PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 20P
To determine
The equilibrium flow and travel time before and after reconstruction begins.
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Two routes connect an origin-destination pair with performance functions t₁ = 5 + (x₁/2)² and t₂ = 7+ (x2/4)² (with t's in minutes and x's in thousands of vehicles per hour). It is known that at user equilibrium, 75% of the origin-destination demand takes route 1. What percentage would take route 1 if a system-optimal solution were achieved, and how much travel time would be saved?
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
7
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.
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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- 4. Two busses start at the same time towards each other from terminals A and B, 8 km apart. The time needed for the bus to travel A to B is 8 minutes, and of the second bus from B to A is 10 minutes. How much is the time needed by each bus to meet each if they travelled at their respective uniform speeds?arrow_forward8.25 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?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_forward
- A bus line has stops at every intersection, 200 m apart. The speed of traffic and of the buses except for their stopping at bus stops is 30 km/h, but for every stopping, busses lose a total of ts = 20 seconds. Passengers are uniformly distributed along the line and walk to/from its stops at a speed of Vw = 4.8 km/h. How would a passenger’s travel total time , including access to/from stops and travel on buses, change if every other stop was abandoned, i.e., the spacing between stops was increased from 200 m to 400 m, if the average trip length on the line is(a) 4 km; (b) 6 km; (c) 8 km? For what passenger trip length Lp will the total travel time remain the same?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_forwardhree 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 conditionarrow_forward
- to 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_forward8.18 Two routes connect an origin and a destination. Routes 1 and 2 have performance functions t₁ = 2 + x₁ and t₂ = 1 + x2, where the 's are in minutes and the x's are in thousands of vehicles per hour. The travel times on the routes are known to be in user equilibrium. If an observation for route 1 finds that the gaps between 30% of the vehicles are less than 6 seconds, estimate the volume and average travel times for the two routes. (Hint: Assume a Poisson distribution of vehicle arrivals, as discussed in Chapter 5.)arrow_forwardA bus route has stops at every intersection, 200 m apart. The speed of traffic and of the buses except for their stopping at bus stops is 30 km/h, but for every stop, buses lose a total of ts=20 seconds. Passengers are uniformly distributed along the route and walk to/from its stops at a speed of Vw= 4.8 km/h. a. How would a passenger's total travel time (consider only access to stops and travel on buses) change if every other stop was abandoned (i.e., the spacing between stops was increased from 200 m to 400 meters, if the average trip length on the line is: i) 4 km; ii) 6 km; and iii) 8 km? b. For what passenger trip length Lp will the total travel time remain the same?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_forwardThe total number of trips from ABC to XYC is 4500. All of the trips are made using car. The government proposed two alternatives, a train and a bus. The utility is given by the equation: U = -0.05(TT)-0.04(WT) - 0.07(W) - 0.2(F) - 0.2(P) TT in-vehicle travel time WT- walking time to terminal W-waiting time F-fare P-parking cost The travel time for private car is 20 minutes, 12 for bus and 10 for train. Walking time for different terminals for bus and train is 10 and 15 minutes respectively. The waiting time is 8 and 6 minutes for bus and train respectively, and the fare for car, bus and train is at $20, $8.5 and $7 dollars respectively. Parking cost for car is $3. What is the total number of trips by train?arrow_forwardProblem: There are 2 routes connecting two cities. The total demand is 1000 veh/hr. The first route has travel time function as t₁ = 10 + 0.03.V₁ and the second route as t₂ = 12 +0.05.V₂, where V₂ and V₂ are traffic volume on route 1 and 2. Note that V₁ + V₂= 1000 veh/hr. Use incremental all-or-nothing assignment with p₁ = 0.4, p2 = 0.3, p = 0.2 and P4 = 0.1 to determine the route traffic flows.arrow_forward
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