PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 15P
To determine
The system equilibrium, system optimal route travel time, total travel time and route flows.
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Students have asked these similar questions
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.
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
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.
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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Similar questions
- 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 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?arrow_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
- 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?arrow_forwardDetermine the share (proportion) of person-trips by each of two modes (private auto and mass transit) using the multinomial logit model and given the following informa- tion: Utility function: U = A - 0.05 T – 0.04 T, – 0.03 T, –0.014 C Parameter Private Auto Mass Transit = access time (min.) T. T = waiting time (min.) T, = riding time (min.) C = out-of-pocket cost (cents) Calibration constant, A 14 20 25 %3D 50 70 250 100 -0.012 -0.068arrow_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
- 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_forwardVehicles arrive at the parking booth of SM City Tarlac at a rate of 250 vehicles per hour. If the attendant can process a vehicle in 12 seconds, determine the average length of the queue if both the arrivals and departures are exponentially distributed. Note: Answer must be whole number. No need to include the unit. (i.e. 2)arrow_forwardGiven the utility function: U = AA- 0.35(TT) – 0.08(WT) – 0.005(C) Question 2 where AA is the mode specific variable; TT is the travel time in minutes; WT is the waiting time in minutes; and Cis the travel cost in cents. The attributes of trips between two traffic analysis zones are shown in the table below. Calculate the probability of car and bus. Variable Car Bus AA -0.46 -0.07 TT 20 30 WT 8 320 100arrow_forward
- 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_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_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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