1(a) 3 One lane of a highway is carrying 540 vehicles per hour. Assuming that vehicle arrival rates at any point along the lane follow a Poisson distribution, determine the number hour travelling along that lane at of vehicles per headway of 4 seconds or More?
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- road construction The 20-year projection of annual average daily traffic of a two-way roadway is 36.500 vehicles. Theroad serves as a highway between a residential area and a business area and the expected directionaldistribution factor is D=0.6. The 30th peak hour factor for the roadway is K=0.15. During an hourly vehiclecount, the following values were registered: 1st 15 minutes: 200 cars, 2nd 15 minutes: 130 cars, 3rd 15minute 230 cars, 4th 15 minutes. 180 cars. Estimate the peak hour factor . What is the designdirectional hourly volume for this route?Problem 1. 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 secondsAt 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.
- 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.. A traffic enforcer counts the number of vehicles at a specific location in the highway. In hiscounting, there are 420 vehicles arrived in span of 1 hour. Assuming that the arrival of vehicles isPoisson distributed, estimate the probabilities of having 7 or more vehicles arriving over a 30-secondtime intervalA 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%
- From the following data of a freeway surveillance, there are 4 vehicles counted for a length of 200 m and the following distances each had travelled when observed on the photographs taken every 3 seconds apart. Compute the following:i. Density of flow in vehicles per km (vpk). ii. Space mean speed in kph. iii. Flow rate, in vehicles per hour. SHOW COMPLETE SOLUTION. NEED ASAP. THNAK YOUVehicles arrive according to a Poisson process (random arrival) to a parking lotwith mean arrival rate of 3 vehicles/min, and are processed (they pay parking fee) at a Poisson process(random Departure) rate of 240 vehicles/hour.(1) What type of queuing is this problem?D/D/1 M/D/1 M/M/1(2) What is the traffic intensity?(3) Determine (I) the average waiting time and (II) the average length of the queThe average queue length at the intersection of the two roads with a stop signs is 4 vehicles. If the arrival rate of vehicles at the stop sign is 300 vehicles per hour, determine the service rate of the road in vehicles per hour. Assume both arrival and departure rates are exponentially distributed.
- On an expressway, it was recorded that there is an average of 22 vehicles that are passing the said portion of the highway in every minute. Evaluate the value of the flow of traffic on that day in veh/hr.What is the probability that the headway between successive vehicles will be between 7 and11seconds if there is an average of 6 cars that passes the segment of the highway every minute?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?