In this paper, we propose a new smart parking system that determines the optimal parking allocation in the long run. In this system, the demand situation is acquired earlier than the respective parking start time by motivating drivers to apply for early parking, and the system performs long-term optimization instead of optimization only for the current time. We propose three optimization methods focusing on the time axis. The first one ignores the time axis constraint, the second one has the time axis constraint but lacks driver motivation, and the third one is the proposed method that solves those problems. Finally, numerical simulations will be used to confirm the effectiveness of the proposed method.