PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 39P
To determine
The saved vehicles hours of travel time,
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8.25 Two routes connect an origin and destination
with performance functions t₁ = 5 + 3x₁ and t₂ = 7+
X2, with t's in minutes and x's in thousands of
vehicles per hour. Total origin-destination demand is
7000 vehicles in the peak hour. What are user-
equilibrium and system-optimal route flows and total
travel times?
4. Three routes connect and origin and a destination with performance functions
t₁ = 8 + x₁, t₂ = 1 + 2x₂, and t3 = 1 + 0.5x3 (with x's in thousands of vehicles per hour
and t's in minutes). If the peak-hour traffic demand is 3400 vehicles, determine user-
equilibrium traffic flows on each route. [Ans: x₂ = 0.68]
hree routes connect an origin and a destination with performance functions: ?1=8+0.5?1; ?2=1+2?2; and ?3=3+0.75?3; with the x’s being the traffic volume expressed in thousands of vehicles per hour and t’s being the travel time expressed in minutes. If the peak hour traffic demand is 3400 vehicles, determine user equilibrium traffic flows. [Hint: Note that one of the paths will not be used under the equilibrium condition
Chapter 8 Solutions
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 6PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10P
Ch. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 27PCh. 8 - Prob. 28PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 32PCh. 8 - Prob. 33PCh. 8 - Prob. 34PCh. 8 - Prob. 35PCh. 8 - Prob. 36PCh. 8 - Prob. 37PCh. 8 - Prob. 38PCh. 8 - Prob. 39P
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- Two routes connect a city and suburb. During the peak-hour morning commute, a total of 5000 vehicles travel from the suburb to the city. Route 1 has a 50km/hr speed limit and 5km in length, Route 2 has a 55km/hr speed limit and 4 km in length. Studies show that the total travel time on route 1 increases 2 mins for every extra 500 vehicles added. Mins of travel time on route 2 increase with the square of the no. of vehicles expressed in 000’s. Determine user equilibrium travel times.arrow_forwardto no congestion on the road further downstream of the railway grade crossing. QUESTION 5: Consider trip distribution within 5 zones in an area. The total trip production from zone 1 is 1000. The travel times from zone 1 to zones 2, 3, 4 and 5 are 5, 10, 20, and 30 minutes, respectively. The trip attraction to zones 2, 3, 4 and 5 are 50, 200, 75, and 450, respectively. Assume that the number of trips produced from zone 1 to zones 2, 3, 4 and 5 is inversely proportional to the inter-zonal travel time. (a) Estimate the number of trips from zone 1 to zones 2, 3, 4 and 5 using the gravity model. (b) Assume that the future trip production from zone I will increase to 1,250 and the future trip attraction to zones 2, 3, 4 and 5 will increase to 100, 225, 100, and 600, respectively. Predict the number of trips from zone 1 to zones 2, 3, 4 and 5. The inter-zonal travel times remain the same. (c) Compare the number of trips from zone 1 to each destination zone between (a) and (b). Identify the…arrow_forwardAn origin-destination pair is connected by a route with a performance function tj = 8 + X1, and another with a function t2 = 1 + 2x2 (with x's in thousands of vehicles per hour and t's in minutes). If the total origin destination flow is 4000 veh/h, determine user equilibrium and system-optimal route travel times, total travel time (in vehicle- minutes), and route flows.arrow_forward
- A study showed that during the peak-hour commute on two routes connecting a suburb with a large city, there are a total of 5500 vehicles that make the trip. Route 1 is 7 miles long with a 65-mi/h speed limit and route 2 is 4 miles long with a speed limit of 50 mi/h. The study also found that the travel time on route 2 increases with the square of the number of vehicles, while the route 1 travel time increases two minutes for every 500 additional vehicles added. Determine the user-equilibrium travel time in minutes.arrow_forward8.5 If small express buses leave the origin described in Example 8.5 and all are filled to their capacity of 20 travelers, how many work-trip vehicles leave from origin to destination in Example 8.5 during the peak hour?arrow_forwardThree routes connect an origin to a destination with the following link performance functions: t_1 = 8 + 0.5 x_2 t_2 = 1 + 2x_2 t_3 = 3 + 0.75x_3 where t's in minutes and x's in thousands of vehicle per hour. If the peak-hour traffic demand is 4000 vehicles, determine the user equilibrium (UE) flows.arrow_forward
- Three routes connect an origin and destination with performance function tj = aj + bjxj/cj (with t's in minutes and x's in thousands of vehicles per hour). If the total origin-to-destination hourly demand is 10,000 vehicles, what is a travel time in minutes (input answer in a form 00,00 minutes). Route 1 Route 2 Route 3 a 13 8 9 b 1.9 2.5 2.1 6. 8 7arrow_forwardA certain single lane/on-ramp highway was estimated to have a utilization ratio of 0.893. The rate of arrival of vehicles follows a negative exponential distribution with an average of 296 vehicles per hour. If the service rate is also known to be stochastic, a.Compute the service rate in vehicles/hr. b.Compute the average waiting time at the stop sign per vehicle in seconds. c.Compute the average time spent in the system in seconds.arrow_forwardTwo routes are available to carry 1200 vehicles in peak-hour traffic. Route 1 has a posted speed limit of 45 mph and is 5 miles long. The travel time increases by 2x2, where x is vehicles in thousands. Route 2 has a limit of 55 mph and is 6.7 miles long, and the travel time increases by 1.5x. Find the user-equilibrium travel flow and travel time.arrow_forward
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