Min-max fair car-parking slot assignment

Empirical studies show that cruising for car parking accounts for a non-negligible amount of the daily traffic, especially in central areas of large cities. Therefore, mechanisms for minimizing traffic from cruising directly affect the dynamics of traffic congestions. One way to minimizing cruising traffic is efficient car-parking-slot assignment. Usually, the related design problems are combinatorial and the worst-case complexity of optimal methods grows exponentially with the problem sizes. As a result, almost all existing methods for parking slot assignment are simple and greedy approaches, where each car or the user is assigned a free parking slot, which is closer to its destination. Moreover, no emphasis is placed to optimize any form of fairness among the users as the a social benefit. In this paper, the fairness as a metric for modeling the aggregate social benefit of the users is considered. An algorithm based on Lagrange duality is developed for car-parking-slot assignment. Numerical results illustrate the performance of the proposed algorithm compared to the optimal assignment and a greedy method.