Probability-Aware Parking Selection

TL;DR

The probability-aware parking selection problem is introduced, which aims to direct drivers to the best parking location rather than straight to their destination, and an adaptable dynamic programming framework is proposed for decision-making based on probabilistic information about parking availability at the parking lot level.

Abstract

Current parking navigation systems often underestimate total travel time by failing to account for the time spent searching for a parking space, which significantly affects user experience, mode choice, congestion, and emissions. To address this issue, this paper introduces the probability-aware parking selection problem, which aims to direct drivers to the best parking location rather than straight to their destination. An adaptable dynamic programming framework is proposed for decision-making based on probabilistic information about parking availability at the parking lot level. Closed-form analysis determines when it is optimal to target a specific parking lot or explore alternatives, as well as the expected time cost. Sensitivity analysis and three illustrative cases are examined, demonstrating the model's ability to account for the dynamic nature of parking availability. Acknowledging the financial costs of permanent sensing infrastructure, the paper provides analytical and empirical assessments of errors incurred when leveraging stochastic observations to estimate parking availability. Experiments with real-world data from the US city of Seattle indicate this approach's viability, with mean absolute error decreasing from 7% to below 2% as observation frequency grows. In data-based simulations, probability-aware strategies demonstrate time savings up to 66% relative to probability-unaware baselines, yet still take up to 123% longer than direct-to-destination estimates.

Figures (6)

• Figure 1: Visualization of the specified MDP. Orange states represent successful parking at the given lot $(\cdot, o)$, and are terminal. Purple states represent those where the driver visits a lot, cannot immediately park, and thus must decide whether to visit another lot or wait at the current lot $(\cdot, u)$. Actions ($a$) are shown with their associated probabilities ($p$), except where omitted for clarity of presentation. To avoid over-complication, only select rewards are shown; the full reward scheme is described in the main text.
• Figure 2: Visualization of the three illustrative cases for dynamic probabilities. The ego vehicle is indicated with a star, the rectangles represent parking lots, and vehicles are arranged such that lower vehicles arrive earlier.
• Figure 3: Error (shaded area) between an estimate $\hat{p}$ and the true value $p$ when $p$ is varying linearly and observation times are generated via a Poisson process.
• Figure 4: Discrepancy in observed and true probabilities when the true probability is a bounded random walk beginning at 50% for (a) lower observation rate ($\lambda=10$ veh/hr, $r=10$% adoption) and (b) higher observation rate ($\lambda=20$ veh/hr, $r=20$% adoption). The observation rate is a function of both the overall vehicle arrival rate $\lambda$ and connected user adoption fraction $r$.
• Figure 5: Distribution of mean absolute errors (MAEs) between observed and true probabilities across 100 different random walks as a function of (a) arrival rates (with $r=20$%) and (b) adoption rates (with $\lambda=20$). The distributional mean is indicated by a triangle and individual MAEs more than 150% beyond each box's inter-quartile range are indicated with dots.

Theorems & Definitions (5)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Proposition 5