At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour. What is the probability of observing at least 2 vehicles in 30 minutes?
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- A volume of 320 veh/h. Assume that the vehicle arrivals are Poisson distributed. What is the probability that the headway between successive vehicles more than 20 seconds? 18.20% 20.40% 14.60% 16.90%Assume vehicle arrivals are random. On average, six vehicles arrive in one minute. Calculate theprobability of observing less than three vehicles over three minutes. Calculate the probability ofobserving a headway of less than eight seconds.Two 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?
- TRAVEL TIME AND DELAY STUDIES • The shows data obtained in a travel time study on a section of highway using the moving-vehicle technique. Estimate (a) the travel time and (b) the volume in each direction at this section of the highway Run Direction/ Number Northward 2 4 5 6 7 8 9 10 Southward 3 4 6 7 8 9 10 No. of Vehicles Travel Traveling in Time Opposite Direction (min) 5.25 5.08 5.30 5.15 5.00 5.51 5.38 5.41 5.12 5.31 4.95 4.85 5.00 4.91 4.63 5.11 4.83 4.91 4.95 4.83 100 105 103 110 101 98 97 112 109 107 85 88 95 100 102 90 95 96 98 90 PARKING STUDIES No. of Vehicles That Overtook Test Vehicle 3 1 0 1 3 0 1 0 0 2 1 1 No. of Vehicles Overtaken by Test Vehicle 2 1 1 0 3 1 0 1 2 PROB 1. Data collected at a parking lot indicate that a total of 300 cars park between 8 a.m. and 6 p.m. 10% of these cars are parked for an average of 2 hr, 30% for an average of 4 hr, and the remaining cars are parked for an average of 10 hr. Determine the space-hours of demand at the lot PROB 2. If 10% of…Vehicles 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?At 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.
- At a specified point on a highway, vehicles are known to arrive according to a Poissonprocess. Vehicles are counted in 30-second intervals, and vehicle counts are taken in 120 ofthese time intervals. It is noted that no cars arrive in 18 of these 120 intervals. a) Approximate the number of these 120 intervals in which exactly three cars arrive. b) Estimate the Percentage of time headways that will be 10 seconds or greater andthose that will be less than 6 seconds.Vehicles 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.Data on a traffic accident recorded on a certain intersection for the past 7 years has an accident rate of 4288 per million entering vehicles (ARMV). If the average daily traffic entering the intersection is 492, find the total number of accidents during the 7-year period a.5390 b.5388 c.5391 d.5389
- A volume of 320 veh/h. Assume that the vehicle arrivals are Poisson distributed. What is the probability that the headway between successive vehicles will be less than 10 seconds. choices: 62.70%, 58.90%, 56.30%, 60.00%Given that the value of a segment of roadway is 720 vehicle/hr, where the arrival of vehicles is a Poisson distribution. Calculate the following: 1. No. of headways if it is less than 5 seconds 2. No. of headways if it is more than 5 seconds 3. Plot the probability curves of the 2 conditions stated aboveAn 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%