  Designing efficient car parking mechanisms that can be potentially integrated
into future intelligent transportation systems is of crucial importance.
Usually, the related design problems are combinatorial and the worst-case
complexity of optimal solution approaches grows exponentially with the problem
sizes. Therefore, such optimal approaches are not scalable and practically
undesirable. As a result, almost all existing methods for parking slot
assignment are simple and greedy approaches, where each car is assigned a free
parking slot, which is closer to its destination. Moreover, no emphasis is
placed to optimize the social benefit of the users during the parking slot
assignment. In this paper, the fairness as a metric for modeling the aggregate
social benefit of the users is considered and a distributed algorithm based on
Lagrange duality theory is developed. The proposed algorithm is gracefully
scalable compared to the optimal methods. In addition, it is shown that the
proposed car parking mechanism preserves privacy in the sense that any car
involved in the algorithm will not be able to discover the destination of any
other car during the algorithm iterations. Numerical results illustrate the
performance of the proposed algorithm compared to the optimal assignment and a
greedy method. They show that our algorithm yields a good tradeoff between the
implementation-level simplicity and the performance. Even though the main
emphasis in this paper resides in the car parking slot assignment problem, our
formulation and the algorithms, in general, can also be applied or adopted in
fair agent-target assignment problems in other application domains.
