PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 30P
To determine
The user equilibrium route flows and total vehicle travel time,
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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?
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?
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.
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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- An 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_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_forwardThree 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_forward
- 2. 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_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_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
- A 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_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
- Vehicles arrive at a toll bridge at a rate of 420 veh/h (the time between arrivals is exponentially distributed). Two toll booths are open and each can process arrivals (collect tolls) at a mean rate of 12 seconds per vehicle (the processing time is also exponentially distributed). What is the total time spent in the system by all vehicles in a 1-hour period? Final Answer should be: 164.706 minarrow_forwardThe average queue length at the intersection of the two roads with a stop signs is 4 vehicles. If the arrival rate of vehicles at the stop sign is 300 vehicles per hour, determine the service rate of the road in vehicles per hour. Assume both arrival and departure rates are exponentially distributed.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_forward
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