1. A multilane highway has two northbound lanes. Each lane has a capacity of 1500 vehicles per hour.
Currently, northbound traffic consists of 3100 vehicles with 1 occupant, 600 vehicles with 2 occupants, 400 vehicles with 3 occupants, and 20 buses with 50 occupants each. The highway’s performance function is t = t0[1 + 1.15(x/c)6.87], where t is in minutes, t0 is equal to 15 minutes, and x and c are volumes and capacities in vehicles per hour. An additional lane is being added (with 1500 veh/h capacity). What will the total person-hours of travel be if the lane is (a) open to all traffic, (b) open to vehicles with two or more occupants only, and (c) open to vehicles with three or more occupants only? (Assume that all qualified higher-occupancy vehicles use only the new lane, no unqualified vehicles use the new lane, and there is no mode shift.)
2. Consider the new lane addition in above. First, suppose 500 one-occupant vehicle travelers take 10 buses (50 on each bus), and the new lane is open to vehicles with two or more occupants. What would the total person-hours be? Second, referring back to part (a), what is the minimum mode shift from one-occupant vehicles to buses (with 50 persons each) needed to ensure that the person-hours of travel time on the highway with the new lane (which is restricted to vehicles with two or more occupants) is as low as if all three lanes (the two existing lanes and the new lane) were open to all traffic? (Set up the equation, and solve to the nearest 100 one-occupant vehicles.)
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