Many counter$-$service restaurants today allow orders to be placed both in$-$person and online,

forcing their employees to juggle a physical queue of customers at the restaurant with a virtual

queue of online orders. One can model this juggling act as an MDP:

Imagine you are a server at Quick Oven Pizza in charge of two customer queues, Queue $1$

and Queue $2.$ You$$ll make decisions on a minute$-$by$-$minute basis, where:

$$ Each minute begins with your attention focused on only one queue $(1$ or $2),$ and you can

choose to spend the minute serving a single customer in that queue $($if there is one$)$ who

will then leave when the minute is over, or switching your attention to the other queue

$$ no one will be served, but you$$ll be ready to serve a customer in the other queue at

the start of the next minute.

$$ During the course of each minute, a new customer a