PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 5, Problem 17P
At the end of a sporting event, vehicles begin leaving a parking lot at
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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 figure
7. Queue Theory:
At the end of a sporting event, vehicles begin leaving a parking lot at 2(1) = 12 - 0.25t and
vehicles are processed at u(t) = 2.5 + 0.5t (t is in minutes and 2(t) and u(t) are in vehicles per
minute). Assume D/D/1 determine: Time when queue clears and total vehicle delay.
At 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of (t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of (t) = 2.1 + 0.3t ((t) and (t) are in vehicles per minute and t is in minutes after 8:00 A.M.). Assuming D/D/1 queuing, what is the maximum queue length, and what would the total delay be from 8:00 A.M. until the queue clears? (Also Draw the D/D1)
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 a parking lot, vehicles arrive according to a Poisson process and are processed (parking fee collected) at an exponentially distributed rate at a single station. The mean arrival rate is 4 veh.min and the processing rate is 5 veh/min. Determine the average length of queue (in vehicles), time spent in the system and waiting time spent in the queue.arrow_forwardThe arrival function and departure functions at a traffic facility are given below: Arrival function, A(t) = 8t+0.95t2 • Departure function, D(t) = 2t+1t2 where, t = time in minutes. Determine the value of t (in minutes) at which the queue length is the maximum.arrow_forwardAt 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of (t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of (t) = 2.1 + 0.3t ((t) and (t) are in vehicles per minute and t is in minutes after 8:00 A.M.). Assuming D/D/1 queuing, what is the maximum queue length, and what would the total delay be from 8:00 A.M. until the queue clears?arrow_forward
- The Arrival time of vehicles at the entrance of a baseball stadium has a mean value of 30 veh/ hr. If it takes 1.5 min for the issuance of parking tickets to be bought for occupants of each car. a.) Determine the expected length of queue , not including the vehicle being served. b.) What will be the average waiting time of a vehicle in the queue in min.?arrow_forwardThe gate entrance to a park opens at 8:00 AM and there are 18 vehicles in the queue waiting to enter. Vehicles continue to arrive (from 8:00 AM onward) at a constant rate of 8 veh/min. The gate attendant processes vehicles at a constant rate of 1 vehicle every 6 seconds. Assume D/D/1 queuing for the vehicle arrival and departure processes at this gate. What is the average delay per vehicle (min/veh) from 8:00 AM until the queue clears? 0.9 1.1 4.5 9 Ο Ο 81arrow_forwardQUESTION 12 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 900 veh/h, and at the booths, drivers take an average of 12 seconds to pay their tolls. Both the arrival and departure headways can be assumed to be exponentially distributed. How would the average waiting time in the queue change if a fifth toll booth were opened? The waiting time is reduced by 2.5 seconds. O The waiting time is reduced by 4.7 seconds. The waiting time is reduced by 6.1 seconds. The waiting time is reduced by 7.9 seconds. O The waiting time is reduced by 9.8 seconds.arrow_forward
- 1. Estimate the queue dissipation time, maximum queue length, and total delay, given: Time Arrival Rate (veh/hour/lane) Departure Rate (veh/hour/lane) 3:30 4:00 PM 4:00 8:00 PM 3:00 - 3:30 PM 1200 1800 1200 1200 900 1800arrow_forwardVehicles arrive according to a Poisson process (random arrival) to a parking lot with mean arrival rate of 180 veh/hour, and are processed (they pay parking fee) at a uniform deterministic rate of 4 veh/min. (1) What type of queuing is this problem? D/D/1 M/D/1 M/M/1 (2) Determine: (I) the average waiting time and (II) the average length of the queuearrow_forwardPassenger 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_forward
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