You have just finished allocating the available green time to a two-phase cycle. The actual (design) flow rates for the two critical lanes are 350 pcu/hr and 700 pcu/hr respectively. The optimum cycle length was 55 seconds and of the available green time, 14 seconds were allocated to phase one (350 pcu/hour) and 27 seconds were allocated to phase two (700 pcu/hr). Both phases have intergreen intervals of 6 seconds. The lengths of the pedestrian WALK intervals for phases one and two are 10 seconds and 16 seconds respectively. The width of the intersection for phases one and two is 48 ft and 68 ft respectively. Assume the saturation flow rate is 1900 pcu/hr for both lanes. Does this timing scheme require any adjustments? If so, what should the final signal timing plan be?[Solution Shown Below]
The first thing we will check is the capacities of the two critical lanes. We'll calculate the capacities by multiplying the green ratio (g/C) by the saturation flow rate (s). For phase one, the green ratio is 14/55 and the saturation flow rate is 1900 pcu/hr. This gives a capacity of 484 pcu/hr, which is more than adequate to handle the 350 pcu/hr design flow rate. Phase two has a capacity of 933 pcu/hr, which is also more than adequate to handle its design flow rate.
Next, we will check the minimum length of the green interval based on pedestrian movements. In phase one, the WALK interval is 10 seconds long and the crossing time is 48 ft/(4 ft/s), or 12 seconds. The total time required for pedestrians is 22 seconds. The vehicular movement provides only 14 seconds of green and 6 seconds of intergreen. Thus, the total time before the next phase begins is only 20 seconds. To remedy this, two seconds should be added to both the total cycle time and the green interval for phase number one. Pedestrians in phase number two receive 16 seconds of WALK time and require 68 ft/(4 ft/sec) = 17 seconds of crossing time. The total time required for the pedestrians in phase number two is, therefore, 33 seconds. The green interval and intergreen interval for phase number two add up to 33 seconds, which perfectly matches the pedestrian crossing time.
As it turns out, phase one's green interval needed to be increased by two seconds in order to serve the pedestrian movements. The total cycle length and phase one's green interval were both increased by two seconds, while all the other signal timing variables were left untouched.