Question

Finished products arrive at a rate of 12 per hour at a packaging station via a roller

conveyor spur. The time between arrivals is exponentially distributed. The worker takes 4 minutes
and 35 seconds on the average to pick up a unit from the conveyor and pack it in the shipping carton
at the packaging station. Assume that this time is also exponentially distributed and that the conveyor
is used only for units that are waiting for the packaging station. Finished products that arrive when
the spur is full will recirculate in the conveyor system and enter the spur when space is available.
a) How long should the conveyor spur be so that it will not be full more than 10% of the time?
b) Are the products recirculating in the conveyor system part of the queue for the packaging
station? Why or why not?
c) What is the average number of units waiting on the conveyor spur?

Answer 1

The products recirculating in the conveyor system are not part of the queue for the packaging station.

Step-by-step explanation:

b) The products recirculating in the conveyor system are not part of the queue for the packaging station. This is because the conveyor is only used for units that are waiting for the packaging station. Once the units are picked up and packed, they are no longer on the conveyor and are not considered part of the queue.