Glossary

Discuss About The Economic Evaluation Traffic Safety Measures.

Many cities and town around the world highly depend on the application of traffic signal to efficacy control the road users like pedestrians, vehicles, motorcycles among others (Stokes, 2014). Several towns worldwide have employed the principle of time-sharing to effectually prevent problems that may arise in the roads as a result of the overwhelming number of traffic in major cities (OECD, 2016). Many benefits arose from the usage of traffic signals to manage the traffics, this includes but not limited to ensuring the traffic move orderly, various intersections have increased in their effective capacity, and lastly design an intersection signal does not require much rocket science, since designing such geometry is quite simple (Zyczkowski, 2013).

Notwithstanding the numerous advantages accrued to such intersections, some challenges arise in their usage. This includes delays due to large stoppage times and their design and implementation are relatively complex (Rampino, 2012). Regardless of the overall stoppage being less compared to those in the rotary systems especially in higher volumes, so users have cried foul due to they’re characteristically delays in stoppages (Vogt, 2014).This report tries to analyze the various concepts and theories in signal intersection design that encompasses matters such as the design of phase, the design of cycle length and green splitting. The theory surrounding the saturation flow is and calculating lost time are equally highlighted in the report. This report adopts some notations and some technical definition that shall be used in the subsequent sub-headings (Studies, 2013).

The following notations and definition is deemed important to be used in interpreting the signal design

1. Intervals:

This shows alternations from one signal stage to the next. Two types exist in the interval domain, change interlude and clearance interlude (trafikinstitut, 2017). Change duration similarly referred to as time of the yellow signal shows the duration between red and green traffic signals during one approach whereas go-ahead also referred to as all red is the duration when the traffic signal shows all red mainly used to clear vehicles in the other side of the intersections (Guthrie, 2011).

1. Phase:

 This is a combination of green interval and the change plus clearance which follows. In the green interval, the movement which is not conflicting gets assigned into their respective phases (Peden, 2013).

• Lost Time:

This shows the time when a particular intersection does not fully get used for any traffic movement. This is typical when a front driver takes too long to react to a new green signal and takes some time to speed off.

1. Green interval:

Phase Design

This is the duration when it is a go for a particular section of the intersection usually represented by means of G_i. This is the real time when the light is turns green.

1. Red Interval:

This is the duration when the intersection signal shows red in a particular movement.

1. Cycle:

A complete cycle of the traffic through all the various points of indications used.

• Cycle length

Is the time measured in seconds for the traffic signal to finish all the indications in the cycle. In other words, it measures the time taken for green light to reappear again. In the report, C will denote it (Mohan, 2016).

Design of a signal is a typical ten Webster’s Method. This includes,

1. Design of Phase
2. determination of amber and the subsequent clearance time
3. Determination of length cycle
4. Green time apportionment
5. Requirements for pedestrian crossing
6. Evaluation of performance.
7. Checking the porotypes
8. Testing the workability
9. Webster analysis
10. Hypothesis of Webster

     The main objective of the design is to give a difference in movement conflicts in the underlying step. This warrants no conflict in the phases (Transport, 2011). It is the aim of a civil engineer to develop a flawless design that has minimal conflicts in the intersection. A standard methodology has not been adopted for designing the intersections since it is a subject of the geometry of the various intersections, and the flow magnitude (Pierse, 2011). The defector standard has been a trial and error approach to the solution. However, the design of phase is quite vital in the whole process and if not well-designed can adversely affect the other steps and hence the whole intersection performance. And this can be illustrated in the diagram below for the four lagged intersection.

Cycle time is actually the time a signal takes to complete a cycle. C represents cycle time, Departure from the intersection illustrated in diagram above is as follows, immediately the signal resets, the interval in time amid two motor vehicles also referred to as headway. The primary headway denotes the interval of time from the beginning of green indication to the instantaneous vehicle intersecting the restriction stripe   other headways following are plotted as shown in the figure above (Lucas, 2013). It is assessed that the opening movement will be comparatively lengthier since much time is lost during the driver reaction time and his/her effective acceleration. It is also assumed that the second driver’s headway will be ahead of the first driver headway because of lower reaction time compared to the first drive. Once few vehicles have crossed the intersections, the headways are deemed to be constant, until they reach a saturation headway represented by the symbol h, which is the headway that can be reached at through a constant movement of a pool of automobiles (Transport, 2014).

Cycle Time

This is the available time an automobiles taken to cross safely an juction. It is a summation of the effective green phase (G_i ) and yellow signal to border amount of  lost time (Stern, 2012). The time lost can be understood as per the summation of entirely the time lost during start-up (l₁) and time lost during clearance (l₂) (Andersson, 2011). Therefore the actual green time depicts the following formulae,

G_i=G_i+Y_i-t_{o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .}

Lane Capacity

The calculation of the ratio between the effective green time and the length of the cycle g_i/C gives us the green ratio and as defined earlier, saturation flow is the number of automobile flowing through an intersection in one hour with the assumption that it will always be green throughout (Bartolomeos, 2012). Thus lane capacity is depicted as follows,

c_i =

Where the c_i represent the lane capacity in a automobile for every hour, while s_i  represent capacity of traffic flow measured in a automobile for every hour per lane, C represents time of cycle measured in seconds (Mohan, 2012).

This report indicates the various steps to be followed in measuring the effectiveness and efficiency of an intersection based on its lane capacity, saturation, the green ratio among other mathematical representation. The above notation is vital in the analysis of the intersection shown

Several approaches have been developed to aid in developing algorithms to design signal timing for intersections especially the four-legged type provided in the assignment, A typical algorithm that encompasses ten steps was developed by a British Mathematician called Dr. Mehmet M. Kunt. The algorithm is called Webster and detailed usage in the analyzing and design of the timing of signals for the above intersection is explained below (Forum, 2014).

Considering the below four-legged geometry of an intersection, //diagram. There are many design issues in the above figure, first, the design necessities to be either a two, three even more phases for the intersection. And in this design, a four-phase signal design is ideal for implementation purposes.

Operational Green Time

The Webster method design assumes that the driver is able to make a stop at exactly the stoppage line when the signal turns red (Lucraft, 2015). To calculate the change interval for the intersection, the following algorithm has been adopted

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Where y=duration of the yellow interludes in seconds

t=driver’s reaction time

v_85=85th percentile speediness of impending vehicles in m/s

the a=braking rate of vehicles

g=rating of approach in decimal

To perfectly design timing of signal for a particular intersection, the aim of the designer is to come up with the maximum effective traffic flow capacity approaching the intersection. The design should also purpose at guaranteeing the smallest magnitude of interruptions and building comparatively smaller queue and again providing the maximum chance of the traffic passing on the first particular period for mainstream users (Dawson, 2011). The timing of the signal should take into a lot of consideration the general flow of traffic through the intersection. The length of the cycle is generally 40 to 60 seconds for two-phase signal, longer ones are designed for more complex traffic with more than two phases (Krul, 2011).

For a design to be achieved, the following algorithm should be used,

• First, find the volume of traffic for different roads and or directions
• Finding the breadth of the roads
• The product attained are key inputs for the results of the road traffic capacity, planning signal timing centered on the procedures provided by a specific method of design

The volume of the total traffic, V_t Is the summation of the individual traffics through the various intersection approaches.

Volume traffic from the southern approach (V_s) is calculated as the summation of the total number of vehicles passing from south

i.e  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

=714 vehicles

The volume of traffic approaching from the western, WV side of the intersection is the summation of all the traffic through the individual lanes of the approach.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

Lane Capacity

     =538 vehicles

The amount of traffic flowing from the northern approach V_n of the intersection is the summation of the traffic through the individual lanes through the northern approach.

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    =662

The volume of traffic flowing from the eastern approach  is the summation of the individual traffic in the lanes in the eastern approach of the intersection,

From the calculation, it is evident that the total number of vehicles to schedule to pass through the intersection is 3001 vehicles, Both the commercial and other vehicles, To drill it down further, the total number of commercial vehicles from different approaches can also be determined from the above diagram.

The total volume of commercial vehicles  approaching the intersection from the southern approach is the individual summation of the commercial vehicles in the individual lanes from the southern approach,

The total volume of commercial vehicles approaching the intersection from the western  appthe roach is the summation of the individual commercial traffic from the lanes from the western approach,

The total volume of a commercial vehicle approaching the intersection from the northern approach  of the intersection is in the individual sum of commercial vehicles in the individual lanes in the intersection from the northern approach.

The total volume of the commercial vehicles approaching the intersection from the eastern approach of the intersection is the summation of the individual commercial vehices in the individual lanes,

Total number of commercial vehicles deemed to pass through the intersection   is summation of the individual commercial vehicles from the different approaches

The noncommercial vehicles passing through the intersection from the given approaches is the difference between the total vehicles through the specific approach and the commercial vehicles through that approach.

The non-commercial through the southern approach  is given as follows

The non-commercial vehicles through the western approaching  is given as follows

The non-commercial vehicles through the northern approach  is given as follows

The noncommercial vehicles through the eastern approach  is given as follows

The width of the road is as well a significant parameter in the signal timing design and it determines the rate of traffic flow, from the four-legged intersections in question, the width of the two roads can be obtained using the following equations

Above in the assignment

The width of the road projecting from the north to south trajectory  is as follows

The width of the road projecting from the west to east trajectory  is as showsn below

Total width =9.3+6.4

=15.7

Signal timing  therefore is deduced by the following equation  

St = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

St =

=

The signal timing for the intersection is therefore 46.6s

Webster method employed in the above calculation have some assumption, these assumptions includes the following;

1. Usage of a permanent cycle distance
2. Disregarding the existence of a common lane

• Presumptuous that demand disparity will follow at one method only

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