=Assume an origin is connected to a destination with two routes. Assume the travel time of eachroute has a linear relationship with the traffic flow on the route (t₁ = α₁ + b₁×₁ ; t₂b2x2). Determine under what condition (e.g. a relationship among the parameters of theperformance functions) tolling cannot reduce the total travel time of the two routes.a2+

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Answered: = Assume an origin is connected to a…

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter2: Transportation Systems And Organizations

Section: Chapter Questions

Problem 4P

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8.19 Three routes connect an origin and a destination with performance functions t₁ = 8+ 0.5x1, t2 = 1 + 2x2, and t3 = 3 + 0.75x3, with the x's expressed in thousands of vehicles per hour and the 's expressed in minutes. If the peak-hour traffic demand is 3400 vehicles, determine user-equilibrium traffic flows.
Consider the following static route choice problem where 110 vehicles travel from point A to point B. The corresponding travel time (in minutes) of each link is as follows: t₁ = x1; t₂ = x2 + 20; t3 = x3 + 10; t₁ = 3x4 where x; denotes the number of vehicles that choose link i. Find the number of vehicles that travel on each link when a. The user equilibrium condition (UE) is satisfied, where vehicles select the route with the minimum travel time; and b. The system optimum condition (SO) is satisfied, where the total travel time is minimised. C. Report the total delay savings when satisfying SO instead of UE. 2 A B 3 4
8.15 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.
8.20 Two routes connect a suburban area and a city, with route travel times (in minutes) given by the expressions t₁ = 6 + 8(x₁/c₁) and t₂ = 10 + 3(x2/c2), where the x's are expressed in thousands of vehicles per hour and the c's are the route capacities in thousands of vehicles per hour. Initially, the capacities of routes 1 and 2 are 4000 and 2000 veh/h, respectively. A reconstruction project on route 1 reduces the capacity to 3000 veh/h, but total traffic demand is unaffected. Observational studies note a 35.28-second increase in average travel time on route 1 and a 68.5% increase in flow on route 2 after reconstruction begins. User-equilibrium conditions exist before and during reconstruction. If both routes are always used, determine equilibrium flows and travel times before and after reconstruction begins.
The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to bePoisson with a mean of 30 mi/h. It takes an average of 1.5 min for the necessary tickets to be bought for occupants of each car. (a) What is the expected length of queue at the ticket gate, not including the vehicle being served? (b) What is the probability that there are no more than 5 cars at the gate, including the vehicle being served? (c) What will be the average waiting time of a vehicle?
The Jeffersonville Transportation Study area has been divided into four traffic zones. The following data have been compiled. Travel Time (min) District Productions Attractions 1 2 3 4 1 3,000 3,000 5 8 12 15 2 1,000 400 8 5 10 8 3 2,000 4,500 12 10 5 7 4 2,500 600 15 8 7 5 Travel Time 1 5 6 7 8 10 12 15 Fij 2.00 1.30 1.10 1.00 0.95 0.85 0.80 0.65 After the first iteration, the trip table was as follows. District 1 2 3 4 Ps 1 1,415 138 2 367 67 1,306 141 493 73 3 522 4 641 74 125 As 2,945 404 1,478 256 4,550 601 3,000 1,000 1,273 131 2,000 2,500 Complete the second iteration. District 1 2 3 4 Computed A 1 2 3 4 Computed P

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