mem·o·ry·less·ness

This is an interesting discussion of queueing theory as it applies to pumpkin patches.

This weekend, my family and I went to a pumpkin patch. Everyone else had the same idea. The line stretched out of the pumpkin patch gates and through the parking lot. We waited in line for ten minutes and then balked. When we left, about 90% of those that were leaving did not have pumpkins. We arrived in the morning on Sunday. It was only going to get busier. I cannot imagine the amount of revenue that was lost. We found out later that it took nearly two hours to get through the line.

During our short wait and on our drive to another orchard, we discussed queuing and pumpkin patches.

This link is an interesting perspective on Little’s Law, L = λW (a fundamental law in queueing theory), which turns 50 this year. (Strictly speaking, it’s the proof of the law that’s turning 50.)

According to the editors of Operations Research:

Little proves that under very general conditions, the average length of a queue, in steady state, will be equal to the arrival rate into the queue times the average wait in the queue. Remarkably, this relationship is not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else. Nor does it depend on the structure of the queueing system: “Little’s Law” holds not just at the individual queue level but also at the system level.

More:  John Little’s new paper about his law - “Little’s Law as Viewed on Its 50th Anniversary”