Principles of Highway Engineering and Traffic Analysi (NEW!!)
6th Edition
ISBN: 9781119305026
Author: Fred L. Mannering, Scott S. Washburn
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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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)
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?
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
Chapter 5 Solutions
Principles of Highway Engineering and Traffic Analysi (NEW!!)
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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- 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)arrow_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 3(t)= 6.1-0.22t where 3(t) is in vehicles per minute and t is in minutes after 6:00A.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.arrow_forward1. 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_forward
- 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_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_forward
- There is a single gate at an entrance to a recreational park where arriving vehicles must stop to pay their tickets. The park opens at 8:00AM, at which time vehicles begin to arrive at a rate of 480 veh/hr. After 20 minutes the arrival flow rate declines to 120 veh/hr, and it continues at that level for the remainder of the day. If the service time is 15 seconds per vehicle, and assuming D/D/1 queuing, determine the Length of Queue at 8:1OAM. Note: Round off your answers to the nearest whole number. Only include the numeric value of your answer without the unit (i.e. 22).arrow_forwardAnswer questions 13, 14, 15 and 16 using the following paragraph: Vehicles arrive at the carpark of an airport. Vehicles have to queue at the single entrance gate of the carpark at 9:00 AM. The arrival rate is constant at 240 veh/hr. However, between 9:00 and 9:40 AM, the parking ticket machine at the entrance works slowly due to a malfunction, and consequently, each vehicle spends 30 seconds to take the parking ticket. After 9:40 AM, the problem is solved and vehicles spend only 10 seconds at the gate to take the ticket. What is the longest vehicle queue? Select one: a.70 b.64 c.80 d.20 OOarrow_forwardLet us suppose a 15-minute count of vehicles bound for Quezon City was conducted at a particular location on España Avenue during afternoon peak period. A summary is shown in the table below: Type Passenger Car Unit (PCU) Equivalence 15-Minute Count Car/Van Jeepney Bus Truck 1.0 1.4 2.5 3.0 476 350 20 32 Estimate the flow rate in pcu per hour. (Note: PCU is simply the number of vehicles multiplied by the PCU Equivalence.arrow_forward
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