PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 28P
To determine
Whether user-equilibrium and system-optimal solution can be equal at some feasible value.
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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
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b
1.9
2.5
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6.
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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
Two 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
3
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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- 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.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_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
- 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_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
- Vehicles 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_forwardA simple work-mode-choice model is estimated from data in a small urban area to determine the probabilities of individual travelers selecting various modes. The mode choices include automobile drive-alone (DL), automobile shared-ride (SR), and bus (B), and the utility functions are estimated as: UDL = 2.2-0.2(costp)-0.03(travel timepz) USR 0.8 – 0.2(costsR) – 0.03(travel timesR) Us = -0.2(costa)- 0.01(travel time,) where cost is in dollars and time is in minutes. Between a residential area and an industrial complex, 4000 workers (generating vehicle-based trips) depart for work during the peak hour. For all workers, the cost of driving an automobile is $6.00 with a travel time of 20 minutes, and the bus fare is $1.00 with a travel time of 25 minutes. If the shared-ride option always consists of two travelers sharing costs equally, how many workers will take each mode?arrow_forwardA work-mode-choice model is developed from data acquired in the field in order to determine the probabilities of individual travelers selecting various modes. The mode choices include automobile drive alone (DL), automobile shared-ride(SR), and bus (B). The utility functions are estimated as: UDL = 2.6 – 0.3(costDL) – 0.02(travel time DL) USR = 0.7 – 0.3(costSR) – 0.04(travel time SR) UB = –0.3(costB) – 0.01(travel time B) where cost is in dollars and time is in minutes. The cost of driving an automobile is $5.50 with a travel time of 21 minutes, while the bus fare is $1.25 with a travel time of 27 minutes. How many people will use the shared-ride mode from a community of 4500 workers, assuming the shared-ride option always consists of three individuals sharing costs equally?arrow_forward
- A toll bridge carries 10,000 veh/day. The current toll is $3.00/vehicle. Studies have shown that for each increase in toll of 50 cents, the traffic volume will decrease by 1000 veh/day. It is desired to increase the toll to a point where revenue will be maximized. Let V be the Volume X be the increase in toll charge (a) Write the expression for travel demand on the bridge related to toll increase and current volume. (b) Determine the increase in toll charge (c) Determine the new toll charge to maximize revenues. (d) Determine traffic in veh/day after toll increase. (e) Determine total revenue increase with new toll.arrow_forward3. 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.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_forward
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