Inputs
Example Data Table
| Phase | v (veh/h) | s (veh/h) | y=v/s | Lost (s) |
|---|---|---|---|---|
| 1 | 520 | 1900 | 0.2737 | 4 |
| 2 | 460 | 1900 | 0.2421 | 4 |
| 3 | 380 | 1800 | 0.2111 | 4 |
| 4 | 300 | 1800 | 0.1667 | 4 |
Formula Used
This calculator applies Webster’s optimum cycle length for isolated intersections:
- yi = vi / si (critical flow ratio for phase i)
- ΣY = Σ yi (sum of critical ratios)
- L = Σ li (total lost time per cycle, seconds)
- C* = (1.5L + 5) / (1 − ΣY) (optimum cycle, seconds)
After computing C*, the cycle is constrained by your min/max limits and rounded. Effective green is C − L, then allocated proportional to each yi.
How to Use This Calculator
- Choose the number of phases that serve your movements.
- Enter critical flow v and saturation flow s for each phase.
- Set lost time per phase using start-up and clearance assumptions.
- Define practical min/max cycle bounds and a rounding step.
- Press Calculate to view cycle length and green allocation above.
Cycle length as a capacity balancing tool
Signal cycle length is the primary lever for balancing intersection capacity and user delay. Short cycles reduce pedestrian wait and improve progression response, but they can waste time in repeated start‑up losses. Long cycles increase discharge opportunity for heavy movements, yet they raise average delay and queue risk when arrivals fluctuate. This calculator supports an evidence‑based cycle choice using critical ratios and lost time inputs.
Critical flow ratio and saturation concepts
Each phase is represented by a critical flow v and a saturation flow s. The ratio y=v/s estimates how much of the cycle that phase needs under stable discharge. When the sum ΣY approaches 1.00, the intersection is near saturation and small demand changes create large delay. Engineers typically verify v from turning counts and s from lane use, heavy vehicles, grades, and local driver behavior.
Lost time components you should document
Lost time L combines start‑up losses and clearance intervals that do not serve demand. Start‑up loss occurs when the queue accelerates after green, while clearance loss covers yellow and all‑red safety intervals. Because L repeats every cycle, reducing unnecessary clearance can improve performance without adding lanes. Use consistent assumptions across alternatives so comparisons remain fair.
Interpreting the computed cycle and green splits
The computed optimum cycle C* is then constrained by your practical bounds and rounded to a field‑friendly value. Effective green is C−L and is distributed proportional to each phase’s y. After allocation, check that minimum pedestrian and turn storage needs are met, then adjust splits if required. If ΣY is high, consider rephasing, adding protected turns, or improving saturation flows.
Example data you can validate quickly
Example four‑phase inputs: v=[520, 460, 380, 300] veh/h, s=[1900, 1900, 1800, 1800] veh/h, and lost time 4 s per phase. These give ΣY≈0.8936 and total lost time L=16 s. With practical limits 40–180 s and 5 s rounding, the final cycle is about 90 s and effective green about 74 s.
- Phase 1 y≈0.2737 → green ≈22.6 s
- Phase 2 y≈0.2421 → green ≈20.0 s
- Phase 3 y≈0.2111 → green ≈17.4 s
- Phase 4 y≈0.1667 → green ≈14.0 s
FAQs
1) What is a “critical flow” value in this tool?
Use the highest-lane-group demand that governs each phase. It is typically the movement with the largest v/s in that phase, expressed in vehicles per hour.
2) How do I choose saturation flow for local conditions?
Start with a local guideline or field observations. Adjust for lane width, grade, heavy vehicles, parking friction, turning radii, and driver compliance, then keep assumptions consistent across alternatives.
3) What does ΣY tell me about intersection performance?
ΣY is the demand-to-capacity indicator for the critical movements. Values near 1.00 mean oversaturation risk. Values below about 0.85 usually provide more stable operation under typical fluctuations.
4) Why does lost time matter so much?
Lost time repeats every cycle and does not serve vehicles. Higher lost time forces longer cycles to achieve the same effective green. Accurate start-up and clearance estimates improve timing decisions.
5) When should I override the computed cycle length?
Override when pedestrian clearance, coordination plans, transit priority, rail preemption, or storage constraints dominate. Use the computed cycle as a baseline, then fine-tune for site-specific safety and operations.
6) Can this be used for coordinated corridors?
Yes, as a starting point for selecting a cycle range. Coordination also requires offsets and consistent cycle lengths across intersections, so you may select a common corridor cycle after evaluating progression.
7) What should I do if the tool reports ΣY ≥ 1?
Demand exceeds available capacity for the current phasing. Consider adding lanes, changing phasing, restricting turning movements, improving saturation flow, or applying demand management before selecting a cycle.