Consider an airport where taxis and customers arrive(exponential interarrival times) with respective rates of 1and 2 per minute. No matter how many other taxis arepresent, a taxi will wait. If an arriving customer does notfind a taxi, the customer immediately leaves.a Model this system as a birth–death process (Hint:Determine what the state of the system is at any giventime and draw a rate diagram.)b Find the average number of taxis that are waiting fora customer.c Suppose all customers who use a taxi pay a $2 fare.During a typical hour, how much revenue will the taxisreceive?

Consider an airport where taxis and customers arrive(exponential interarrival times) with respective rates of 1and 2 per minute. No matter how many other taxis arepresent, a taxi will wait. If an arriving customer does notfind a taxi, the customer immediately leaves.a Model this system as a birth–death process (Hint:Determine what the state of the system is at any giventime and draw a rate diagram.)b Find the average number of taxis that are waiting fora customer.c Suppose all customers who use a taxi pay a $2 fare.During a typical hour, how much revenue will the taxisreceive?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

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Concept explainers

Inventory Management

The supply chain is crucial to a firm's operations as it manages the inflow and outflow of products that are manufactured from the initial stage to the end product. It also considers the raw materials needed at different stages of production and when the work is in progress. Inventory management functions consist of ordering, storing, and procuring the organization's inventory like raw materials, factors, and finished products. It's also used for controlling the number of products for trade and helps manage the organization's inventory and stock. Inventory Management has been defined as having the right inventory, of the right volume, at the right cost.

Question

Consider an airport where taxis and customers arrive
(exponential interarrival times) with respective rates of 1
and 2 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 a birth–death process (Hint:
Determine what the state of the system is at any given
time and draw a rate diagram.)
b Find the average number of taxis that are waiting for
a customer.
c Suppose all customers who use a taxi pay a $2 fare.
During a typical hour, how much revenue will the taxis
receive?

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