nn (1) shows the number of vehicles overtaken by the te the number overtaking the test vehicle, (3) shows the numb ng against traffic stream, (4) is the travel time with the traffic: ravel time against the traffic (s). Assuming linear speed-de is the maximum flow, speed, and density the following fol ake. Show the details of the calculation.
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- 7) In studying of traffic flow at a highway toll booth over a course of 60 minutes, it is determined that the arrival and departure rates are deterministic, but not uniform. The arrival rate is found to vary according to the function A(t) = 1.8+0.25t - 0.00312. The departure rate function is u(t) = 1.4 +0 .1lt. In both of these functions, t is in minutes after the beginning of the observation and (t) and „u(t) are in vehicles per minute. At what time does the maximum queue length occur? a) 49.4 min, b) 2.7 min ,c) 19.4 min, d) 60.0 minQuestion 1 In studying traffic flow at a highway toll booth over a course of 60 minutes, it is determined that the arrival and departure rates are deterministic, but not uniform. The arrival rate is found to vary according to the function of A (t) = 1.8 2 +0.25t -0.0030t. The departure rate function is u(t) =1.4 + 0.11 t. In both of these functions, t is in minutes after the beginning of the observation and X(t) and u(t) are in vehicles per minutes. (i) When will the queue that forms be cleared? (ii) What time does the maximum queue length occur and what will be the corresponding queue length? (iii) Determine the total delay (iv) Estimate the average time delay per vehicleThe average speed of vehicles on an expressway is being studied. a. Suppose observation on 50 vehicles yielded a sample mean of 65 km/hr. Assume that the standard deviation of vehicle speed is known to be 6 km/hr. Determine the two-sided 99% confidence intervals of the mean speed. b. In part (a), how many additional vehicles' speed should be observed such that the mean speed can be estimated to within + 1 km/hr with 99% confidence? C. Suppose John and Mary are assigned to collect data on the speed of vehicles on this expressway. After each person has separately observed 10 vehicles, what is the probability that John's sample mean will exceed Mary's sample mean by 2 km/hr? d. Repeat part (c) if each person has separately observed 100 vehicles instead?
- 1. Assume you are observing traffic in a single lane of a highway at a specific location. You measure the average headway and average spacing of passing vehicles as 3 seconds and 150ft, respectively. What is the average speed of the traffic stream? Note: you can use two methods to conduct the calculation. 2. Assume the speed and density at a freeway location follows a linear relationship. You observe traffic flow rate of 2250 vehicles/hour at 45 mph and 3000 vehicles/hour at 30 mph. What are the jam density, free flow speed (max speed), and capacity of this freeway location? How about the density and speed (i.e., the critical density and the critical speed) at the capacity?A car is stopped at an entrance ramp to a freeway; its driver is preparing to merge. At a certain moment while stopped, this driver observes a platoon of vehicles a distance x0 upstream and initiates the merge maneuver. The platoon approaches the entrance ramp at a constant speed v. The stopped car can accelerate from speed 0 to v at uniform acceleration rate a. Find the latest time at which the stopped car can safely start the merge maneuver; i.e., derive an expression for the “latest safe start time” in terms of the variables x0, v and a. Assume this latest time enables the platoon to maintain its constant speed and "just touch" the merging car's trajectory. Ignore the physical dimensions of the car.A vehicle moving at a speed of 50 mph is slowing traffic on a two-lane highway. What passing sightdistance is necessary, in order for a passing maneuver to be carried out safely? Calculate the passingsight distance. In your calculations, assume that the following variables have the values given: Passing vehicle driver's perception/reaction time = 2.5 sec Passing vehicle's acceleration rate = 1.47 mph/sec Initial speed of passing vehicle = 50 mph Passing speed of passing vehicle = 60 mph Speed of slow vehicle = 50 mph Speed of opposing vehicle = 60 mph Length of passing vehicle = 22 ft Length of slow vehicle = 22 ft Clearance distance between passing and slow vehicles at lane change = 20 ft Clearance distance between passing and slow vehicles at lane re-entry = 20 ft Clearance distance between passing and opposing vehicles at lane re-entry = 250 ft
- Two cars P and Q are moving in a racing track continuously for two hour. Assume that no other vehicles are using the track during this time. The expressions relating the distance travelled d (in km) and time t (in hour) for both the vehicles are given as P: d = 60t Q: d = 60t² Within the first one hour, the maximum space headway would beThe gap between 2 consecutive automobiles is 25 meters. At a certain time the front vehicle is traveling at 85 kph and the following vehicle at 60 kph. If both vehicles start accelerating at the same time, determine the gap between two vehicles after 21 seconds if the acceleration of the vehicles can be assumed to take the following forms: du / dt = 1.04 – 0.080ut (leading vehicle) du / dt = 1.03 - 0.075ut ( following vehicle)Assume that the speed-density function of a section of a highway follows the Greenshields model. The free-flow speed is 75 mph and the jam density is 176 veh/mi/In. Derive V as a function of S. In 15 minutes, you have counted that V = 150 veh/15-minute/In. Estimate the two possible speeds S (in mph) during this 15-minute period.
- (b) Consider a stop-controlled intersection between a major and a minor street shown in the figure below. Traffic on the major street is arriving in a random manner (Poisson distributed vehicle arrivals) and passes through the intersection unimpeded, without having to stop. Traffic on the minor street must wait at the stop sign and can enter the major street only when there is a minimum headway tm = 2.5 seconds (gap) in the major street. Suppose that the flow rate on the major street is Q= 200 vehicles per hour, and only one vehicle can enter the major street during each acceptable gap. Estimate the maximum number of vehicles per hour that can be accepted to the major street (which is also the capacity) of the minor street approach. Major Street Minor StreetFor a national highway, the free mean velocity and jam density are 80 kmph and 45 Veh/km respectively. A student mistakenly takes the quadratic relation between the velocity and traffic density in Green-Shield model as shown below: V = All the symbols have the usual meaning. Find the magnitude of error in maximum capacity of the road in Veh/hr (upto two places after decimal)F] Vehicles travel at constant speeds on a one-lane one-way street between sections X and Y. An observer located at point X observes the four vehicles passing point X during a period of 10 seconds. The speeds of the vehicles are measured as 45, 45, 40, and 30mph, respectively. Calculate the average flow, density, time mean speed, and space mean speed.