1. An observer notes that an approach to a pretimed signal has a maximum of 8 vehicles in a queue in a given cycle. If the saturation flow rate is 1440 veh/h and the effective red time is 40 seconds, how much time will it take this queue to clear after the start of the effective green (assuming that approach capacity exceeds arrivals and D/D/1 queuing applies)?
2. An approach to a pretimed signal with a 60- second cycle has 9 vehicles in the queue at the beginning of the effective green. Four of the 9
vehicles in the queue are left over from the previous cycle (at the end of the previous cycle’s effective green). The saturation flow rate of the approach is 1500 veh/h, total delay for the cycle is 5.78 vehicle minutes, and at the end of the effective green there are 2 vehicles left in the queue. Determine the arrival rate assuming that it is unchanged over the duration of the observation period (from the beginning to the end of this 5.78–vehicle-minute delay cycle). (Assume D/D/1 queuing.)
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