Datacenter at the Airport: Reasoning about Time-Dependent Parking Lot Occupancy

Recently, Olariu et al. [3], [7], [18], [19], [20] proposed to refer to a dynamic group of vehicles whose excess computing, sensing, communication, and storage resources can be coordinated and dynamically allocated to authorized users, as a vehicular cloud. One of the characteristics that distinguishes vehicular clouds from conventional clouds is the dynamically changing amount of available resources that, in some cases, may fluctuate rather abruptly. In this work, we envision a vehicular cloud involving cars in the long-term parking lot of a typical international airport. The patrons of such a parking lot are typically on travel for several days, providing a pool of cars that can serve as the basis for a datacenter at the airport. We anticipate a park and plug scenario where the cars that participate in the vehicular cloud are plugged into a standard power outlet and are provided Ethernet connection to a central server at the airport. In order to be able to schedule resources and to assign computational tasks to the various cars in the vehicular cloud, a fundamental prerequisite is to have an accurate picture of the number of vehicles that are expected to be present in the parking lot as a function of time. What makes the problem difficult is the time-varying nature of the arrival and departure rates. In this work, we concern ourselves with predicting the parking occupancy given time-varying arrival and departure rates. Our main contribution is to provide closed forms for the probability distribution of the parking lot occupancy as a function of time, for the expected number of cars in the parking lot and its variance, and for the limiting behavior of these parameters as time increases. In addition to analytical results, we have obtained a series of empirical results that confirm the accuracy of our analytical predictions.