A morning peak traffic count at an urban residential intersection yields the following data.

Figures in brackets indicate commercial vehicles. Unbracketed figure is all vehicles.

The approaches from the north and south comprise three lanes; 2.8m left lane, 3.5m middle lane and 3.0m right lane. Approach gradient is 2% uphill. All other approaches are level with two 3.2m lanes.

Design signal timing for this intersection using Webster’s method.

(Note: follow the ten steps proposed in Webster method. Make reasonable assumptions where necessary and state them clearly).

Provide signal phasing, signal cycle and signal timing diagrams.

Provide a discussion about the performance of the intersection.

Provide suggestions to improve the intersection performances, if needed

## Signalized Intersection Design Concepts and Definitions

This design paper on road and traffic engineering is about signalized intersection design of a morning peak traffic count at an urban residential intersection by analyzing numerous theories and concepts in signalized intersection design that incorporates aspects such as green splitting, the design of cycle length, and design of phase. Intersections may be signalized to improve crossing opportunities for vehicles and pedestrians and also address the road safety, operation or efficiency issue. Numerous urban areas rely on the use of traffic signals heavily across the world to efficiently and effectively regulate the movement of road users and also vehicles. These signalized intersections are normally installed at the intersections of the major roads and generally entails numerous lanes of approach on every leg (Akcelik, 2011).

The parameters commonly used for evaluation of performance of signalized intersection include cycle failure, queue length, and control delay. There is need of collecting vehicle control delay data manually when measuring intersection performance. Signalized intersections should provide operation and space conditions to support all the road users. The signalized design can be designed to accommodate a variety of road users and can be either temporal or spatial separation depending on the diverse users targeted. At signalized intersections, numerous movements are separated in time and hence the risk to submissive cyclists is normally lower compared to unsignalized intersections. Some of the significance of signalized intersection include it does not need much during designing since it is very simple, numerous intersections have effectively improved in their capacity, and also the smooth movement of the traffic. However, these signalized intersections are faced with some shortcomings, such as complex in its implementation and design, and also delays caused by stoppage durations (Australian, 2013).

The following are some of the signal intersection concepts and definitions which are used in the signalized intersection design interpretation:

Cycle: This is the complete cycle of all the traffic through the used indication points

Red Interval: This is the time taken for the signal at the intersection to show red signal during a given movement

Cycle length: This is the time taken for green light to reappear again and it is measured in second. It is denoted by C.

Interval: This is the signal alternation from one stage of the signal to another. There are two different types of interval domain, namely, clearance interlude and change interlude. Go-ahead duration is also known as all red and is the time when the traffic signal indicates all red, basically used to clear vehicle in a particular intersection side. Change duration is also known as the time of the yellow signal and it indicates the time between green and red traffic signals during a single approach. (Bell, 2011)

## Webster's Method for Signalized Intersection Design

Green interval: This is the time when it indicates a go for a given intersection section normally denoted by G_{i}. It is the actual duration when the lights change to green.

Red interval: This is the time when the signal of intersection indicates red at a given movement.

Phase: It is the summation of the following change plus clearance and green interval.

Lost time: This indicated the duration when a given intersection does not completely apply to any movement of traffic (Florida, 2016).

The signal design is a procedure involving six steps, namely:

- Phase design
- Amber determination and succeeding clearance time

- Length cycle determination

- Distribution of green time
- Pedestrian crossing requirement
- Performance evaluation(Guberinic, 2009)

The phase design provides a separation of conflict movement in the steps which ensures that there is zero phase conflict. There is need to provide a phased design that has low conflicts in the intersection through the adoption of a standard methodology which is a subject of the geometry of numerous intersections and magnitude of flow (Guberinic, 2009). This phase design is a very significant process since it affects the entire performance of intersection adversely. The figure below shows the four-legged intersections for the urban intersection:

Figure 1: Intersection of four legs

This is the time taken for the signal to complete an entire cycle. The cycle time is denoted by the symbol C. Figure 1 above shows that as soon as the signal begins, the time interval between to vehicles also referred to as headway. The initial headway denotes the periodic interval from the beginning of green signal to the immediate vehicle intersecting the restricted stripe. The flow of other headways is portrayed in the above figure. It can be noted that instant movement is expected to be longer since a lot of duration is wasted as a result of the reaction time of the driver and the effective acceleration of the vehicle (Wolhuter, 2015). The assumption made is that the headway of the driver will be in front of the first driver headway due to the low time of reaction than the first driver. After a given number of the vehicles have passed the intersection, the headways are expected to be constant, until a saturation headway id reached and it is denoted by h (Wade, 2011).

This is the available time that a vehicle can take to cross the junction safely. Effective green time can be determined by adding the effective green phase, G_{i} and yellow signal to reduce the duration of time lost. The lost time can be determined by summing the whole time lost during clearance (1_{1}) and time lost during start-up (1_{2}). The real effective green time can be determined by:

## Signal Timing Algorithm for Signalized Intersection Design

G_{i }= G_{i} + Y_{i} - t_{o} (i)

The green ratio is the ratio between the effective green time and the cycle length (Gi/C). The saturation flow is the is the number of vehicles moving in one hour through an intersection while assuming that it will always be green (University, 2009). Therefore, the lane capacity can be determined by:

c_{i }= CI gi/C (ii)

Where C = cycle time in seconds, s_{i} is traffic flow capacity for every hour per lane, c_{i} is the lane capacity.

From the green ratio, saturation, and lane capacity, the efficiency and effectiveness of the intersection can be determined.

Figure 2: Signal timing of the Intersection

There have been numerous approaches that can be used in developing algorithms which can assist in designing the intersection signal timing particularly for the four-legged intersection shown in the figure above. The type of algorithm to be used in this signalized intersection design is known as Webster and involves ten steps (Sarna, 2009). This algorithm was developed by Dr Mehmet who was a British Mathematician and involves detailed usage in the design and analyzing the signal timing shown in figure 2 above.

By considering the four-legged intersection geometry shown in the figure above, there are numerous issues concerning design in the figure above, most importantly is that the design needs to be either three or more intersection phases (Pratelli, 2013). For this signalized intersection design, a four-phase design signal is ideal for the purposes of implementation.

The assumption made while using the Webster design is that the driver has been the capability of making a stop at the exact line of stoppage when the signal changes to red. The intersection interval change can be determined by first adopting the algorithm below:

(iii)

Where g is the approach rating in decimal, a is the breaking rate of vehicles, v85 is the percentile speediness of the vehicles impending in m/s, t is the reaction time for the driver, and y is the duration of the yellow interludes in seconds (Guberinic, 2009).

There is need to provide the optimum effective capacity of traffic flow of the intersection approaching to efficiently and effectively design signal timing. There should also be the low vehicle of interruptions and also small queue while issuing the optimum opportunity for the traffic passing on the given duration for mainstream users. The signal timing should seriously consider the normal traffic flow through the intersection. The cycle length is normally 40 seconds to 60 seconds for the 2-phase signal while longer cycle length is designed for traffics that are more complex than 2-phases (Australian, 2013). The algorithm that should be used while designing the signal includes:

- Finding the traffic volume for different directions and roads
- Determining the breadth of the roads

- The product acquired is the major input for the outcome of the capacity of rad traffic, planning the timing of the signal centred on the methods delivered by a given design method(Sarna, 2009).

## Discussion about the Performance of the Intersection

The total traffic volume, V_{t} is the sum of the particular traffic through the numerous approaches of the intersection.

Figure 3: Intersection approaches

The volume of traffic approaching from the Easter direction can be determined by summing the provided lanes of traffic approaching from the East of the intersection as shown below:

The traffic volume approaching from the northern direction, V_{n} of the intersection can be determined by summing the traffic through the given lanes from the north of the intersection as shown below:

The traffic volume approaching from the west of the intersection, V_{w} can be determined by summing the individual traffic lanes through the North of the intersection as shown below:

The volume of the traffic from the southern approach (V_{s}) can be determined by summing the total number of vehicles from the southern direction as shown below:

The total traffic volume, can be determined through the summation of the traffic volume in all the directions:

From the calculations above, it is clear that the quantitative number of vehicles scheduled to pass through the intersection is 3001 vehicles for both ordinary vehicles and commercial vehicles. This can further be simplified by determining the quantitative number of commercial vehicles from the different approaches as shown in the figure above (Pratelli, 2013). The total number of commercial vehicles approaching the intersection from the East side of the intersection, can be determined by summing the commercial vehicles in the given lanes as shown below:

The total number of approaching commercial vehicles from the northern side of the intersection, can be determined by summing the commercial vehicles in the northern lane from the north side of the intersection as shown below:

The total number of approaching commercial vehicles from the west side of the intersection, can be determined by summing the commercial vehicles approaching from the western section of the intersection as shown below:

_{ }

The total number of approaching commercial vehicles from the southern side of the intersection, can be determined by summing the commercial vehicles from the south side of the intersection as shown below:

The quantitative number of commercial vehicles expected to pass through the intersection, can be determined by summing the given commercial vehicles from all the different approaches as shown below:

The non-commercial vehicles approaching the intersection from all the four approaches is the difference between the total number of vehicles and the commercial vehicles through that particular direction.

## Suggestions to Improve Intersection Performances

The non-commercial vehicle through the east section of the intersection, can be determined by:

Non-commercial vehicles

The non-commercial vehicle through the north section of the intersection, can be determined by:

Non-commercial vehicles

The non-commercial vehicle through the west section of the intersection, can be determined by:

Non-commercial vehicles

The non-commercial vehicle through the west section of the intersection, can be determined by:

NNn-commercial vehicles

The dimension of the road is an important notation in the design of signal timing and it defines the traffic flow rate. From this design of the four-legged intersection, the width of the road can be determined by:

The width of the road from North to South path, ,

= (3.0+3.5+2.8)m

= 9.3m

When using the Webster, some of the assumptions made include the disparity in demand will follow at a single method specifically, the common lane is disregarded, and there is the use of permanent cycle distance.

One of the proven ways of improving the intersection performance is servicing the left-turn phase twice in the cycle. The measure of effectiveness can be used to determine the relative performance of the alternative left-turn phase strategies which should include the average intersection delay per cycle length and hourly in the entire left-turn phases. From the investigation, it can be recommended that the dual left-turn phases in a cycle can be considered an effective method of improving the efficiency of signalized intersection in the situation above. Other ways of ensuring that efficiency of signalized intersection include optimization of signal timing, giving considerations to all turning movements at the intersection, and maintaining continuity lane.

Conclusion

The signalized design can be designed to accommodate a variety of road users and can be either temporal or spatial separation depending on the diverse users targeted. At signalized intersections, numerous movements are separated in time and hence the risk to submissive cyclists is normally lower compared to unsignalized intersections. The steps involved in signalized intersection design include phase design, amber determination and succeeding clearance time, length cycle determination, distribution of green time, pedestrian crossing requirement, and performance evaluation.

References

Akcelik, R. (2011). Signalised Intersection Capacity Workshop. Melbourne: Northwestern University.

Australian, B. (2013). Road & Transport Research, Volume 12. Perth: Australian Road Research Board.

Bell, M. (2011). Transport Planning and Traffic Engineering. Gold Coast: Elsevier,

Florida, D. (2016). Determination of an Optimal Analytical Intersection Design Procedure. Florida: University of Florida, Transportation Research Center.

Guberinic, S. (2009). Optimal Traffic Control:. London: CRC Press.

Michael, B. (2011). Transport Planning and Traffic Engineering. Sydney: Elsevier.

Pratelli, A. (2013). Urban Street Design & Planning. Michigan: WIT Press.

Sarna, A. (2009). Design and performance characteristics of signalised intersections. California: Central Road Research Institute.

University, M. (2009). Traffic Engineering & Control, Volume 35. Michigan: Printerhall.

Wade, K. (2011). Traffic Engineering Practice. Perth: Monash University.

Wolhuter, K. (2015). Geometric Design of Roads Handbook. Colorado: CRC Press.

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