Signal timing: roads H 12 m and F 9.6 m

Isolated two-phase signal with pedestrian indications for road H (12 m) and road F (9.6 m). The ambers are given (5 s and 4 s), so the approach speeds are not needed for them.

Design basis (IRC:93-1985, Guidelines on Design and Installation of Road Traffic Signals, with Webster's method): two-phase signal, Phase 1 = road H moves, Phase 2 = road F moves. Pedestrians cross a road while the traffic on the cross road has green. Assumed (not given): saturation flow 1800 PCU/h per lane, start-up lost time 2 s per phase, pedestrian walking speed 1.2 m/s and initial walk (pedestrian start-up) time 5 s.

Step 1: Amber (change) time

Amber times are given: road H = 5 s, road F = 4 s.

Step 2: Pedestrian crossing time

Time to cross = initial walk + width / walking speed:

$$\begin{aligned} t_{p,H} &= 5 + \frac{12}{1.2} = 15.0\ \text{s}\\ t_{p,F} &= 5 + \frac{9.6}{1.2} = 13.0\ \text{s} \end{aligned}$$

Pedestrians crossing road H walk during Phase 2, so Phase 2 green must be at least 15.0 s. Pedestrians crossing road F walk during Phase 1, so Phase 1 green must be at least 13.0 s.

Step 3: Webster cycle time from traffic

$$\begin{aligned} y_H &= \frac{475}{1800} = 0.264, \quad y_F = \frac{325}{1800} = 0.181, \quad Y = 0.444\\ L &= (2+5) + (2+4) = 13\ \text{s}\\ C_0 &= \frac{1.5L+5}{1-Y} = \frac{1.5(13)+5}{1-0.444} = 44.1\ \text{s} \end{aligned}$$ $$\begin{aligned} g_H &= \frac{0.264}{0.444}(31.1) = 18.5\ \text{s}, \quad G_H = g_H + 2 = 20.5\ \text{s}\\ g_F &= \frac{0.181}{0.444}(31.1) = 12.6\ \text{s}, \quad G_F = g_F + 2 = 14.6\ \text{s} \end{aligned}$$

Step 4: Check against pedestrian needs

Adopted cycle length $C = 21 + 5 + 15 + 4 = 45$ s.

Final timings

Pedestrian signals: pedestrians crossing road F get WALK for 5 s then flashing (clearance) for 8 s during Phase 1 (total 13 s of 21 s green); pedestrians crossing road H get WALK for 5 s then flashing for 10 s during Phase 2 (total 15 s of 15 s green). All pedestrian indications show DON'T WALK (red man) while their cross traffic moves.

Phase diagram

Cycle = 45 s
Road H: [GREEN 21][A 5][  RED 19  ]
Road F: [ RED 26 ][GREEN 15][A 4]
Ped crossing F: [WALK+FLASH 21][DON'T WALK 24]
Ped crossing H: [DON'T WALK 26][WALK+FLASH 15][DW]