Last week, the Wall Street Journal tried to offer insights on checkout lines. This week, they back the process a couple of steps and consider finding a parking place at the mall (Quick, Find a Parking Space, Dec 15).
For those who do not have online access to the Journal, here is video discussing the article.
Vodpod videos no longer available.
There are a couple of interesting points here. First, there is generally more parking than you would think at most malls.
Circling around a parking lot hunting for a space is one of most irritating experiences, especially this time of year. Truth is, though, there are usually available spots—most mall lots fill to just 30% to 35% of capacity, research shows. Shoppers in a rush just don’t want to walk.
“We rarely see mall parking lots that are full” except for the day after Thanksgiving and Christmas Eve, says Tom Diamond, president of Remote Sensing Metrics, a Chicago-based consulting firm that uses satellite imaging of parking lots to gauge retailer traffic. Lots fill up in an almost perfect bell-curved shape, with spaces at the front and directly opposite the entrance claimed first, Mr. Diamond says.
The misperception of availability, of course, matters to mall operators since having a tough time parking gets the visit off to a bad start and can ultimately reflect poorly on the convenience and desirability of going to a mall. Hence, as the article points out, mall operators are throwing all sorts of technology at the problem to ease the hassle of finding a spot.
A second point here is that parking lots and check out lines have more in common than just being featured in the Journal. One can think of them as basically functioning the same way. Users show up at random times and once they enter service (i.e., begin having their items rung up or park their cars), they hold the resource (i.e., the cashier or the parking spot) for a random period of time. Mathematically, they are very similar and if you are willing to make enough assumptions, one can calculate how many customers are in line or what’s the chance that all the good parking spots are taken.
The real difference between most queuing systems and parking lots is that in parking lots the routing is random. Users have to hunt for an available server (i.e., a spot) rather than being routed to an open agent at a call center or being able to choose which cashier to line up for at the supermarket. Many of the technology solutions malls are employing are trying to address this issue by better informing customers as to where spots are likely to be available.
A final point, I am not sure about the lie in wait strategy articulated in the graphic above. Yes, I can write out a model in which the average parking spot is held for 180 minutes and watching 20 of them will give an average time until someone leaves of 180/20 = 9 minutes. But that will require that the times are exponentially distributed — a very specific assumption. (Even if you are OK with that assumption, you should know that the chance you will wait more than 15 minutes for one of twenty spots to open is about 19%.)
Without assuming people are in the mall for an exponentially distributed amount of time, figuring out the expected time is rather hard but it easy to see that it won’t necessarily be 9 minutes. For example, suppose that everyone spends exactly 180 minutes in the mall. Further suppose that the lot begins to fill up at 9:30AM and that all the best spots are taken by 10:30AM. You roll in at 10:45AM. Should you wait for a prime spot to open? Clearly not. None of the good spots are going to be available until 12:30, which means almost a two-hour wait. That is, the assertion that “probability factors” indicate a short wait may be a little optimistic.