PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 5, Problem 29P
To determine
The average length of the queue, the average time spent in the traffic and the average waiting time in the queue.
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2.) Queuing Theory:
At a single toll booth, you were able to observe an average vehicle arrival rate of 10 vehicles per minute starting from 7:00 AM. 30 minutes later, average vehicle arrival rate has become 4 vehicles per minute and continues throughout the day at that rate. If the toll booth is able to process one vehicle every 10 seconds, how many minutes after 7:00 AM will the first queue clear up? What is the longest queue length, expressed in number of vehicles? Assume a D/D/1 queuing model.
At exactly 8:00 AM, vehicles start to enter a single toll gate at a rate of 8 veh/min following a deterministic distribution. Due to the teller being late, the toll booth opened at 8:10 AM having a service rate of 10 veh/min following a deterministic distribution. What is the Maximum Queue Length in the system?
o 70 vehicles
o 90 vehicles
o 80 vehicles
o 60 vehicles
At 10 am, vehicles arrive at a toll booth facility at the rate of 480vehicles/hour. Initially, the toll booth is closed from 10:00 am until 10:15 am. Then it opens from 10:15with a service rate of 6 seconds per vehicle. Assuming D/D/1 queuing, determine:(1) At what time queue disappears? (2) What is the total delay? (3) What is the maximum Queuelength? (4) What is the queue length at 10:00 am? (5) What is maximum delay? (6) What is thedelay for the 140th and 170th vehicle?
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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- At 9 am, vehicles arrive at a toll booth facility at the rate of 480 vehicles/hour. Initially, the toll booth is closed from 9:00 am until 9:15 am. Then it opens from 9:15 with a service rate of 600 vehicles/hour. Assuming D/D/1 queuing, determine: (1) At what time queue disappears? (2) What is the total delay? (3) What is the maximum Queue length? (4) What is the queue length at 10:00 am? (5) What is maximum delay? (6) What is the delay for 160th vehicle?arrow_forwardVehicles arrive at a toll system at random at an average rate of 12 vehicles per minute. If there are 2 tollbooths each at random at an average of 6 seconds after services are done for every vehicle at the tollsystem, calculate the following:1. Queuing characteristics2. If one toll ticket booth is closed and service time is reduced by 3 seconds, what are theQueuing characteristics?3. Plot the arrival distribution curve for the traffic conditions stated above.arrow_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_forward
- The arrival rate at a parking lot is 6 veh/ min. Vehicles start arriving at 6:00 P. M., and when the queue reaches 36 vehicles, service begins. If company policy is that total vehicle delay should be equal to 540 veh-min, what is the service rate? (Assume D/ D/ 1 queuing and a constant service rate.)arrow_forwardA theme park has a single entrance gate where visitors must stop and pay for parking. The average arrival rate during the peak hour is 150 veh/h and is Poisson distributed. It takes, on average, 20 seconds per vehicle (exponentially distributed) to pay for parking. What is the average waiting time for this queuing system in minute/vehicle? Answer in two-decimal placesarrow_forwardAt an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 1200 veh/h, and at the booth, drivers take an average of 10 seconds to pay their tolls. Both the arrival and departure rates can be assumed to be exponentially distributed. How would the average queue length, time in the system change if a fifth toll booth were opened? Queue Analysis - Numerical M/M/N - Average length of queue Ō - Average time waiting in queue - Average time spent in system A = arrival rate = 11 W= Pop-1 1 NIN (1-p/NY P/N<1.0 p+Ō_1 2 i=P+Q 2 μl = departure rate M/M/N - More Stuff 1 - Probability of having no vehicles 1 P₁ P₁ = N-10²² pN Σ + n = n! N!(1-p/N) - Probability of having n vehicles p"Po for n ≤N n! www P = P₁ = n - Probability of being in a queue PAN Pop NIN(1-p/N) A = arrival rate p"Po NT-NN! p: P/Narrow_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_forwardVehicles begin to arrive to a parking lot at 7:00 AM at a rate of 2000 veh/hour, but the demand reduces to 1000 veh/hour at 7:30 AM and continues at that rate. The ticketing booth to enter the parking lot can only serve the vehicles at 1000 veh/hour until 7:15 AM, after which the service rate increases to 2000 veh/hour. Assuming D/D/1 queuing, draw a queuing diagram for this situation. Find: a) the time at which the queue clears, b) the total delay, c) the longest queue length, and d) wait time of the 500th and 2000th vehicles to arrive to the parking lot (assuming FIFO conditions)?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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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