At the Order Fulfillment Center of a Major Mail-Order Firm,customer

question 51

Essay

At the order fulfillment center of a major mail-order firm,customer orders,already packaged for shipment,arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address.The arrival rate at the sorting machine 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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Definitions:

Nonfamilial Day Care

Child care provided outside of the family setting, often by professionals, in facilities like daycare centers or preschools.

Proximal Parenting

A style of parenting that involves close physical and emotional contact between the parent and child, emphasizing attachment and responsiveness.

Self-Aware

The recognition and understanding of one’s own personality, feelings, motives, and desires.

Compliant

Ready to adapt oneself to another's wishes or specifications, often by conforming to rules or standards.