A left-turn movement at a signalized intersection has a saturation flow of 900 veh/h per lane. The signal is allocated 19 s of green time in a 120 s cycle with 4 s of yellow and 1 s of all-red. The signal has typical start-up and clearance lost times. At the beginning of a cycle’s effective red there are no vehicles in the queue and vehicles arrive throughout the cycle at a rate of v(t) = 0.10 + 0.000278t [with v(t) in veh/s and t in seconds after the beginning of the effective red]. An analyst wants to consider the effects of autonomous vehicles (driverless cars controlled by computers and appropriate sensor technology) on this left-turn movement. With autonomous vehicles it is estimated that the saturation flow rate will increase from 900 veh/h to 2800 veh/h (since vehicles can follow more closely and maintain a high safety level because drivers’ reaction time is no longer a factor). In addition, there is no longer the need for yellow and all-red times since vehicle-to-infrastructure communication tells vehicles in advance of a change from displayed green to displayed red. So the green time for this left-turn movement is increased from 19 to 24 seconds. With autonomous vehicles, start-up lost time is reduced to just 1 second (it still exists to account for the time for the vehicles to accelerate to their saturation-flow speeds). How much shorter would the total delay for this movement be in this cycle (in veh-s, assuming the cycle length and green time do not change) if autonomous vehicles were present instead of conventional vehicles? (Assume D/D/1 queuing.)
SOLUTION Note: Open boxes in equations “ ” are to be completed by the reader
This problem demonstrates the potential benefits of autonomous vehicles at signalized intersections. To begin, the delay for the conventional-vehicle case needs to be determined. We will start by calculating the number of vehicles that arrive and depart at the left-turn movement during the cycle. The total arrivals during the 120 s cycle [with the arrival rate given as v(t) = 0.10 + 0.000278t]
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