PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Textbook Question
Chapter 5, Problem 26P
Vehicles begin to arrive at a parking lot at 6:00 A.M. with an arrival rate function (in vehicles per minute) of
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The 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
81
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
1800
vehicles start to arrive at a parking area at 6 am with an arrival rate function(vehicles per minute) of lambda(t)=1.2+(0.3)t, where t is in minutes. At 6:15 am, the parking area opens and processed vehicles at a rate of 12 per minute.
a)Determine when does the queue clear?
b)find the total delay?
c)find the maximum queue length?
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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- delay? 4. The gate entrance to a park opens at 9:00 A.M. At 9:00 A.M. there are 32 vehicles in the queue waiting to enter. Vehicles continue to arrive (from 9:00 A.M. onward) at a rate of X(t) = 4.2-0.05t (with X(t) in veh/min and t in minutes after 9:00 A.M.). The gate attendant processes vehicles at a rate of u(t) = 3 + 0.3t [with u(t) in veh/min and t in minutes after 9:00 A.M.]. Assuming D/D/1 queuing, what is the maximum queue length and total vehicle delay from 9:00 A.M. onward? A.20 mph nohorarrow_forwardThe 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_forward9- Vehicles arrive at a recreational park booth at a uniform deterministic rate of 4veh/min. If uniform deterministic processing of vehicles (collecting of fees) begins 30 minutes after the first arrival and the total delay is 3600 veh-min, how long after the arrival of the first vehicle will it take for the queue to be cleared?arrow_forward
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