Signal timing: roads A 15 m and B 12 m

Isolated two-phase signal with pedestrian indications for road A (15 m) and road B (12 m). Approach speeds are not needed because the ambers are given (3 s and 2 s).

Design basis (IRC:93-1985, Guidelines on Design and Installation of Road Traffic Signals, with Webster's method): two-phase signal, Phase 1 = road A moves, Phase 2 = road B 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 A = 3 s, road B = 2 s.

Step 2: Pedestrian crossing time

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

$$\begin{aligned} t_{p,A} &= 5 + \frac{15}{1.2} = 17.5\ \text{s}\\ t_{p,B} &= 5 + \frac{12}{1.2} = 15.0\ \text{s} \end{aligned}$$

Pedestrians crossing road A walk during Phase 2, so the Phase 2 green must be at least 17.5 s. Pedestrians crossing road B walk during Phase 1, so the Phase 1 green must be at least 15.0 s.

Step 3: Webster cycle time from traffic

$$\begin{aligned} y_A &= \frac{300}{1800} = 0.167, \quad y_B = \frac{250}{1800} = 0.139, \quad Y = 0.306\\ L &= (2+3) + (2+2) = 9\ \text{s}\\ C_0 &= \frac{1.5L+5}{1-Y} = \frac{1.5(9)+5}{1-0.306} = 26.6\ \text{s} \end{aligned}$$

With $C_0 - L = 17.6$ s of effective green:

$$\begin{aligned} g_A &= \frac{0.167}{0.306}(17.6) = 9.6\ \text{s}, \quad G_A = g_A + 2 = 11.6\ \text{s}\\ g_B &= \frac{0.139}{0.306}(17.6) = 8.0\ \text{s}, \quad G_B = g_B + 2 = 10.0\ \text{s} \end{aligned}$$

Step 4: Check against pedestrian needs

The pedestrian requirement governs. Adopted cycle length $C = 15 + 3 + 18 + 2 = 38$ s.

Final timings

Pedestrian signals: pedestrians crossing road B get WALK for 5 s, then flashing (clearance) for 10 s during Phase 1 (total 15 s of the 15 s green); pedestrians crossing road A get WALK for 5 s, then flashing for 13 s during Phase 2 (total 18 s of the 18 s green). All pedestrian indications show DON'T WALK (red man) while their cross traffic moves.

Phase diagram

Cycle = 38 s
Road A: [GREEN 15][A 3][  RED 20  ]
Road B: [ RED 18 ][GREEN 18][A 2]
Ped crossing B: [WALK+FLASH 15][DON'T WALK 23]
Ped crossing A: [DON'T WALK 18][WALK+FLASH 18][DW 2]