Question

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 101 per hour following a Poisson distribution. The machine sorts at the constant rate of 165 per hour. The center operates 10 hours per day. During operating hours, what is the average number of packages waiting to be sorted at any given time?

Answer 1

The solution:

Arrival rate λ = 101 packages per hour

Service rate µ = 165 packages per hour

In this problem, the service rate is constant, so it is called the M/D/1 model.

The average number of packages waiting to be sorted is Lq

1012 L 2H(-2) 2* 165(165 - 101) 10201 330(64) = 0.48300 packages

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