Signal timing: roads A 18 m and B 12 m

Isolated two-phase signal with pedestrian indications for road A (18 m) and road B (12 m).

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 $I = t_r + \dfrac{v}{2a}$ with reaction time $t_r = 1$ s and comfortable deceleration $a = 3\ \text{m/s}^2$, kept within the IRC:93 range of 2-4 s:

$$\begin{aligned} I_A &= 1 + \frac{55/3.6}{2(3)} = 3.55 \to 4\ \text{s}\\ I_B &= 1 + \frac{40/3.6}{2(3)} = 2.85 \to 3\ \text{s} \end{aligned}$$

Step 2: Pedestrian crossing time

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

$$\begin{aligned} t_{p,A} &= 5 + \frac{18}{1.2} = 20.0\ \text{s}\\ t_{p,B} &= 5 + \frac{12}{1.2} = 15.0\ \text{s} \end{aligned}$$

Pedestrians crossing road A walk during Phase 2, so Phase 2 green must be at least 20.0 s. Pedestrians crossing road B walk during Phase 1, so Phase 1 green must be at least 15.0 s.

Step 3: Webster cycle time from traffic

$$\begin{aligned} y_A &= \frac{300}{1800} = 0.167, \quad y_B = \frac{250}{1800} = 0.139, \quad Y = 0.306\\ L &= (2+4) + (2+3) = 11\ \text{s}\\ C_0 &= \frac{1.5L+5}{1-Y} = \frac{1.5(11)+5}{1-0.306} = 31.0\ \text{s} \end{aligned}$$ $$\begin{aligned} g_A &= \frac{0.167}{0.306}(20.0) = 10.9\ \text{s}, \quad G_A = g_A + 2 = 12.9\ \text{s}\\ g_B &= \frac{0.139}{0.306}(20.0) = 9.1\ \text{s}, \quad G_B = g_B + 2 = 11.1\ \text{s} \end{aligned}$$

Step 4: Check against pedestrian needs

Adopted cycle length $C = 15 + 4 + 20 + 3 = 42$ 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 15 s green); pedestrians crossing road A get WALK for 5 s then flashing for 15 s during Phase 2 (total 20 s of 20 s green). All pedestrian indications show DON'T WALK (red man) while their cross traffic moves.

Phase diagram

Cycle = 42 s
Road A: [GREEN 15][A 4][  RED 23  ]
Road B: [ RED 19 ][GREEN 20][A 3]
Ped crossing B: [WALK+FLASH 15][DON'T WALK 27]
Ped crossing A: [DON'T WALK 19][WALK+FLASH 20][DW]