Flexible progressive system is the traffic signal system in which the cycle length and cycle division are automatically varied. This system is designed to adapt to the changing traffic demands and optimize the traffic flow at intersections.

Flexibility in Cycle Length:
In a flexible progressive system, the cycle length can vary based on the traffic conditions. The cycle length refers to the total time taken for a complete sequence of signal indications at an intersection. It includes the green, yellow, and red phases for all the approaches. By automatically adjusting the cycle length, the system can accommodate varying traffic volumes and minimize delays.

Flexibility in Cycle Division:
Cycle division refers to the allocation of time within a cycle for each approach or movement at an intersection. In a flexible progressive system, the cycle division is also automatically varied based on the real-time traffic demands. This means that the green time for each approach can change dynamically depending on the traffic conditions. Approaches with higher traffic volumes may be allocated more green time to reduce congestion and improve traffic flow.

Benefits of Flexible Progressive System:
1. Improved Traffic Flow: By automatically adjusting the cycle length and cycle division, the flexible progressive system can optimize the traffic flow and reduce delays at intersections. It ensures that the green time is allocated efficiently to the approaches with higher traffic demands.

2. Adaptive to Changing Traffic Conditions: As traffic volumes change throughout the day, the system can adapt and automatically adjust the signal timings accordingly. This ensures that the traffic signal system remains responsive to the real-time traffic demands and minimizes congestion.

3. Reduces Fuel Consumption and Emissions: By optimizing the traffic flow and reducing delays, the flexible progressive system can help in reducing fuel consumption and emissions. Smoother traffic flow reduces the number of stops and starts, which leads to improved fuel efficiency and lower emissions.

4. Cost-Effective Solution: Implementing a flexible progressive system can be a cost-effective solution compared to other traffic management strategies. It utilizes the existing infrastructure and can be easily integrated with modern traffic signal controllers.

In conclusion, the flexible progressive system is a sophisticated traffic signal system that automatically varies the cycle length and cycle division based on real-time traffic conditions. It offers numerous benefits such as improved traffic flow, adaptability to changing traffic demands, reduced fuel consumption and emissions, and cost-effectiveness.