PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 5, Problem 7P
To determine
The probability of the observer counting exactly
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5.7 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.
10.6 It is observed that on an average 240 vehicles
pass through a point on the highway in every
hour. Using Poisson distribution, compute the
probability of 1 vehicle arriving at a 30 sec time
interval.
Consider only a single lane of a highway. Based on extensive data from an urban freeway it is assumed thatfree-flow speeds (i.e., there are no jams) can best be represented by a Normal distribution with mean andstandard deviation 119 km/h and 13.1 km/h, respectively.1. What is the probability that the speed of a randomly selected vehicle is between 100 and 120 km/h?2. What is the expected number of vehicles between two vehicles that exceed the posted speed limit of100 Km/h?
You can use the Z table for calculating the final answer. You can also write your final answer in form ofR functions or as PDF/CDF of statistical distributions with correct arguments.
Chapter 5 Solutions
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
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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- Question 3: (a) A section of highway is known to have a free-flow speed of 95 km/h and a capacity of 3300 veh/h. Your summer student indicates that the average time in between passing vehicles was 1.6 seconds during an hour of monitoring. If the linear speed-density relationship applies, what was the space-mean speed of the vehicles during the hour of monitoring?arrow_forwardA major road intersection is traversed by vehicles at an average rate of (62.9) vehicles per hour. Find: a. Find the probability that none passes in 20 seconds. b. What is the expected number passing in three minutes? c. Find the probability that this expected number actually pass through in a given three-minute period.arrow_forwardAt time ? = 0, when the border inspection station was scheduled to open, eight vehicles were already waiting in a queue in front of an inspection booth. Vehicles continued to arrive at a rate of 4 veh/minute. The officer did not start the inspection until ? = 4 minutes. When ?≥4 minutes, the barrier was lifted and vehicles left at a rate of 7.5 veh/minute. Draw the vehicle arrival and departure curves in the following graph. From the graph, determine the maximum queue length and the time the queue disappears. Assume D/D/1 queuing.arrow_forward
- Traffic 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 number of traffic accident that occur on particular stretch of road during a month follows a Poisson distribution with a mean of 7. Find the probability of observing exactly three accidents on this stretch of road next month. H.W2/ In the entrance of car parking, the vehicle arrival in each counting period of 100 sec. is shown in table below, check whether the arrival distribution of vehicle can be assumed random or not. Vehicle per 100 sec. Frequency 0 60 1 28 2 16 3 8 24 0arrow_forwardTwo observers have determined that the time headways between successive vehicles are exponentially distributed and that 70% of the headways are 8s or greater. If one of observer decides to count traffic in 40s intervals, and the other in 35s intervals, estimate the probability of each observer counting 5 or more vehicles in their own intervals?arrow_forward
- 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)?arrow_forwardVehicles arriving at an intersection from one of the approach road follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds is.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
- Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicle per minute. The probability (round off to two decimal places) that at least 2 vehicles will arrive in any given 1-minute interval isarrow_forwardQ.47 An observer counts 240 veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probability of having one vehicle arriving over a 30- second time interval isarrow_forwardVehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds isarrow_forward
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