An automated car wash will wash a car in 10 minutes.Arrivals occur an average of 15 minutes apart (exponentiallydistributed).a On the average, how many cars are waiting in linefor a wash?b If the car wash could be speeded up, what wash timewould reduce the average waiting time to 5 minutes?

An automated car wash will wash a car in 10 minutes.Arrivals occur an average of 15 minutes apart (exponentiallydistributed).a On the average, how many cars are waiting in linefor a wash?b If the car wash could be speeded up, what wash timewould reduce the average waiting time to 5 minutes?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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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

An automated car wash will wash a car in 10 minutes.
Arrivals occur an average of 15 minutes apart (exponentially
distributed).
a On the average, how many cars are waiting in line
for a wash?
b If the car wash could be speeded up, what wash time
would reduce the average waiting time to 5 minutes?

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