Consider an airport where taxis and customersarrive (exponential interarrival times) with respective rates of one and two per minute. No matter howmany other taxis are present, a taxi will wait. If anarriving customer does not find a taxi, the customerimmediately leaves.a. Model this system as an MyMy1 queue. (Hint:Think of the taxis as the “customers.”)b. Find the average number of taxis that are waitingfor a customer.c. Suppose all customers who use a taxi pay a$10 fare. During a typical hour, how much revenuewill the taxis receive?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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Consider an airport where taxis and customers
arrive (exponential interarrival times) with respective rates of one and two per minute. No matter how
many other taxis are present, a taxi will wait. If an
arriving customer does not find a taxi, the customer
immediately leaves.
a. Model this system as an MyMy1 queue. (Hint:
Think of the taxis as the “customers.”)
b. Find the average number of taxis that are waiting
for a customer.
c. Suppose all customers who use a taxi pay a
$10 fare. During a typical hour, how much revenue
will the taxis receive?

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