Network Origin-Demand Estimation Using Percolation

Key Takeaways

• Percolation search allocates trips by expanding cost layers
• Destination capacities deplete as trips are assigned
• Competing origins cause diversion to farther destinations
• No gravity or logit functions required
• Captures bottlenecks and heterogeneous acceptance

Summary

The paper introduces Network Origin‑Demand Estimation (NODE), a percolation‑based method for generating origin‑destination (OD) matrices. NODE expands outward from each origin in order of increasing generalized cost, matching trip productions to destination attractions while depleting destination capacities. When multiple origins compete, later trips are rerouted to more distant alternatives, producing a network‑aware OD matrix without relying on gravity functions or logit models. The approach reproduces classic gravity results in simple cases but diverges when capacity limits, bottlenecks, or heterogeneous acceptance are present.

Pulse Analysis

Traditional origin‑destination estimation relies heavily on gravity‑type equations or discrete‑choice logit models, which assume smooth demand flows and often ignore the physical constraints of the transport network. These methods can misrepresent travel patterns in dense urban cores or regions with limited infrastructure, leading to biased forecasts and suboptimal investment decisions. By contrast, the newly proposed Network Origin‑Demand Estimation (NODE) embeds the network topology directly into the allocation process, offering a more realistic representation of how trips actually propagate through a system.

NODE’s core mechanism mirrors a percolation process: starting from each origin, the algorithm expands outward in incremental cost layers, pairing trip productions with destination attractions until each destination’s capacity is exhausted. When several origins vie for the same limited attractions, later‑arriving trips are automatically diverted to farther, less congested alternatives. This competitive allocation captures the effects of bottlenecks, capacity constraints, and heterogeneous destination acceptance without the need for calibrated gravity parameters or complex utility functions, delivering a transparent and computationally efficient solution.

For transportation planners and mobility analysts, NODE provides a practical tool for scenario testing, especially in contexts where network disruptions, emerging mobility services, or rapid urban growth alter traditional travel patterns. Its capacity‑aware framework can be integrated with real‑time traffic data, enabling dynamic demand forecasting and more resilient infrastructure design. As cities seek smarter, data‑driven planning, NODE’s blend of simplicity and network fidelity positions it as a compelling complement—or even replacement—for legacy OD estimation techniques.