8.15 An origin-destination pair is connected by aroute with a performance function t₁ = 8+ x1, andanother with a function t₂ = 1 + 2x2 (with x's inthousands of vehicles per hour and t's in minutes). Ifthe total origin-destination flow is 4000 veh/h,determine user-equilibrium and system-optimal routetravel times, total travel time (in vehicle minutes),and route flows.

If you want in compute the numerical solutions here is the solution.

Answered: 8.15 An origin-destination pair is…

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter6: Fundamental Principles Of Traffic Flow

Section: Chapter Questions

Problem 26P: The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to bePoisson...

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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.
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 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
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?

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