Practice Problems: Traffic Flow Theory
Question 1
A traffic engineer is analyzing traffic flow on a highway segment during morning rush hour. The following data were collected over a 15-minute observation period:
Number of vehicles passed: 450 vehicles
Average spacing between vehicles: 80 feet
Segment length: 2,640 feet (0.5 miles)
What is the traffic density on this highway segment in vehicles per mile?
(a) 33 veh/mi
(b) 66 veh/mi
(c) 82 veh/mi
(d) 120 veh/mi
Question 2
A transportation planning agency is evaluating a freeway section where the following traffic conditions were observed:
Traffic flow: 2,400 vehicles per hour
Average speed: 60 mph
What is the traffic density in vehicles per mile for this freeway section?
(a) 20 veh/mi
(b) 30 veh/mi
(c) 40 veh/mi
(d) 50 veh/mi
Question 3
A civil engineer is conducting a time-mean speed study on an urban arterial. Five vehicles were timed over a 1-mile section with the following speeds recorded:
Vehicle 1: 35 mph
Vehicle 2: 40 mph
Vehicle 3: 32 mph
Vehicle 4: 38 mph
Vehicle 5: 45 mph
What is the time-mean speed for this traffic stream?
(a) 36 mph
(b) 38 mph
(c) 40 mph
(d) 42 mph
Question 4
A traffic consultant is analyzing the same five vehicles from the previous study to calculate the space-mean speed. The vehicles traveled 1 mile with the following speeds:
Vehicle 1: 35 mph
Vehicle 2: 40 mph
Vehicle 3: 32 mph
Vehicle 4: 38 mph
Vehicle 5: 45 mph
What is the space-mean speed for this traffic stream?
(a) 36.8 mph
(b) 37.6 mph
(c) 38.0 mph
(d) 39.2 mph
Question 5
A highway operations engineer is analyzing traffic flow on a freeway segment using the Greenshields model. The following parameters were determined:
Free-flow speed: 70 mph
Jam density: 140 vehicles per mile
What is the maximum flow capacity of this freeway segment in vehicles per hour?
(a) 2,100 veh/h
(b) 2,450 veh/h
(c) 2,800 veh/h
(d) 3,150 veh/h
Question 6
A traffic engineer is evaluating a rural two-lane highway where the following traffic stream characteristics were observed:
Average headway: 3.0 seconds
Standard deviation of headway: 0.5 seconds
What is the traffic flow rate in vehicles per hour on this highway?
(a) 900 veh/h
(b) 1,200 veh/h
(c) 1,500 veh/h
(d) 1,800 veh/h
Question 7
A transportation engineer is conducting a traffic study on a highway using loop detectors. Over a 5-minute period, the following data were collected:
Number of vehicles detected: 180 vehicles
Total detector occupancy time: 72 seconds
Average vehicle length: 18 feet
What is the space-mean speed of vehicles in mph?
(a) 48 mph
(b) 54 mph
(c) 60 mph
(d) 66 mph
Question 8
A traffic analyst is studying queuing characteristics at a highway bottleneck. The following conditions exist:
Arrival flow rate: 2,000 veh/h (constant)
Capacity during incident: 1,200 veh/h
Incident duration: 45 minutes
What is the maximum queue length in vehicles that will form during the incident?
(a) 450 vehicles
(b) 600 vehicles
(c) 750 vehicles
(d) 900 vehicles
Question 9
A highway design engineer is analyzing traffic flow using the Greenshields linear speed-density relationship. The following parameters apply:
Free-flow speed: 65 mph
Jam density: 130 veh/mi
Current density: 45 veh/mi
What is the current traffic speed in mph?
(a) 42.5 mph
(b) 47.0 mph
(c) 52.5 mph
(d) 57.5 mph
Question 9 (Revised)
A highway design engineer is analyzing traffic flow using the Greenshields linear speed-density relationship. The following parameters apply:
Free-flow speed: 70 mph
Jam density: 140 veh/mi
Current density: 42 veh/mi
What is the current traffic speed in mph?
(a) 49 mph
(b) 56 mph
(c) 63 mph
(d) 70 mph
Question 9 (Final)
A highway design engineer is analyzing traffic flow using the Greenshields linear speed-density relationship. The following parameters apply:
Free-flow speed: 70 mph
Jam density: 140 veh/mi
Current density: 35 veh/mi
What is the current traffic speed in mph?
(a) 49.0 mph
(b) 52.5 mph
(c) 56.0 mph
(d) 60.0 mph
Question 10
A traffic operations engineer is analyzing shockwave propagation due to a traffic incident. The following conditions were observed:
Upstream flow: 1,800 veh/h at 55 mph
Downstream flow (queue): 0 veh/h at 0 mph
Upstream density: 32.7 veh/mi
Jam density: 120 veh/mi
What is the shockwave speed in mph?
(a) -20.6 mph
(b) -18.4 mph
(c) -15.2 mph
(d) -12.8 mph
Question 11
A consulting engineer is evaluating passenger car equivalents (PCE) on a highway segment. The following traffic composition was observed during a 1-hour period:
Passenger cars: 850 vehicles
Trucks (PCE = 2.5): 120 vehicles
Buses (PCE = 2.0): 30 vehicles
What is the equivalent hourly flow rate in passenger cars per hour?
(a) 1,000 pc/h
(b) 1,110 pc/h
(c) 1,210 pc/h
(d) 1,310 pc/h
Question 11 (Revised for correct answer)
A consulting engineer is evaluating passenger car equivalents (PCE) on a highway segment. The following traffic composition was observed during a 1-hour period:
Passenger cars: 900 vehicles
Trucks (PCE = 2.5): 120 vehicles
Buses (PCE = 2.0): 30 vehicles
What is the equivalent hourly flow rate in passenger cars per hour?
(a) 1,000 pc/h
(b) 1,110 pc/h
(c) 1,260 pc/h
(d) 1,310 pc/h
Question 12
A municipal traffic engineer is analyzing the dissipation time of a queue formed during a 30-minute incident. The following data apply:
Arrival rate: 2,400 veh/h (constant before, during, and after incident)
Service rate during incident: 1,200 veh/h
Service rate after incident: 2,800 veh/h
Incident duration: 30 minutes
How long after the incident clears will it take for the queue to dissipate completely?
(a) 15 minutes
(b) 25 minutes
(c) 30 minutes
(d) 45 minutes
Question 12 (Revised)
A municipal traffic engineer is analyzing the dissipation time of a queue formed during a 20-minute incident. The following data apply:
Arrival rate: 2,400 veh/h (constant before, during, and after incident)
Service rate during incident: 1,200 veh/h
Service rate after incident: 3,200 veh/h
Incident duration: 20 minutes
How long after the incident clears will it take for the queue to dissipate completely?
(a) 15 minutes
(b) 20 minutes
(c) 25 minutes
(d) 30 minutes
Question 13
A traffic engineer is conducting a gap acceptance study at an unsignalized intersection. The following critical gaps were observed for 8 drivers:
3.5, 4.2, 3.8, 4.5, 3.6, 4.0, 3.9, 4.1 seconds
What is the mean critical gap for this sample?
(a) 3.85 seconds
(b) 3.95 seconds
(c) 4.05 seconds
(d) 4.15 seconds
Question 14
A transportation consultant is analyzing traffic flow on a freeway section. Using the Greenberger logarithmic model, the following parameters were calibrated:
Jam density (kj): 150 veh/mi
Constant c: 35 mph
Current density: 50 veh/mi
What is the predicted speed at the current density?
(a) 33.5 mph
(b) 38.5 mph
(c) 43.5 mph
(d) 48.5 mph
Question 15
A highway operations engineer is analyzing traffic at a bottleneck with the following characteristics:
Pre-queue density: 25 veh/mi traveling at 60 mph
Queue density: 100 veh/mi traveling at 15 mph
What is the speed of the forward recovery shockwave when the bottleneck is removed?
(a) 30 mph
(b) 35 mph
(c) 40 mph
(d) 45 mph
Question 15 (Revised)
A highway operations engineer is analyzing traffic at a bottleneck with the following characteristics:
Pre-queue conditions: density 20 veh/mi traveling at 65 mph
Queue conditions: density 95 veh/mi traveling at 20 mph
What is the speed of the forward recovery shockwave when the bottleneck is removed?
(a) 20 mph
(b) 25 mph
(c) 30 mph
(d) 35 mph
Question 15 (Final)
A highway operations engineer is analyzing the forward recovery shockwave at a bottleneck. The following characteristics apply:
Upstream (queue) conditions: flow = 1,500 veh/h, density = 100 veh/mi
Downstream (recovered) conditions: flow = 2,400 veh/h, density = 40 veh/mi
What is the speed of the forward recovery shockwave in mph?
(a) 10 mph
(b) 15 mph
(c) 20 mph
(d) 25 mph
Question 16
A traffic analyst is studying platoon flow characteristics on an arterial street. A platoon of 15 vehicles passes a point with the following time headways (in seconds):
First vehicle: lead vehicle (no headway)
Vehicles 2-15: average headway = 2.2 seconds
What is the flow rate for this platoon in vehicles per hour?
(a) 1,527 veh/h
(b) 1,636 veh/h
(c) 1,745 veh/h
(d) 1,854 veh/h
Question 17
A freeway management engineer is analyzing capacity reduction during rain. Under dry conditions:
Capacity: 2,400 pc/h/lane
Free-flow speed: 70 mph
During light rain, capacity reduces to 2,100 pc/h/lane and free-flow speed reduces to 60 mph
Using the Greenshields model, what is the jam density during rainy conditions in veh/mi?
(a) 120 veh/mi
(b) 130 veh/mi
(c) 140 veh/mi
(d) 150 veh/mi
Question 18
A transportation planning engineer is evaluating level of service on a freeway segment. The following conditions were observed:
15-minute vehicle count: 675 vehicles
Number of lanes: 3
Peak hour factor (PHF): 0.90
What is the hourly flow rate per lane in pc/h/ln?
(a) 900 pc/h/ln
(b) 1,000 pc/h/ln
(c) 1,100 pc/h/ln
(d) 1,200 pc/h/ln
Question 19
A traffic engineer is analyzing acceleration characteristics at a freeway on-ramp merge area. A vehicle accelerates from 25 mph to 55 mph over a distance of 800 feet. Assuming constant acceleration:
Initial speed: 25 mph (36.7 ft/s)
Final speed: 55 mph (80.7 ft/s)
Distance: 800 feet
What is the acceleration rate in ft/s²?
(a) 2.0 ft/s²
(b) 2.4 ft/s²
(c) 3.0 ft/s²
(d) 3.6 ft/s²
Question 20
A municipal engineer is studying traffic signal progression along an arterial. The following data apply:
Distance between signals: 1,320 feet (0.25 miles)
Cycle length: 90 seconds
Average travel speed: 35 mph
Signal offset required for progression: based on travel time
What should be the signal offset in seconds to achieve proper progression?
(a) 18 seconds
(b) 22 seconds
(c) 26 seconds
(d) 30 seconds
