In some ways, yes. Although it's less of a math model, and more of a server (as in waitstaff) model. A good server will make suggestions and upsell you on things like premium side-dishes or other add-ons, without making it seem like they are doing so.
A well mannered and sales-oriented waitperson can easily bump up the average per-seat revenue by 10-15%, without making the diners feel rushed.
A model could take into account who is coming (given caler ID), today's events, weather, traffic accidents, etc. and see if there is effect on how late people come and how long they stay.
Now of course a good waiter would be very helpful in that customers will not have to wait to order deserts and so they can leave earlier. Good waitiers however are very rare and once found can not be easily scaled like a good model can.
The problem, IME (past sous chef) is that it is really really really hard to manage the aspect of getting the people in the door, and turning the tables in any scheduled manner. World events, the weather, another restaurant featured in the paper or on TV all can greatly affect your ability to get asses in seats.
It's more achievable to maximize revenue through sales than through anticipated table turns.
From my experience (as a business coach) a good math model will usually help a business find extra turnover and profit.
In the examples here, though, it probably wouldn't be the best use of strategic time. Good marketing / positioning, creating solid referral relationships, as well as staff training (which brk nicely discusses) would probably add more than the math model would.
Which is almost a shame, since modeling is so much fun!
But what if you can centralize modeling? If all restaurants pooled their resoruces and hired someone to do it? Like opentable, for example, already handles reservations over internet - somethin no individual restaurant could afford.
Most operations courses in B-schools use the "Benihana of Tokyo" case (http://harvardbusinessonline.hbsp.harvard.edu/b02/en/common/...), which is all about maximizing profit per square foot. I was sort of shocked by the times they gave in this article, after recalling that article. Clearly the restaurants talked about are more upscale.
