PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 19P
To determine
The user equilibrium traffic flow.
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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
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?
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?
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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- Three 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_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_forwardAn origin-destination pair is connected by a route with a performance function t₁ = 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
- An 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_forwardExample: A busy travel corridor connecting a suburb with the city center is served by two routes having a typical travel time function, t =a + b(q/c), where t is the time in minutes, q is the vehicular flow in veh/hr, and c is the capacity of the route in veh/hr. The existing characteristics of the two routes is as follows: Route a b c 1 34 3000 2 4 2 4000 (a) If the existing peak-hour demand is 5000 veh/hr, what is the traffic distribution on the two routes? (b) If repair work on Route 1 reduces its capacity to 2000 veh/hr, what is likely to be the traffic distribution on the two routes for the duration of the repairs? (c) It is anticipated that after the repairs are completed on Route 1, its capacity will be 4200 veh/hr. How will this affect the distribution.arrow_forwardTwo 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_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_forward2. There are two routes in use between Zones 1 and 2. The volume-delay functions for the two routes are as follows: V1 V2 t1 = 22 + 250 t2 = 15 + 150 where t = travel time(minutes) V = traffic volume If the total traffic volume is 6,950 vehicles per hour between the two zones, what are the traffic volumes and travel times on each of the two routes at a user-equilibrium (UE) condition?arrow_forward8.21 Three routes connect an origin and destination with performance functions t₁ = 2 +0.5x₁,₂ = 1 + x2 and 13 = 4 + 0.2x, (with f's in minutes and x's in thousands of vehicles per hour). Determine user- equilibrium flows if the total origin-to-destination demand is (a) 5000 veh/h.arrow_forward
- 8.18 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_forwardThree routes connect an origin-destination pair with performance functions:t₁ = 20 +0.5x1t2 = 4+ 2x2t3=3+0.2x3with t in minutes and x in thousand vehicles per hour.(a) Determine the User Equilibrium flow on each route if q = 4000veh/h. (b) What is the minimum q (origin-destination demand) to ensure that all the three routes are used under user equilibrium? (c) Suppose that Route 1 is closed for repair. Find the system optimal flow on routes 2 and 3 and compute the total travel times.arrow_forwardThe performance function for a highway connecting a suburb with the business district can be represented by a straight line of the form t = a + bq, where t is the travel time in minutes, q is the traffic flow in vehicles per hour, and a and b are constants equal to 15 minutes and 0.01 minute/vehicle-hour, respectively. The demand function, also represented by a straight line, is q = c - dt, where c and d are constants equal to 6000 vehicles/hr and 150 vehicles/hour/minute, respectively. (a) Find the equilibrium flow (q*) and the corresponding equilibrium time (t*) algebraically, and sketch the functions. (b) If the length of this highway is 25 miles, what is the average speed of vehicles along this highway? (c) It is proposed to improve this highway such that constant b is now 0.005. What would be the new values of t* and q* and what would be the average speed on this highway?arrow_forward
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