Principles of Highway Engineering and Traffic Analysi (NEW!!)
6th Edition
ISBN: 9781119305026
Author: Fred L. Mannering, Scott S. Washburn
Publisher: WILEY
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Chapter 5, Problem 7P
To determine
The probability of the observer counting exactly
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An observer has determined that the time headways between successive vehicles on a section of highway are exponentially distributed and that 65% of the headways between vehicles are 9 seconds or greater. If the observer decides to count traffic in 30-second time intervals, estimate the probability of the observer counting exactly four vehicles in an interval.
At a specified point on a highway, vehicles are known to arrive according to a Poisson process. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. It is noted that no cars arrive in 18 of these 120 intervals. Approximate the number of these 120 intervals in which exactly three cars arrive.
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds.
A. What is the probability that the arrival time between vehicles is 12 seconds or less (to 4 decimals)?
B. What is the probability that the arrival time between vehicles is 6 seconds or less (to 4 decimals)?
C. What is the probability of 30 or more seconds between vehicle arrivals (to 4 decimals)?
Chapter 5 Solutions
Principles of Highway Engineering and Traffic Analysi (NEW!!)
Ch. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10P
Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - The arrival rate at a parking lot is 6 veh/min....Ch. 5 - Prob. 16PCh. 5 - At the end of a sporting event, vehicles begin...Ch. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Vehicles begin arriving at a single toll-road...Ch. 5 - Vehicles begin to arrive at a toll booth at 8:50...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Vehicles begin to arrive at a parking lot at 6:00...Ch. 5 - At a parking lot, vehicles arrive according to a...Ch. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Vehicles arrive at a recreational park booth at a...Ch. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - A truck weighing station has a single scale. The...Ch. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Vehicles leave an airport parking facility (arrive...Ch. 5 - Vehicles begin to arrive at a parking lot at 7:45...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - A theme park has a single entrance gate where...Ch. 5 - Prob. 54PCh. 5 - Prob. 55P
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- Vehicle time headways and spacings were measured at a point along a highway, from a single-lane rural roadway, over the course of an hour. The average values were calculated as 2.5 seconds per vehicles for headway and 200 feet per vehicle for spacing. What is the density, in vehicle per mile?arrow_forward1. Vehicles are known to arrive according to a poisson process at a specific spot on a highway. Vehicles are tallied at 20-seconds interval, with 150 of these intervals be in 20 seconds intervals. In 20 of the 150 periods, no automobiles have arrived. Estimate the number of these 150 intervals in which four automobiles arrive at the same time.arrow_forwardVehicles are known to arrive according to a Poisson Equation at a specific spot on a highway. Vehicles are recorded at 25-second intervals, with 250 of these intervals being 25-second intervals. In 25 of the 250 periods, 3 automobiles have arrived. Estimate the number of these 250 intervals in which four automobiles arrive at the same time. solve and show your complete solution please.arrow_forward
- An observer counts 360 veh/h at a specific highway location. Assuming that the arrival of vehicles at this highway location is Poisson distributed, estimate the probabilities of having at least 5 vehicles arriving over a 25-second time interval. choices: 8.57%, 10.88%, 4.20%, 6.89%arrow_forwardTraffic data are collected in 60-second intervals at a specific highway location as shown in the Table. Assuming the traffic arrivals are Poisson distributed and continue at the same rate as that observed in the 15 time periods shown, what is the probability that six or more vehicles will arrive in each of the next three 60-second time intervals (12:15 P.M. to 12:16 P.M., 12:16 P.M. to 12:17 P.M., and 12:17 P.M. to 12:18 P.M.)?arrow_forwardThe time between arrivals of vehicles at particular intersection follows an exponential probability distribution with a mean of 15 seconds. What is the probability that the arrival time between vehicles is 9 seconds or less?arrow_forward
- An observer counts 360 veh/h at a specific highway location. Assuming that the arrival of vehicles at this highway location is Poisson distributed, estimate the probabilities of having at most 3 vehicles arriving over a 20-second time interval . choices: 74.29%, 85.71%, 93.23%, 67.66%arrow_forwardThe arrival of vehicles at a specified roadway location is Poisson distributed. The flow count shows 540 veh/hr at this roadway location. - What is the probability that headway between successive vehicles will be less than 6 seconds? - What is the probability that headway between successive vehicles will be greater than than 12 seconds? - What is the probability that headway between successive vehicles will be between 6 and 12 seconds? - Draw the probability density function of the exponential distribution and show the key items in the graph. - Draw the cumulative distribution of the exponential distribution and show the key items in the graph.arrow_forwardVehicles arrive at an intersection at a rate of 400 veh/h according to a Poisson distribution. What is the probability that more than five vehicles will arrive in a one-minute interval? Answer in three-decimal places.arrow_forward
- After observing arrivals and departures at a highway toll booth over a 60-minute time period, an observer notes that the arrival and departure rates (or service rates) are deterministic, but instead of being uniform, they change over time according to a known function. The arrival rate is given by the function, ?(?) = 2.2 + 0.17? − 0.0032?^2, and the departure rate is given by ?(?) = 1.2 + 0.07?, where t is in minutes after the beginning of the observation period and ?(?) and ?(?) are in vehicles per minute. Determine the total vehicle delay at the toll booth and the longest queue, assuming D/D/1 queuing.arrow_forwardVehicles arrive at an intersection at a rate of 450 veh/h according to a Poisson distribution. What is the probability that 3 or more vehicles will arrive in two successive 30-second interval?arrow_forwardA vehicle pulls out onto a single-lane highway that has a flow rate of 300 veh/h (Poisson distributed). The driver of the vehicle does not look for oncoming traffic. Road conditions and vehicle speeds on the highway are such that it takes 1.7 seconds for an oncoming vehicle to stop once the brakes are applied. Assuming a standard driver reaction time of 2.5 seconds, what is the probability that the vehicle pulling out will get in an accident with oncoming traffic?arrow_forward
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