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An expressway off-ramp consisting of a single lane leads directly to a tollbooth. The rate of arrival of vehicles at the expressway can be considered to be Poisson with a www.Civil08.com - The Download Monster Chapter 6 Fundamental Principles of Traffic Flow 263 mean of 50 veh/h, and the rate of service to vehicles can be assumed to be exponen- tially distributed with a mean of 1 min. (a) What is the average number of vehicles waiting to be served at the booth (that is, the number of vehicles in queue, not including the vehicle being served)? (b) What is the length of the ramp required to provide storage for all exiting vehicles

An expressway off-ramp consisting of a single lane leads directly to a tollbooth. The rate of arrival of vehicles at the expressway can be considered to be Poisson with a www.Civil08.com - The Download Monster Chapter 6 Fundamental Principles of Traffic Flow 263 mean of 50 veh/h, and the rate of service to vehicles can be assumed to be exponen- tially distributed with a mean of 1 min. (a) What is the average number of vehicles waiting to be served at the booth (that is, the number of vehicles in queue, not including the vehicle being served)? (b) What is the length of the ramp required to provide storage for all exiting vehicles

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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An expressway off-ramp consisting of a single lane leads directly to a tollbooth. The rate of arrival of vehicles at the expressway can be considered to be Poisson with a 6-24 www.Civil08.com - The Download Monster Chapter 6 Fundamental Principles of Traffic Flow 263 mean of 50 veh/h, and the rate of service to vehicles can be assumed to be exponen- tially distributed with a mean of 1 min. (a) What is the average number of vehicles waiting to be served at the booth (that is, the number of vehicles in queue, not including the vehicle being served)? (b) What is the length of the ramp required to provide storage for all exiting vehicles 85% of the time? Assume the average length of a vehicle is 20 ft and that there is an average space of 5 ft between consecutive vehicles waiting to be served. (c) What is the average waiting time a driver waits before being served at the toll- booth (that is, the average waiting time in the queue)?
Transcribed Image Text:An expressway off-ramp consisting of a single lane leads directly to a tollbooth. The rate of arrival of vehicles at the expressway can be considered to be Poisson with a 6-24 www.Civil08.com - The Download Monster Chapter 6 Fundamental Principles of Traffic Flow 263 mean of 50 veh/h, and the rate of service to vehicles can be assumed to be exponen- tially distributed with a mean of 1 min. (a) What is the average number of vehicles waiting to be served at the booth (that is, the number of vehicles in queue, not including the vehicle being served)? (b) What is the length of the ramp required to provide storage for all exiting vehicles 85% of the time? Assume the average length of a vehicle is 20 ft and that there is an average space of 5 ft between consecutive vehicles waiting to be served. (c) What is the average waiting time a driver waits before being served at the toll- booth (that is, the average waiting time in the queue)?
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