# Model for Determining Parking Demand Using Simulation-Based Pricing
## 2 Methodology
The basic requirement must be met alongside the goal of revenue maximization:  
* Occupancy \(Occ_{t}\) must not exceed 95%: \[Occ_{t}\leq\ 0.95,\ \ \ for\ all\ t=1,\ldots,24.\] (4)
* Revenues should be maximized for parking accumulations \(A_{kt}=A_{kt}(P_{k})\) by user categories forecasted after price simulations \(P_{k}\): \[\underset{P_{k}}{max}\Bigg{(}\sum_{t=1}^{24}\sum_{k\in K}(P_{k}\cdot A_{kt}(P_ {k}))\Bigg{)}.\] (5)  
\(P_{k}\) represents the hourly equivalent price for each user category. For STU (short-term users), \(P_{k}\) corresponds directly to the hourly parking rate applied at the time of usage. The revenue for STU is calculated based on the actual number of vehicles per hour and the corresponding hourly price. For CMP, DMP, and NMP categories (monthly and daily passes), the hourly equivalent price is computed by dividing the total subscription price by the total number of hours covered by that subscription. The revenue function in Equation (5) represents the sum of revenues from all user categories. The total revenue is calculated as follows:  
\[Total\ revenue=\sum_{i}P_{sim,i}Q_{sim,i}(P_{sim,i})\]  
where \(i\) indexes the user categories (STU, DMP, NMP, CMP). The optimization process simultaneously adjusts the vector of prices \(P_{sim,i}\) to maximize the combined total revenue, subject to operational constraints such as the maximum occupancy limit of 95%. The model implements a constraint to maintain maximum occupancy at 95% to guarantee parking availability and minimize user frustration from searching for unoccupied spaces. The threshold derives from empirical data collected at the Gorica PG and recognized best practices in urban parking management. The study in [22] proposes that the best operational performance for parking systems occurs when occupancy levels stay within the 85 to 95 percent capacity range to maintain equilibrium between utilization and space availability. A flexible policy parameter within the simulation sets a limit for maximum occupancy at the 95% threshold. It can be adjusted by planners depending on strategic objectives; setting a lower threshold improves accessibility and turnover while a higher threshold emphasizes maximizing revenue. For instance, \(A_{NMPt}(P_{NMP})\) is the accumulation of NMP users based on the simulated price, calculated after determining the formula \(A_{NMPt}(P_{NMP})\). The associated occupancy is derived using the total accumulation formula:  
\[\eta(P)=\frac{\frac{dQ(P)}{Q(P)}}{\frac{dP}{P}}=Q^{\prime}(P)\cdot\frac{P}{Q(P )}=\frac{P\cdot Q^{\prime}(P)}{Q(P)}\ \leq\ 0. \tag{1}\]0  
Once the number of vehicles in the garage at the beginning of an hourly interval is recorded, entry and exit data for users in that hour are used to determine individual accumulations \(A_{kt}\) per category and hour, and to calculate the corresponding occupancy using Formula (6). From vehicle accumulation data, key parameters of demand functions \(Q(P_{k})\) are calculated separately for each user category. Separate data was extracted for short-term and long-term parking. For simulated prices and resulting demand, revenues are calculated using Formula (5) under the main condition (4). This ensures sustainable garage operation with increased revenue. Condition (4) ensures that the occupancy level does not exceed capacity, thereby ensuring enough free parking spaces. It is crucial to influence the composition of users at specific times of day using pricing to ensure availability of spaces (condition 4), forecasted by demand functions (3), and to increase revenues (5). A challenge in data analysis lies in the fact that the existing system does not calculate basic parking demand parameters. Through detailed analysis of collected data, it is possible to precisely determine the composition of users based on garage monitoring data, thus enabling the development of a model for determining parking demand using simulation-based pricing.