PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 29P
To determine
The user equilibrium flows for the given condition.
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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?
Suppose that the projected road vehicle traffic flow in a corridor is 5000 vehicle-trips per hour
in one direction. The average perceived user cost functions of the two major highways (Route
1 and Route 2 in the corridor are as follows (in dollars):
Route 1: Ci =1 +8(qı/5000)
Route 2: C2 = 1+10(q2/2500)
Where: qi and q2 are the traffic flows on Route 1 and Route 2 respectively.
Calculate the volume of traffic during the peak hour on each route, if users were free to
choose their own routes.
3. Three routes connect an origin-destination pair with performance functions:
ti=20 +0.51
t₂ = 4+2x2
tε = 3 +0.2x²
with t in minutes and r 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.
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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- Example: 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_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_forwardTwo routes connect an origin and destination with performance function t; = aj + (xj/cj)2 (with t's in minutes and x's in thousands of vehicles per hour). It is known that at user equilibrium, 65% of the origin-destination demand takes route 1. How many vehicles (in thousands) will take route 1 if system optimal equilibrium is archived? Route 1 Route 2 a 7 2 3arrow_forward
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