Question

A multilane highway has two northbound lanes. Each lane has a capacity of 1500 vehicles per hour. Currently, northbound traffic is consists of 3100 vehicles with 1 occupant, 600 vehicles with 2 occupants, 400 vehicle 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 vehicle 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.)

Answer 1

We are given the lane capacity, so we can calculate total capacity to be 1500 * 2 = 3000 vehicles

# of lanes	Lane Capacity (veh/hour)	Total Capacity
2	1500	3000

Now when you add a new lane the capacity becomes 4500 vehicles

We are given our travel time functions and vehicle compositions, so we can calculate travel time for diffeent vehicle types as follows

for exammple for single occupancy vehicles, no of persons = 3100* 1 = 3100

a) travel time = 15* ( 1+ 1.15 * (3100/4500) 6.87) = 15 * (1 + 1.15 * .68896.87) = 16.633 minutes

Total person travel time (in hours) = # of persons * travel time(min)/60 = 3100 * 16.633/60 = 843.88 person hours

Same way calculate for double, triple and buses

Total person hours = 1694

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b) Additional lane is open only to double or higher occupancy

So that means the capacity will be different for different combinations

for single occupancy car - it can only go in two lanes, so its capacity in calculations will be 3000, all other occupancy vehicles will have a capacity(for use in calculations) as 4500 because they can use all three lanes

So we can calculate travel time and total person travel time as follows

for example

for TRIPLE occupancy we have

travel time = 15* ( 1+ 1.15 * (400/4500) 6.87) = 15 * (1 + 0) = 15 minutes

so total person travel time(hours) = # of persons * travel time(min)/60 = 1200 * 15/60 = 300 person hours

Like this calculate for all occupancy vehicles as follows

Total person hours = 2741

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c) In this case all 3 occupancy cars and buses will use ONLY THE NEW LANE. so they will have a capacity of 1500 vehicles

single and double occupancy vehicles can use only the other two lanes, so their capacity(for calculations) will be 3000 vehicles.

So we can calculate travel time and total person travel time as follows

This doesnt change the total person travel time much.

total person travel time = 2741 person hours