Distance Decay
What It Does
Section titled “What It Does”Distance decay describes how much less likely a customer is to visit as distance increases. The API models this with a single beta (β) parameter that controls the rate of decay. Beta is shared across Huff and Gravity models — a higher beta means steeper drop-off (more local), a lower beta means people are willing to travel further.
Decay Functions
Section titled “Decay Functions”The API uses two functional forms:
Exponential decay (convenience dining):
attraction = A × e^(-β × distance)Power decay (destination dining):
attraction = A × distance^(-β)Power decay has a heavier tail — customers at 2 km are less penalised than exponential. This matches destination dining behaviour where people seek out specific restaurants.
Current Implementation
Section titled “Current Implementation”Beta is set by calcBeta() before any spatial model runs. The same beta is passed to both Huff and Gravity:
| Service model / price band | β | Decay type | Rationale |
|---|---|---|---|
| Delivery | 0.3 | Exponential | Flat within 2 km delivery zone; distance matters much less |
| Takeaway | 0.5 | Exponential | Walk ~300 m willingly; steeper beyond |
| High-end HKD 200+ | 2.5 | Power | Destination dining — patrons travel specifically for experience |
| Premium HKD 100–200 | 1.5 | Power | Semi-destination; some distance tolerance |
| Budget / Mid (dine-in) | 0.8 | Exponential | Convenience: most customers within 400 m |
Interpretation
Section titled “Interpretation”- Low β (0.3–0.8): A restaurant 1 km away still gets meaningful traffic. Good for delivery-first or destination concepts.
- High β (1.5–2.5): Distance strongly suppresses traffic. Critical for budget walk-in concepts — being 200 m further than a competitor is a serious disadvantage.
Known Limitations
Section titled “Known Limitations”- Beta is fixed per service/price category — real decay varies by day of week, time of day, and individual preference
- No separate beta for tourist vs resident behaviour
- Does not account for physical barriers (harbour crossing, highway, etc.)
Changelog
Section titled “Changelog”| Date | Change |
|---|---|
| 2026-02-10 | Initial implementation with 5-tier beta parameterization |