Sometimes a hostess says it will be ten minutes and it takes twenty. Other times thirty minutes takes only ten even though the restaurant is crowded and several parties are queued ahead. Hostesses and servers estimate wait times based on instinct, and their guesstimate could prove fairly accurate or wildly off.
Weston Dornhecker, a manager at Grandma's Saloon and Grill in Canal Park, said they predict wait times most accurately during tourist season when the crowd is most uniform. "We accurately predict wait times to within five minutes in the summer," Dornhecker said.
Grandma's was one of 23 area restaurants I visited this weekend, with the ultimate goal of creating a mathematical methodology that would take the guesswork out of wait times. There are only two factors which determine how long patrons must wait for a table to open up: the restaurant's number of tables and how long diners take to finish their meals. If patrons all took precisely the same time to eat then wait times could be calculated exactly.
The issue is that dining times can range from thirty minutes to several hours. Thus, my first inquiry was obtaining average dining times for a typical group on a typical night. How long a party dines, from the time they sit down to the time they leave, is called 'table turn time.'
At those 23 restaurants around Duluth, I asked employees to give me an average table turn time estimate for a party of four during dinnertime on a weekend. Average times varied from 40 minutes at Mexico Lindo and Red Lobster to an hour and forty five minutes at Va Biene. Most employees gave a range and in such cases the middle value was recorded. The overall average was 61 minutes with a standard deviation of 18 minutes.
Two other metrics were recorded at each establishment: number of tables, split into categories of two-tops, four-tops, and tables seating six or more. A two-top is hospitality lingo for a table that can seat only two. The most expensive item on the menu was also noted as a proxy for how expensive the place was.
Once the data was compiled, simple linear regression analysis found no correlation between a restaurant's table turn time and the price of their most expensive entree. Variations in table sizes were not statistically associated with table turn time either, after removing influential outliers.
Lack of correlation between price or table size could mean each restaurant has its own culture---some like Va Biene attract patrons wishing to savor the French delicatessens, and others draw crowds who eat and run.
Or, this lack of correlation could mean that hostesses and employees were not very good at estimating their patrons' dining times. Bad guesses would mean that, to predict wait times, we should take the overall average table turn time for estimating waits. For the sake of fairness we will use the average, so that all of the following calculations use the average table turn time at the 23 restaurants I visited.
A Poisson process was used to predict expected wait times using an average table turn time of 61 minutes and each respective restaurant's number of tables.
For example, say you have four in your party and there are three parties ahead of you. In such case you can expect to wait six minutes at Grandma's, 12 minutes at Valentini's, 17 minutes at Fitger's and 21 minutes at Burrito Union. Note that these calculations exclude bar seats and outdoor seating. 'Expected wait time' corresponds to a 75% chance of having been seated in the aforementioned times---that is, after 12 minutes of waiting at Valentini's, there is a 75% chance you would have been seated already in the given scenario.
See below for a chart of expected wait times at some local establishments. The times assume a party of four waiting fourth in line for a table, i.e., the same situation in the last paragraph. These are expected wait times for a table--the numbers can be biased for some restaurants since the calculation excludes bar seating. For example, 7-West has few tables but many bar seats.
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