41.6. Determination of cycle length

The cycle length or cycle time is the time taken for complete indication of signals in a cycle. Fixing the cycle length is one of the crucial steps involved in signal design.

The cycle length refers to the duration it takes for all traffic signals at an intersection to complete one full sequence. This includes all phases, like green, yellow, and red signals. Establishing the cycle length is vital because it directly impacts how efficiently traffic flows through the intersection.

Think of the cycle length like a complete lap in a race. Just as a racecar must complete a lap before it can begin again, traffic signals need to go through all their signals before repeating to manage the flow of vehicles.

If t is the start-up lost time for a phase i, then the total start-up lost time per cycle, L = N t, where N is the number of phases.

Start-up lost time refers to the delay incurred when the traffic light changes from red to green. If each phase (the complete signal for a direction) has a start-up lost time of 't' seconds and there are 'N' phases in total, the total start-up lost time for the entire cycle will be 'N multiplied by t.' This considers that each phase experiences this time loss when it starts.

Imagine that each car needs a moment to start moving when the light turns green. If there are four lanes and each lane has a delay of 3 seconds before moving, that adds up! Just like waiting for a train to get moving before it leaves the station.

If start-up lost time is same for all phases, then the total start-up lost time is L = Nt.

When the start-up lost time is consistent across all traffic signal phases, calculating the total lost time becomes straightforward. By multiplying the number of phases (N) by the time it takes for each phase to get started (t), we can efficiently determine how much time is effectively wasted each cycle due to this start-up time.

Consider making toast in the morning, where each piece of toast takes 2 minutes to start cooking. If you toast 4 pieces at once, your total waiting time (lost time before they are done) is simply 4 times 2 minutes.

The total effective green time available for the movement in a hour will be one hour minus the total lost time in an hour.

To find the effective green time, which is the actual time that the signal is green and usable for traffic movement, it's calculated by subtracting the total lost time per hour from 3600 seconds (1 hour). This adjustment reflects how long traffic really has the right of way at the intersection.

Imagine you have an hour to study but you spend 15 minutes distracted by your phone. Your effective study time is now just 45 minutes. The same concept applies to traffic signals — the time they’re actually useful is reduced due to lost time.

Total number of critical lane volume that can be accommodated per hour is given by V as, V = Tg.

The maximum volume of vehicles that can pass through a lane per hour, known as the critical lane volume, depends on the effective green time (T) available in that hour multiplied by the saturation flow rate (g), which is how many vehicles can typically pass per lane (when the light is green) in that hour. This gives an essential idea of how many cars can realistically be managed during green lights.

Think of it as how many people can fit into an elevator at once. If the elevator can hold 10 people, and it runs every 2 minutes (for a total of 30 times in an hour), you can fit a maximum of 300 people in that hour.

Incorporating these two factors in the equation for cycle length, the final expression will be, C = N.t / (1 - Vc / Si × PHF × v).

The final equation for determining cycle length takes into consideration the total start-up lost time, the peak hour factor (PHF), and the ratio of volume to capacity (v/c ratio), providing a comprehensive understanding of how these variables interact to influence the cycle length adjusted for varying traffic conditions. This allows for more efficient traffic signal designs.

It’s like calculating how long a party should last based on how many guests (volume) can fit in your house (capacity), while also accounting for the time it takes for everyone to get to the party (lost time) and how packed your home gets at peak times.

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