Mathematical research and parking: exploring parking functions.

Our latest parking research digs deep into the mathematics of parking functions—a concept that models how drivers choose and fill parking spaces—and transforms these insights into real-world efficiency.

By analyzing tree parking functions and mapping parking functions, we learned how drivers naturally follow a cascading process when their preferred spot is occupied. This elegant mathematical framework enabled us to understand not just the initial choice, but the subsequent redirection and eventual allocation across a network. Our research shows that these patterns aren’t random; they follow predictable routes which, when modelled accurately, can dramatically reduce wasted time circling for a spot.

This understanding is at the heart of our innovative sorting engine. By integrating advanced combinatorial analysis with real-time traffic and occupancy data, our system predicts driver behavior with unprecedented precision. When a driver’s chosen spot is likely to be full upon arrival, our engine proactively directs them to the next optimal location—ensuring that search time is virtually eliminated. It automates the decision-making that operators once manually managed, aligning pricing and routing strategies to create a fluid, stress-free parking experience. Ultimately, our approach marries deep academic research with practical technology. The insights from these parking functions empower us to refine every aspect of the parking process—from dynamic pricing adjustments to personalized space allocation—so that drivers enjoy a seamless journey from reservation to parking. This marriage of theory and practice is transforming how parking is managed, driving operational efficiency while significantly improving the overall experience for every user of the network.

Read our full research paper here.