At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machines to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machines is at the rate of 100 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour. a. What is the utilization rate of the system? b. What is the average number of packages waiting to be sorted? c. What is the average number of packages in the sorting system? d. How long must the average package wait until it gets sorted?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 2E
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At the order fulfillment center of a major mail-order firm, customer
orders, already packaged for shipment, arrive at the sorting
machines to be sorted for loading onto the appropriate truck for
the parcel's address. The arrival rate at the sorting machines is at
the rate of 100 per hour following a Poisson distribution. The
machine sorts at the constant rate of 150 per hour.


a. What is the utilization rate of the system?
b. What is the average number of packages waiting to be sorted?
c. What is the average number of packages in the sorting system?
d. How long must the average package wait until it gets sorted?
e. What would Lq and Wq be if the service rate were exponential,
not constant?

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