Homework Help is Here – Start Your Trial Now!
Engineering
Civil Engineering
11. A police officer is checking the license and registration of the vehicles crossing a control point. The officer takes 2 minutes per vehicle to check the information. After 45 minutes, a second officer arrives (also needs 2 minutes per vehicle). If vehicles arrive at a rate of 40 vehicles per hour, answer the following: (D/D/1)

11. A police officer is checking the license and registration of the vehicles crossing a control point. The officer takes 2 minutes per vehicle to check the information. After 45 minutes, a second officer arrives (also needs 2 minutes per vehicle). If vehicles arrive at a rate of 40 vehicles per hour, answer the following: (D/D/1)

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Subject is Transportation Engineering The answer to the question is provided what need a is a detailed explanation of each part of the question of how the came about the answers shown in simplest terms
11. A police officer is checking the license and registration of the vehicles crossing a control point. The officer takes 2 minutes per vehicle to check the information. After 45 minutes, a second officer arrives (also needs 2 minutes per vehicle). If vehicles arrive at a rate of 40 vehicles per hour, answer the following: (D/D/1) Arrival rate = 40 veh/hr = 0.6667 veh/min Time to check (first 45 minutes) = 2 min/veh Service rate (first 45 minutes) = 0.5 veh/min Time to check (after 45 minutes) = 2/2 min/veh = 1 min/veh Service rate (after 45 minutes) = 1 veh/min Arrival equation (t in minutes): Vehicles = 0.6667 * t Service equation after 45 minutes (t in minutes): Vehicles 1* (t-45) + 0.5 * 45 = t-45+ 22.5 = t - 22.5 Vehicles = t - 22.5 2 equations and 2 unknowns Find the solution when the vehicles are the same: 0.6667 t = t - 22.5 Vehicles (veh) 45 30 22.5 22.5 t 0.6667 t 22.5 0.3333 t t = 22.5/0.3333 t = 67.5 min Therefore: Vehicles = 67.5-22.5 = 45 veh* Italic and orange color to distinguish from the 45 minutes and aid comprehension. b. What is the average queue length? Total delay / Time with queue = 253.125/67.5 = 3.75 veh Total Delay 0.6667 veh/min d. What is the average waiting time in queue? Total delay / Vehicles affected by queue = 253.125/45 = 5.625 min 0.5 veh/min c. What is the maximum queue length? Largest difference between arrivals and serviced vehicles = 30-22.5 = 7.5 veh 45 a. What is the total delay? Think of two triangles in this case where the maximum queue length will be the base for both. Maximum queue length = 0.6667*45-0.5*45 = 7.5 veh 12*7.5*45 + ½ *7.5*(67.5-45) = 253.125 veh-min 1 veh/min Queue length (maximum) 67.5 ▸ Time (min)
Transcribed Image Text:11. A police officer is checking the license and registration of the vehicles crossing a control point. The officer takes 2 minutes per vehicle to check the information. After 45 minutes, a second officer arrives (also needs 2 minutes per vehicle). If vehicles arrive at a rate of 40 vehicles per hour, answer the following: (D/D/1) Arrival rate = 40 veh/hr = 0.6667 veh/min Time to check (first 45 minutes) = 2 min/veh Service rate (first 45 minutes) = 0.5 veh/min Time to check (after 45 minutes) = 2/2 min/veh = 1 min/veh Service rate (after 45 minutes) = 1 veh/min Arrival equation (t in minutes): Vehicles = 0.6667 * t Service equation after 45 minutes (t in minutes): Vehicles 1* (t-45) + 0.5 * 45 = t-45+ 22.5 = t - 22.5 Vehicles = t - 22.5 2 equations and 2 unknowns Find the solution when the vehicles are the same: 0.6667 t = t - 22.5 Vehicles (veh) 45 30 22.5 22.5 t 0.6667 t 22.5 0.3333 t t = 22.5/0.3333 t = 67.5 min Therefore: Vehicles = 67.5-22.5 = 45 veh* Italic and orange color to distinguish from the 45 minutes and aid comprehension. b. What is the average queue length? Total delay / Time with queue = 253.125/67.5 = 3.75 veh Total Delay 0.6667 veh/min d. What is the average waiting time in queue? Total delay / Vehicles affected by queue = 253.125/45 = 5.625 min 0.5 veh/min c. What is the maximum queue length? Largest difference between arrivals and serviced vehicles = 30-22.5 = 7.5 veh 45 a. What is the total delay? Think of two triangles in this case where the maximum queue length will be the base for both. Maximum queue length = 0.6667*45-0.5*45 = 7.5 veh 12*7.5*45 + ½ *7.5*(67.5-45) = 253.125 veh-min 1 veh/min Queue length (maximum) 67.5 ▸ Time (min)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Highway safety
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Structural Analysis
Structural Analysis
Civil Engineering
ISBN:
9781337630931
Author:
KASSIMALI, Aslam.
Publisher:
Cengage,
Structural Analysis (10th Edition)
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Sustainable Energy
Sustainable Energy
Civil Engineering
ISBN:
9781337551663
Author:
DUNLAP, Richard A.
Publisher:
Cengage,
Traffic and Highway Engineering
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS