Parking in Competitive Settings: A Gravitational Approach Daniel Ayala, Ouri Wolfson, Bo Xu, Bhaskar DasGupta University of Illinois at Chicago Department of Computer Science dayala@uic.edu, {wolfson, boxu, dasgupta}@cs.uic.edu Jie Lin University of Illinois at Chicago Department of Civil and Materials Engineering janelin@uic.edu Abstract—With the proliferation of location-based services, mobile devices, and embedded wireless sensors, more and more applications are being developed to improve the efficiency of the transportation system. In particular, new applications are arising to help vehicles locate open parking slots. Nevertheless, while engaged in driving, travelers are better suited being guided to an ideal parking slot, than looking at a map and choosing which slot to go to. Then the question of how an application should choose this ideal parking slot becomes relevant. Vehicular parking can be viewed as vehicles (players) com- peting for parking slots (resources with different costs). Based on this competition, we present a game-theoretic framework to analyze parking situations. We introduce and analyze parking slot assignment games and present algorithms that choose park- ing slots ideally in competitive parking simulations. We also present algorithms for incomplete information contexts and show how these algorithms outperform even algorithms with complete information in some cases. I. I NTRODUCTION Finding parking can be a major hassle for drivers in some urban environments. For example in [1], studies conducted in 11 major cities revealed that the average time to search for curbside parking was 8.1 minutes and cruising for these parking slots accounted for 30% of the traffic congestion in those cities on average. Even if the average time to find parking was smaller, it would still account for a large amount of traffic. Suppose that the average time to find parking were 3 minutes (as opposed to 8.1), each parking slot would still generate 1,825 vehicle miles traveled (VMT) per year [2]. That number would of course be multiplied by the number of parking slots in the city. For example, in a city like Chicago with over 35,000 curbside parking slots [3], the total number of VMT becomes 63 million VMT per year due to cruising while searching for parking. Furthermore, this would account for waste of over 3.1 million gallons of gasoline and over 48,000 tons of CO 2 emissions. The advent of wireless sensors that can be embedded on parking slots has enabled the development of applications that help mobile device users find available parking slots around their locations. A prime example of this type of application is SFPark [4]. It uses sensors embedded in the streets of the city of San Francisco, that can tell if a slot is available. When a user wants to find a parking slot in some area of the city, the application shows a map with marked locations of the open parking slots in the area. While this type of application is useful for finding the open parking slots around you, it does raise some safety concerns for travelers. The drivers have to shift their focus from the road, to the mobile device they are using. Then they have to look at the map and make a choice about which parking slot to choose from all the available slots that are shown on the map. It would be better (safer) if the app just guided the driver to an exact location where they are most likely to find an open parking slot. Then the question arises, which algorithm should the mobile app use to choose such an ideal parking location? Our main concern in this work is to answer the preceding question. Parking can be viewed as a continuous query sub- mitted by mobile devices to obtain information about spatial resources (parking slots). A mobile user wants to know which is the parking slot to visit in order to minimize various pos- sible utilities like: distance traveled, walking distance to their destination, or monetary price of the parking slot. However, parking is also competitive in nature because after making a choice to visit a particular slot, the success in obtaining that slot will depend on if any other vehicles closer to that slot also made the same choice. This competition for resources (slots) lends itself for modeling this situation in a game-theoretic framework. We then present parking slot assignment games (PSAG) for studying competitive parking situations. Two categories of PSAG will be considered in this work, complete and incomplete information PSAG. For the complete information PSAG, we relate the problem of finding the Nash equilibrium to the Stable Marriage problem [5]. We show the equivalency of Nash equilibria and Stable Marriage assignments for instances of PSAG. For the incomplete information PSAG, the model that is most realistic and directly applicable to real-life application of parking slot choice, we present a gravitational approach for choosing parking. The Gravity-based Parking algorithm (GPA) is presented for this model. We evaluate the merits of the algorithm through simulation by comparing it to an algorithm that uses complete information and in which users follow their Nash equilibrium strategies. So in essence, we are comparing an algorithm that uses incomplete information against one that uses complete information. Our results show that in many instances, the GPA actually outperformed the Nash equilibrium on average in terms of driving time to park. The results also held when considering more general costs that 2012 13th International Conference on Mobile Data Management 978-0-7695-4713-8 2012 U.S. Government Work Not Protected by U.S. Copyright DOI 10.1109/MDM.2012.44 27 2012 13th International Conference on Mobile Data Management 978-0-7695-4713-8 2012 U.S. Government Work Not Protected by U.S. Copyright DOI 10.1109/MDM.2012.44 27 2012 IEEE 13th International Conference on Mobile Data Management 978-0-7695-4713-8 2012 U.S. Government Work Not Protected by U.S. Copyright DOI 10.1109/MDM.2012.44 27