PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 5, Problem 37P
To determine
The departure rate so that the queue length does not exceed
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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
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?
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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- The 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_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_forwardQuestion 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_forward
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