Tuesday, October 11, 2016

Menu Basket Queue

This is a view of a basket of menus at a restaurant in Chincoteague, Virginia. Notice the pattern of marks left as groups of menus scratch the wall when they are returned to the basket. As customers are seated at the restaurant, they are given menus that are removed from the right hand side of the basket. After ordering, the menus are returned to the basket and placed to the right of the remaining menus. When a single is menu returned, it nicks the wall at a location that depends on how many menus are currently in the hands of customers. If few menus are out with the customers, more remain in the basket and the wall marks of this returning menu will be further to the right. If many menus are out with customers, say just before the lunch rush, this returning menu will make a mark on the wall further to the left.

But it is not often that a single menu is returned alone. It is much more likely that a group of menus will be returned to the basket in a bunch. The size of the bunch that is returned is random depending on the size of the party seated. Each of the menus in the bunch makes a mark on the wall as they are returned to the basket. What we see is a steady state distribution of the number of seated customers, with menus in hand, waiting for their order to be taken.

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