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Vehicles arrive to a bridge at a rate of 23 vehicles per minute. The capacity of the bridge is typically 3000 veh/hour, but is reduced to 914 veh/hour for 24 minutes. What is the duration of the queue that forms on the bridge in minutes?

Vehicles arrive to a bridge at a rate of 23 vehicles per minute. The capacity of the bridge is typically 3000 veh/hour, but is reduced to 914 veh/hour for 24 minutes. What is the duration of the queue that forms on the bridge in minutes?

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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### Traffic Flow Analysis **Problem Statement:** Vehicles arrive at a bridge at a rate of 23 vehicles per minute. The capacity of the bridge is typically 3000 vehicles per hour, but it is reduced to 914 vehicles per hour for 24 minutes. What is the duration of the queue that forms on the bridge in minutes? **Key Points to Consider:** 1. **Arrival Rate of Vehicles:** - 23 vehicles per minute. 2. **Bridge Capacity:** - Normal Capacity: 3000 vehicles per hour. - Reduced Capacity: 914 vehicles per hour for 24 minutes. **Objective:** Calculate the **duration of the queue** that forms on the bridge in minutes. **Steps to Solve:** 1. **Convert the Reduced Capacity** to vehicles per minute: - Reduced capacity in vehicles per minute = \(\frac{914 \text{ veh/hr}}{60 \text{ minutes/hr}}\). - Reduced capacity = \( \frac{914}{60} \approx 15.23 \) vehicles per minute. 2. **Evaluate the Difference in Rate**: - Excess arrival rate during reduced capacity = Arrival rate - Reduced capacity. - Excess arrival rate = \( 23 \text{ veh/min} - 15.23 \text{ veh/min} \). - Excess arrival rate = \( 7.77 \text{ vehicles per minute} \). 3. **Calculate the Total Excess Vehicles** Arriving During the Reduced Capacity Period: - Total excess vehicles = Excess arrival rate \(\times\) Duration of reduced capacity. - Total excess vehicles = \( 7.77 \text{ veh/min} \times 24 \text{ min} \). - Total excess vehicles = \( 186.48 \text{ vehicles} \). 4. **Determine the Time to Clear the Queue**: - Use the normal capacity rate to clear the excess queue. - Normal capacity in vehicles per minute = \(\frac{3000 \text{ veh/hr}}{60 \text{ min/hr}} = 50 \text{ veh/min}\). - Time to clear the queue = Total excess vehicles / Normal capacity rate. - Time to clear the queue = \( \frac{186.48 \text{ vehicles}}{50 \text{ veh/min}} \). - Time to clear the queue = \( 3.73 \text
Transcribed Image Text:### Traffic Flow Analysis **Problem Statement:** Vehicles arrive at a bridge at a rate of 23 vehicles per minute. The capacity of the bridge is typically 3000 vehicles per hour, but it is reduced to 914 vehicles per hour for 24 minutes. What is the duration of the queue that forms on the bridge in minutes? **Key Points to Consider:** 1. **Arrival Rate of Vehicles:** - 23 vehicles per minute. 2. **Bridge Capacity:** - Normal Capacity: 3000 vehicles per hour. - Reduced Capacity: 914 vehicles per hour for 24 minutes. **Objective:** Calculate the **duration of the queue** that forms on the bridge in minutes. **Steps to Solve:** 1. **Convert the Reduced Capacity** to vehicles per minute: - Reduced capacity in vehicles per minute = \(\frac{914 \text{ veh/hr}}{60 \text{ minutes/hr}}\). - Reduced capacity = \( \frac{914}{60} \approx 15.23 \) vehicles per minute. 2. **Evaluate the Difference in Rate**: - Excess arrival rate during reduced capacity = Arrival rate - Reduced capacity. - Excess arrival rate = \( 23 \text{ veh/min} - 15.23 \text{ veh/min} \). - Excess arrival rate = \( 7.77 \text{ vehicles per minute} \). 3. **Calculate the Total Excess Vehicles** Arriving During the Reduced Capacity Period: - Total excess vehicles = Excess arrival rate \(\times\) Duration of reduced capacity. - Total excess vehicles = \( 7.77 \text{ veh/min} \times 24 \text{ min} \). - Total excess vehicles = \( 186.48 \text{ vehicles} \). 4. **Determine the Time to Clear the Queue**: - Use the normal capacity rate to clear the excess queue. - Normal capacity in vehicles per minute = \(\frac{3000 \text{ veh/hr}}{60 \text{ min/hr}} = 50 \text{ veh/min}\). - Time to clear the queue = Total excess vehicles / Normal capacity rate. - Time to clear the queue = \( \frac{186.48 \text{ vehicles}}{50 \text{ veh/min}} \). - Time to clear the queue = \( 3.73 \text
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