A new Cornell University study uses queuing theory to examine how often pairs of shoppers might overlap in a supermarket – an approach that could be used to predict the transmission of COVID-19, and guide strategies to reduce its spread.
Jamol Pender, associate professor of operations research and information engineering, specializes in queuing theory – essentially the science of waiting in lines. His research has sought to ease traffic congestion, help driverless vehicles navigate and minimize the wait for rides at Disney World. Now, he’s turned his attention to a similar kind of queueing and set out to model the probability of COVID-19 transmission in stores, focusing on where customers might overlap and for how long.
The research started with the simplest scenario: a space with a single entrance and single queue.
This single-server model is admittedly a “ridiculous” extreme, Pender said, at the other end of which is the infinite server, which is a kind of idealized model with an endless number of resources, such as a subway ride with limitless passengers continuing to board.
To analyze the possible configurations of overlapping customers, the researchers created a simulation with two primary variables: the arrival rate – how quickly customers enter the store – and the service rate – how quickly customers are processed in the checkout line.
It turns out the key to limiting overlap, and potential exposure, between customers is to make the checkout process as speedy as possible.
“Arrivals have an effect, but not as strong an effect as the service distribution,” Pender said. “So, if you had a choice, and you could either restrict the arrivals or make your workers faster, I would tell you to make your workers faster, if you want to reduce overlaps.”
Another way to significantly reduce overlap and create a more efficient system is to add another server queue.
“There’s actually a very stark difference between one server and two servers,” Pender said.
While the new study was inspired by COVID-19, the modeling could be applied to other contexts, from barbershops and day cares, to buses and trains. Another application: online security and computer systems, in which the spread of “infection” might be the corruption of data files.
Source: Cornell University