Netflix is a DVD movie rental company. They stock 50 DVDs of a recent blockbuster movie available for rental. Their rental fee is $4 per DVD per day. The inter-arrival time between rental requests for this movie is 2.5 hours, on average, with a standard deviation of 2.5 hours. Demand is steady throughout a 24-hour day (there is no evidence of other arrival patterns). Assume that if all copies of the DVD are rented, then customers are willing to wait for the next one to become available. Also, assume shipping is instantaneous (the shipping time is zero days). A DVD is rented, on average, for 5 days with a standard deviation of 3 days. What is the average number of unrented DVDs in Netflix’s warehouse? Hint: consider the average utilization.

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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Netflix is a DVD movie rental company. They stock 50 DVDs of a recent blockbuster movie available for rental. Their rental fee is $4 per DVD per day. The inter-arrival time between rental requests for this movie is 2.5 hours, on average, with a standard deviation of 2.5 hours. Demand is steady throughout a 24-hour day (there is no evidence of other arrival patterns). Assume that if all copies of the DVD are rented, then customers are willing to wait for the next one to become available. Also, assume shipping is instantaneous (the shipping time is zero days). A DVD is rented, on average, for 5 days with a standard deviation of 3 days. What is the average number of unrented DVDs in Netflix’s warehouse? Hint: consider the average utilization.

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