Min-max fair car-parking slot assignment

Abstract

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.

Enhancing the smart parking assignment system through constraints optimization

“…The proposed parking location is the closest to the destination, reducing overall trip time. Alfonsetti et al [14] proposed PAS based on the walking distance as constraints. The authors here proposed to model the global social benefit of users by developing a distributed algorithm based on Lagrange's theory of duality.…”

MDP: Minimum delay hot-spot parking

“…First, we show the shortage of using the shortest path as the metric in choosing the slot assignment in existing PGI schemes (e.g., [3,7,8]). Then, we show the limit in similar vehicle dispatching (e.g., [10][11][12][13]) that adopt the assignment on slots currently available only. The starvation problem cannot completely solved and its endless delay effect cannot be overlooked; even the centralized resource such as cloud (e.g., [3,14,20,27]) is adopted.…”

“…In an m × n assignment-based scheme (e.g., [10]), m vehicles can be dispatched to n customers when n ≥ m. But when m > n, the same scheme repeated for the rest (m − n) vehicles cannot avoid the starvation problem. For instance, we consider vehicles 1 and 3 in Fig.…”

“…Considering that the above starvation creates an endless delay effect, the aforementioned spatiotemporal resource assignment (dispatching all m vehicles to n places where m >> n) becomes non-trivial. Existing PGI strategies (e.g., [3,[7][8][9]) or similar assignment-based schemes for vehicle dispatching (e.g., [10][11][12][13]) are applied on a sufficient number of targets only. As we will demonstrate later, the starvation cannot be avoided completely when the demands exceeds the supply.…”