PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 5, Problem 16P
To determine
The maximum queue length and the total vehicle delay.
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Students have asked these similar questions
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)
A parking garage has a single processing booth where cars pay for parking.
The garage opens at 6:00 A.M. and vehicles start arriving at 6:00 A.M. at a
deterministic rate of 3(t) = 6.1 - 0.22t where 3(t) is in vehicles per minute
and t is in minutes after 6:00 A.M. What is the
minimum constant departure rate (from 6:00 A.M. on) needed to ensure
that the queue length does not exceed 10 vehicles? Answer in veh/min.
4 (with margin: 0.3)
Vehicles begin to arrive at a toll booth at 7:50 a.m. with an arrival rate of λ (t) = 5.2 – 0.01 t (with t in minutes after 7:50 a.m. and λ in vehicles per minute). The toll booth opens at 8:00 a.m. and serves vehicles at a rate of μ (t) = 3.3 + 2.4 t (with t in minutes after 8:00 a.m. and μ in vehicles per minute). Once the service rate reaches 10 veh/min, it stays at that level for the rest of the day. If queuing is D/D/1, when will the queue that formed at 7:50 a.m. be cleared?
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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- Question 1 In studying traffic flow at a highway toll booth over a course of 60 minutes, it is determined that the arrival and departure rates are deterministic, but not uniform. The arrival rate is found to vary according to the function of A (t) = 1.8 2 +0.25t -0.0030t. The departure rate function is u(t) =1.4 + 0.11 t. In both of these functions, t is in minutes after the beginning of the observation and X(t) and u(t) are in vehicles per minutes. (i) When will the queue that forms be cleared? (ii) What time does the maximum queue length occur and what will be the corresponding queue length? (iii) Determine the total delay (iv) Estimate the average time delay per vehiclearrow_forwardVehicles 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 minarrow_forwardA parking garage has a single processing booth where cars pay for parking. The garage opens at 6:00 A.M. and vehicles start arriving at 6:00 A.M. at a deterministic rate of Ȝ(t) = 6.1 − 0.22t where Ȝ(t) is in vehicles per minute and t is in minutes after 6:00 A.M. What is the maximum constant departure rate (from 6:00 A.M. on) needed to ensure that the queue length does not exceed 10 vehicles? Answer in veh/min. final answer: 8.21arrow_forward
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