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 55P
To determine
The probability of waiting in queue.
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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.
At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute.
Estimate average waiting time of vehicles
Group of answer choices
0.35
0.65
0.45
0.55
Vehicles arrive at a toll bridge at a rate of 420 veh/h (the time between arrivals is exponentially distributed). Two toll booths are open and each can process arrivals (collect tolls) at a mean rate of 12 seconds per vehicle (the processing time is also exponentially distributed). What is the total time spent in the system by all vehicles in a 1-hour period?
Final Answer should be: 164.706 min
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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- 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?arrow_forwardVehicles arrive at a toll system at random at an average rate of 15 vehicles per minute. If there are 2 toll booths each at random at an average of 6 seconds after services are done for every vehicle at the toll system. Calculate the following: 5.1 Average length of queue of vehicles5.2. Average waiting time in a queue5.3. Average time spent in a queue5.4. If one toll ticket booth is closed and service time is reduced by 4 seconds, what are the system’s Q, W and T? And plot the arrival distribution curve for this traffic conditionarrow_forwardAfter 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_forward
- At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute.Estimate average time vehicles spent in the systemGroup of answer choices0.400.500.450.35arrow_forwardAt the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute. Estimate average length of queue formed at the toll gate Group of answer choices 7.09 8.09 9.09 6.09arrow_forwardAssume 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.arrow_forward
- Passenger cars arrive at the stop sign at an average rate of 280 per hour. Average departure time at the stop sign is 12 sec. If both arrivals and departure are exponentially distributed, what would be the average waiting time per vehicle in minutes? Answer in one-decimal place.arrow_forwardVehicles are known to arrive according to a Poisson process at a specific spot on a highway. Vehicles are tallied at 20-second intervals, with 150 of these intervals being 20-second 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. Please do 3 decimal places. Asaaparrow_forwardVehicles arrive at a toll system at random at an average rate of 15 vehicles per minute. If there are 2 toll booths each at random at an average of 6 seconds after services are done for every vehicle at the toll system. Calculate the following:1.1 Average length of queue of vehicles1.2. Average waiting time in a queue1.3. Average time spent in a queue1.4. If one toll ticket booth is closed and service time is reduced by 4 seconds, what are the queuing characteristics of the system? And plot the arrival distribution curve for this traffic conditionarrow_forward
- There are 10 vehicles in a queue when an attendant opens a toll booth. Vehicles arrive at the booth at a rate of 4 per minute. The attendant opens the booth and improves the service rate over time following the function μ(t) = 1.1 + 0.30t, where μ(t) is in vehicles per minute and t is in minutes. When will the queue clear, what is the total delay, and what is the maximum queue length? draw a figurearrow_forwardThe time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 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_forwardDrivers arrive at a toll booth at a rate of 5 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that it will take a) more one minute between consecutive drivers? b) between 30 seconds and 90 seconds between consecutive drivers?arrow_forward
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