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# Optimal strategy for finding a parking space determined

The computer simulation is based on a parking lot from a long row, at the end of which is the destination of the driver. The evaluation takes into account the total time spent searching for a parking space and the time it takes to walk from the parking space to the destination. The results of the study were published in the Journal of Statistical Mechanics .

Physicists have determined the optimal parking strategy using a traffic mathematical model. In addition to the time spent looking for a parking space, the subsequent footpath to the destination is also included.

When looking for a free parking space , most drivers pursue a strategy based on their personal experience that leads to success rather by chance and does not follow any scientific methods. For this reason, physicists from the private research and teaching institute Santa Fe Institute (SFI) and Boston University have investigated whether there is a mathematically optimal strategy for finding a parking space.

## Different search strategies compared:

To determine the optimal search strategy, the scientists compared various behaviors used in everyday life. The first scenario depicts a driver who wants to park his car as close as possible to the destination in order to have a short walk. He drives to the destination and then turns to use the parking lot that is as close as possible to the destination.

In the second scenario, however, the driver wants to spend as short as possible in the car. He therefore chooses a parking space next to the car parked with the greatest distance from the destination so that he does not have to search for long and then runs the longest route. In the middle is the pragmatist shown in scenario three, who always chooses the first gap between two parked cars and must therefore walk an average route to the destination.

## Parking situation changes constantly in the computer model:

So that the computer simulation depicts reality as well as possible, the parking situation there is constantly changing due to vehicles moving away. In addition, vehicles looking for parking spaces cannot view the entire parking space, but only see free spaces when they are in front of them.

According to the study results, the group of pragmatic car park seekers gets to their destination the fastest on average. The advantage over the group that parks as close as possible to the goal is only minimal. In the case of particularly large parking lots, it was also shown that the longer search for the group who wanted to park as close to the destination as possible was offset by the time saved by walking for a shorter time, and that this group was therefore the fastest to arrive. The worst performing group in all parking situations was the group of drivers who park their cars as far as possible, since the long walk could not compensate for the time saved by parking immediately.

If we are looking for a parking space for our car, we try to park as close as possible to our intended destination. But what if there is possibly no longer there? It is also quite annoying if we drive to the destination by car, find no parking space there and our search starts again.

So what to do? Grab the first parking space or drive on and hope for a better parking space? Sid Redner and Paul Krapivsky from Santa Fe Institute, USA, asked themselves these questions – and created a mathematical equation that can calculate the perfect parking space.

## There are these types of parking spaces:

In their study, the scientists differentiate between three types of parking spaces:

• The “on the safe side” who grab the first free parking space
• The “at risk” goers who drive straight to their destination and hope for a parking space there
• The station wagon types that are looking for a parking space in the middle

For you, this means: You don’t take the first parking space straight away, but you don’t race straight to your destination. Instead you drive past a few parked cars and then take one that comes somewhere later. “You don’t search for too long, but you don’t have to walk too far to the goal,” summarizes Ann-Kathrin Horn from Deutschlandfunk Nova.

The scientists Redner and Krapivsky admit that they kept the initial situation for their formulas and equations fairly simple. They assume that there is a long street, the parking spaces are all on one side, all cars are the same size, every car fits into every gap. “The calculation is of course very theoretical,” says Ann-Kathrin Horn. “But there are actually different types of parking spaces.” And you can use that for your search for a parking space.

## What other Soultions Needed:

So other solutions are needed, and research that the physicist Paul Krapivsky from Boston University and his colleague Sidney Redner from the Santa Fe Institute have just published in the “Journal of Statistical Mechanics” may be helpful . It is about the question of which strategy is the most successful when looking for a parking space.

The whole thing is a classic optimization problem: where should you park your car in a large parking lot? Pretty far out there because you don’t want to spend time searching? It may be easier to find a free space there, but it takes longer to finish. Or should you try to find a gap near the destination? In this case, driving around forever threatens if nothing is free. Perhaps a middle ground will bring success where you search a little, but not for too long?

Krapivsky and Redner tried the three strategies in a simulated parking lot and looked at the tactics with which a driver generally takes the least time to reach his destination. For the sake of simplicity, the parking lot consisted of only one long row. They gave the three strategies the names “hesitant” (driver drives up to the first parked car and immediately takes the next free space), “optimistic” (drives directly to the destination and back from there if necessary) and “carefully” (parks not in the first gap, but then takes the next available one).