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. 2025 Mar 5;15:7783. doi: 10.1038/s41598-025-91565-0

Table 2.

Symbols and their descriptions used in the Smart Parking Allocation Framework.

Symbol Description
N Number of parking spaces.
M Number of vehicles requesting parking.
K Number of traffic zones.
P Set of parking space availability states, Inline graphic.
L Set of traffic congestion levels for each zone, Inline graphic.
R Set of vehicle parking requests, Inline graphic.
Inline graphic Search time for vehicles to find a parking space.
Inline graphic Energy consumption of vehicles while searching for parking.
C Traffic congestion level in a specific zone.
U Space utilization, indicating the proportion of utilized parking spaces.
Inline graphic Weights for the multi-objective optimization function.
X Initial population of solutions in Pareto optimization.
Inline graphic Pareto-optimal set of solutions.
Q(SA) Q-value for a state-action pair in the MDP.
S Current state, including parking availability, congestion levels, and requests.
A Action taken, such as assigning a vehicle to a parking space.
R Reward function in the MDP.
Inline graphic Discount factor for future rewards in the MDP.
Inline graphic Velocity of a particle in PSO.
Inline graphic Position of a particle in PSO, representing parking assignments.
Inline graphic Inertia weight in PSO.
Inline graphic Acceleration coefficients in PSO for personal and global best updates.
Inline graphic Random numbers between 0 and 1 used in PSO updates.
Inline graphic Personal best position of a particle in PSO.
Inline graphic Global best position among all particles in PSO.