(a)
The expression for travel demand on the bridge related to toll increase and current volume.
Answer to Problem 4P
The expression for travel demand on the bridge related to toll increase and current volume is
Explanation of Solution
Given:
A toll bridge carries
The current toll is
For each increase in toll of
Concept used:
Write the relation between traffic volume and cost.
Here,
Calculations:
Substitute
Conclusion:
Therefore, the expression for travel demand on the bridge related to toll increase and current volume is
(b)
The toll charge to maximize revenue.
Answer to Problem 4P
The toll charge to maximize the revenue is
Explanation of Solution
Write the expression to calculate the total toll charge.
Here,
Write the expression to calculate the revenue generated.
Here,
Calculations:
Calculate the total toll charge.
Substitute
Calculate volume of traffic expected for a 50 cent increase.
Substitute
For maximum value, calculate the first derivative of above equation and equate to zero.
Substitute
Conclusion:
Therefore, the toll charge to maximize revenue is
(c)
The traffic volume after toll increase.
Answer to Problem 4P
The traffic volume after toll increase is
Explanation of Solution
Calculations:
Calculate the traffic volume after toll increase.
Consider the expression for travel demand on the bridge related to toll increase and current volume.
Substitute
Conclusion:
Therefore, the traffic volume after toll increase is
(d)
The total revenue increase with new toll.
Answer to Problem 4P
The total revenue increase with new toll is
Explanation of Solution
Calculations:
Substitute
Conclusion:
Therefore, the total revenue increase with new toll is
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Chapter 2 Solutions
EBK TRAFFIC AND HIGHWAY ENGINEERING
- The demand and supply function for a bridge are the following where C is cost in cents and V is volume in veh / h . Demand V = 1500 - 10C Supply or cost function: C = 120 + 0.5V (a) What is the equilibrium volume of traffic and the associated cost? (b) 20 cents of toll is added to the cost function, what will be the new cost function and the equilibrium volume?arrow_forwardA city engineer has estimated the annual toll revenues from a proposed highway construction project over 20 years as follows: An = ($2,000,000)(n)(l.06)n-1 n = 1.2 .... ,20.To determine the amount of debt financing through bonds, the engineer was asked to present the estimated total present value of toll revenue at an interest rate of 6%. Assuming annual compounding, find the present value of the estimated toll revenue.arrow_forwardAn existing toll road has an average traffic volume around 6,000 vehicles per day. A project is proposed to widen the toll road to increase the road capacity. It is projected that the traffic volume would increase to 10,000 vehicles if the toll rate is reduced from $5 to $4 per vehicle. Assume that the toll rate is the only factor affecting the traffic volume on the toll road. a) Determine the impact of the toll change on consumer surplus. b) Calculate the point elasticity of demand for the toll road. c) Calculate the arc elasticity of demand for the toll road.arrow_forward
- A bridge has been constructed between the mainland and an island. The total cost (excludingtolls) to travel across the bridge is expressed as C = 50 + 0.5V, where V is the number ofveh/hr and C is the cost/veh in pesos. The demand for travel across the bridge is V = 2500 −10C.a. Determine the volume of traffic across the bridge.b. If a toll of 25 pesos is added, what is the volume across the bridge?c. A tollbooth is to be added, thus reducing the travel time to cross the bridge. The new costfunction is C = 50 + 0.2V. Determine the volume of traffic that would cross the bridge.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_forwardNote: Read the question carefully and give me BOTH right solutions with clear calculations. Vehicles begin to arrive at a toll booth at 5 vehicles per minute from 7 AM to 8 AM. The booth opens at 7:15 AM and services at a rate of 3 vehicles per minute until 7:45 AM. From 7:45 AM until 8 AM the service rate is 6 vehicles per minute. Assuming D/D/1 queuing, (A) have all vehicles that arrived between 7AM and 8AM exited the queue? and (B) what is the total vehicle delay while the queue exists?arrow_forward
- [T] The following table provides hypothetical data regarding the level of service for a certain highway. Plot vehicles per hour per lane on the x-axis and highway speed on the y-axis. Compute the average decrease in speed (in miles per hour) per unit increase in congestion (vehicles per hour per lane) as the latter increases from 600 to 1000, from 1000 to 1500, and from 1500 to 2100. Does the decrease in miles per hour depend linearly on the increase in vehicles per hour per lane? Plot minutes per mile (60 times the reciprocal of miles per hour) as a function of vehicles per hour per lane. Is this function linear? Highway Speed Vehicles per Hour per Lane Density Range (vehicles / mi) > 60 < 600 < 10 60 - 57 600 - 1000 10 - 20 57 - 54 1000 - 1500 20 - 30 54 - 46 1500 - 1900 30 - 45 46 - 30 1900 - 2100 45 - 70 < 30 Unstable 70 - 200arrow_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_forwardDuring morning peak hour, the passenger demand is 600. Assume that passenger demand is evenly distributed within that period and the average load/occupancy is 50 passengers per bus. Calculate the average headway of a city buses? If the passenger demand increases to be 750, calculate the number of bus units need to be added and the headway shorten?arrow_forward
- Vehicles arrive at a toll system at random at an average rate of 15 vehicles per minute. If there are 2 toll booths each at random at an average of 6 seconds after services are done for every vehicle at the toll system. Calculate the following:1.1 Average length of queue of vehicles1.2. Average waiting time in a queue1.3. Average time spent in a queue1.4. If one toll ticket booth is closed and service time is reduced by 4 seconds, what are the queuing characteristics of the system? And plot the arrival distribution curve for this traffic conditionarrow_forward(show your solutions) Compute for the Total Remaining Traffic * A.15,858 vehicles B.15,743 vehicles C.15,862 vehicles D.15,750 vehicles E.None of the abovearrow_forwardAfter 10 years, the public transportation remain unimproved. The modal split will also remain unchanged with 70% of person-trips utilize Public Transportation during peak period. After 10 years, the person-trip demand will increase from 450 to 675. If the overall capacity of the Public Transportation during peak period can carry up to 450 person-trips, the demand / PT supply capacity ratio is _______ (answer shall be in 2 demical places)arrow_forward
- Traffic and Highway EngineeringCivil EngineeringISBN:9781305156241Author:Garber, Nicholas J.Publisher:Cengage Learning