GridScore evaluates road network efficiency by synthesizing graph theory, kinematic motion dynamics, Bureau of Public Roads (BPR) congestion models, Point-of-Interest (POI) gravity attraction, and multi-level grade-separated interchange topologies into a normalized scalar benchmark \(E_{\text{global}} \in [0, 100]\).
The fundamental framework measures network efficiency as the ratio of ideal unconstrained traversal cost to real physical network traversal cost:
The global overall score \(E_{\text{global}}\) is a weighted convex combination of three independent physical-geometric evaluation criteria:
Default weighting parameters: \(w_1 = 0.35\) (Reachable Area Isochrone), \(w_2 = 0.35\) (Intersection Nodal Friction), \(w_3 = 0.30\) (Euclidean Path Ratio).
Measures spatial coverage reachable within a time budget \(t\) (default: 10 minutes) starting from the primary network hub node compared to the theoretical ideal isotropic surface expansion.
Reachable nodes are identified using Dijkstra's algorithm with realistic effective speeds. The convex hull surface area \(A_{\text{actual}}\) (\(\text{km}^2\)) of all reachable nodes is calculated using WGS84 planar projections:
GridScore replaces simple constant-speed assumptions with physical trapezoidal acceleration profiles and Bureau of Public Roads (BPR) traffic volume congestion equations.
Free-flow top speed \(v_{\text{max}}\) is adjusted by weather friction \(\mu_w\), pavement quality \(\rho_{\text{road}}\), and traffic pressure index \(\tau_p\):
Vehicles accelerate at \(a_{\text{acc}} = 2.0 \text{ m/s}^2\) and brake at \(a_{\text{brake}} = 3.0 \text{ m/s}^2\). If segment length \(L\) is shorter than acceleration and braking distance (\(d_{\text{acc}} + d_{\text{brake}} \ge L\)), a triangular profile is applied with peak velocity:
Segment travel time under volume \(V\) (vehicles/hour) and capacity \(C\) is modeled via the empirical BPR polynomial:
Quantifies friction introduced by signal timing, turn conflicts, cognitive load, pedestrian crossings, and lane reduction bottlenecks.
For every intersection node \(i\), total delay penalty \(K_i\) (seconds) is calculated as:
When traffic transitions from a major arterial road to a narrower street class (\(\text{rank}_{\text{out}} > \text{rank}_{\text{in}}\)), a non-linear bottleneck penalty \(K_{\text{squeeze}}\) is applied:
| Node Degree (d) | Intersection Type | k_base (s) | C_cog (s) | Description |
|---|---|---|---|---|
| d = 2 | Continuous Link | 0.0 s | 0.0 s | Uninterrupted through movement |
| d = 3 | T-Junction / Priority | 12.0 s | 2.0 s | Conflict point with 1 turning movement |
| d = 4 | 4-Way Signalized | 25.0 s | 4.0 s | Standard 4-phase traffic signal cycle |
| d ≥ 5 | Complex Multi-Arm | 45.0 + 10(d-5)² s | 7.0 s | High cognitive complexity & multi-phase delay |
Evaluates route directness by comparing crow-flies distance against network shortest path distance across random origin-destination pairs.
Monte Carlo sampling selects \(N = 200\) random node pairs with Euclidean distance \(D_{\text{Euclid}} \ge 500\text{ m}\). Crow-flies distance is computed using the spherical Haversine formula:
Weights road segment importance based on spatial attraction to key urban destinations (hospitals, transit hubs, schools, commercial centers).
An inverse-square spatial gravity model assigns a composite attraction weight \(W_{\text{node}}\) to each intersection node:
Where \(R_k \in [1.0, 5.0]\) is the POI category baseline importance, \(M_k\) is the review count / volume metric, and \(d_k\) is spatial distance in metres. Routes serving high-weight POI nodes are prioritized during path efficiency evaluations.
Rigorous handling of non-planar 3D road structures, grade-separated overpasses, bridges, tunnels, and multi-level stack interchanges.
Standard 2D planar GIS models create false intersections wherever two roads cross in coordinate space. GridScore parses layer tags (`bridge`, `tunnel`, `layer`, `oneway`, `motorway_link`) to construct an accurate 3D MultiDiGraph:
Overpassing motorways and underpassing local streets share 2D coordinates but remain topologically isolated. Zero false signal friction is added to overpasses.
Ramps (`motorway_link`, `trunk_link`) model curvature speed limits (\(v_{\text{ramp}} \le 40\text{ km/h}\)) and merge acceleration friction during ramp transitions.
Directional edge constraints enforce legal turning paths across multi-level cloverleaf, stack, and trumpet interchange structures.
Final network scores are mapped to letter grades aligned with traffic engineering performance standards.
| Grade | Score Range | Network Characteristics | Target Benchmark |
|---|---|---|---|
| Grade A | 80.0 - 100.0 | Optimal geometric directness, continuous arterial flow, minimal bottleneck friction. | Ideal Planned Grids |
| Grade B | 70.0 - 79.9 | High-capacity grid with minor signal delays and small localized detours. | Modern Mixed Orthogonal |
| Grade C | 60.0 - 69.9 | Average urban performance; moderate intersection delays and circuitous secondary routes. | Standard European Organic |
| Grade D | 50.0 - 59.9 | Poor connectivity; frequent dead-ends, severe signal friction, and lane bottlenecks. | Suburban Cul-de-sac Networks |
| Grade F | < 50.0 | Topological failure; severe network fragmentation and bottleneck congestion collapse. | Defective Networks |