up time: From table. 1 and table. 2 we have = 3.5 s , = 0.9. Then at movement 7 computed as: = 3.5 + 0.9 0.1 = 3.59 sec.

- Compute the conflicting flow rate:

- Determining potential capacity:

- Determine the impudence effect of the movement capacity for movement 7:
From the given figure movement 7 is impeded by vehicular movement 4 and 1 and
pedestrian 13 and 15.
- Pedestrian impedance probability computed as:

- Vehicular impedance probabilities are:

- Once the pedestrian and vehicular impedance is determined, the moment
capacity is computed as:

- Pedestrian impedance probability computed as:
- Delay computation:
The delay is Calculated by using the formula

The delay of movement 7 is 18.213 sec/veh. - Determine the level of service: From the computed delay (18.213 se) in step 5 the level of service is LOS C obtained from HCM table.

- Highway Capacity Manual.
*Transportation Research Board*. National Research Council, Washington, D.C., 2000. - W S Homburger.
*Fundamentals of traffic engineering*. 2019. 12th Edition, pp 5-1 to 5-5. - William R McShane, Roger P Roesss, and Elena S Prassas.
*Traffic Engineering*. Prentice-Hall, Inc, Upper Saddle River, New Jesery, 1998.

Prof. Tom V. Mathew 2014-02-19