From Crash Maps to a Travel Demand Model: the Xichang Project

Method

The data have no injury severity grade. So I use casualties per crash as the severity measure K/N. k is the number of casualties and n is the number of crashes. For the 95% confidence interval of the rate k/n I use the Garwood exact Poisson interval:

What I did and results

I built a 6 × 6 matrix of participant pairs. The matrix is symmetric, so I use only the upper triangle. For each cell I computed k/n and its confidence interval.

• Motor vehicle × motor vehicle: 11,407 crashes (57%). Only 0.06 casualties per crash.
• The most dangerous pair is heavy vehicle × pedestrian: 70 crashes, 143 casualties. That is 2.04 per crash (CI 1.72–2.41), 8 times the city mean of 0.26. Next come pedestrian × three-wheeler 1.11, pedestrian × two-wheeler 1.07 and motor vehicle × pedestrian 1.04. Motor vehicle × two-wheeler has 0.66 per crash, but the count is large. It has 1,746 casualties, one third of the total.
• Crashes involving vulnerable road users: 5,223 crashes (26.1%) → 4,050 casualties (79.1%), 0.78 per crash. Other crashes: 14,767 crashes → 1,072 casualties, 0.07 per crash. The ratio is 10.7 times. Every pair with a vulnerable road user is significantly above the mean. Every motor-vehicle-only pair is significantly below it. The confidence intervals of the two groups do not overlap.

Economic reading: in an asymmetric collision, the heavier party causes almost all of the marginal external cost (Lindberg 2001). The lighter party bears that cost. So corrective policy should target the heavier party: speed limits, access restrictions, right-of-way and physical separation. Policy should not rest on "safety education" for vulnerable users.

Method

Comparing total crashes across weather types is wrong. The totals are confounded by the number of days. I use the number of days with each weather as exposure. Then I compute the daily crash rate and the rate ratio relative to sunny days:

The 2023 report said "light rain has the most crashes (8,155, 41%)". That is classic exposure confounding. There were 151 light-rain days, more than the 135 sunny days. After adjusting for days, light-rain and moderate-rain days have crash rates 5–6% lower than sunny days. Only heavy rain is significantly higher. This fits risk compensation (Peltzman 1975). Drivers can perceive mild surface risk. They slow down, keep longer gaps and travel less. This offsets the risk. Heavy rain cuts visibility and floods the road surface. That is beyond what drivers can compensate for.

Planning implication: rainy-day safety campaigns have low marginal benefit. It is more effective to reduce physical risk during heavy rain. Examples: drainage, skid-resistant pavement, signs at flood-prone spots and arterial traffic control during storm warnings.

Method

Place a smooth "kernel", like a small hill, on each crash point. Add up all the hills to get a continuous density surface:

2023 vs 2026

• 2023: ArcGIS Pro Kernel Density tool with a search radius of 0.01. The coordinate system was WGS84, so this meant 0.01 degree ≈ 1.1 km. The output unit was "per square degree", which has no physical meaning. That is why the 2023 report showed peaks such as 273,500.
• 2026: project to UTM 48N first. Use a 250 m Gaussian kernel on a 100 m grid. Density is in crashes/km². Each crash type has its own color scale.

Results

All three crash types share one core. The core is the old commercial district bounded by Chang'an Middle Road, Chang'an South Road, Hangtian Avenue Section 1 and Sanchakou South Road. It also includes the corridor along Chang'an Road, east to the East Coach Station and west to the West Coach Station. Peak densities: angle > 300 crashes/km², rear-end about 180, rollover only 25. Angle and rear-end crashes stretch along arterials and cluster at intersections. Rollovers are more dispersed. Outside the city they form separate clusters on the G5 Jingjiu section and the G348 Heyan section. The cause is curves and grades.

I sorted the 250 m grid cells with crashes in descending order of crash count. Then I plotted the cumulative curve. All three types together have 830 cells with crashes. The densest 5% of cells hold 32% of crashes, 10% hold 48% and 20% hold 67%. The Gini is 0.64 for all types combined. By type: angle 0.59, rear-end 0.57, rollover 0.41.

Reading the marginal-return curve: covering the top 10% of cells reaches almost half of all crashes. These are about 80 cells, about 5 km². The next 10% of cells adds only 19 percentage points. Each further 10% adds fewer than 10 points. This is the direct basis for the proposal of a 30 km/h zone in the core.

Limitation: the modifiable areal unit problem (MAUP). Cell size changes the Gini and the correlation coefficients. For cells of 100–500 m the direction of the results is stable. But I did not report a systematic sensitivity test.

Global Moran's I (Moran 1948)

Local Getis-Ord Gi* (Getis & Ord 1992)

Gi* versus KDE: KDE is a density. It only says "there are many here". Gi* is a statistic. It says "this cell and its neighbors are high together", and too high to be random. Gi* measures how far the neighborhood sum departs from the global mean. So an isolated high cell is not necessarily a hot spot. A connected area of moderately high cells can be one.

What I did and results

The central city has 1,188 cells of 250 m. Gi* uses a 3 × 3 convolution. Moran's I uses queen contiguity without the cell itself and 999 permutations. Result: Moran's I = 0.29 (p = 0.001). There are 156 hot-spot cells at 95% or above, 128 of them at 99%. They are 13% of cells but hold 65% of crashes (3,764). The hot spots form a continuous "hot belt": West Coach Station → Chang'an Road → old commercial district → East Coach Station → southeast along Hangtian Avenue. There are no significant cold spots.

Why: engineering measures are applied to roads and intersections. Grid hot spots are not something engineers can act on. So I snapped each crash point to the nearest segment. Then I summed crashes and crashes per km by road name. For crashes per km, the exposure is the total OSM length of all segments with that name. An intersection is a node with degree ≥ 3. Crashes within 30 m of an intersection count as "intersection-related".

How: I used osmnx to get 3,424 drive segments in the core, plus 2,744 national/provincial highway and arterial segments city-wide. I projected them to UTM 48N. Snapping used geopandas.sjoin_nearest(max_distance=60). Road names came from the OSM name field.

Results

• The top 15 roads are 8.7% of road length but carry 33% of matched crashes. By crash count: Hangtian Avenue 534 (9 per km), Wuda Line 288, First Ring Road 218, Heyan Road Section 2 206, Haibin Middle Road 159. But the highest per km are short streets in the old town: Chang'an Road 88 per km, Chang'an East Road 70, Chuncheng Road 55, Chang'an Middle Road 53.
• By OSM class: trunk 16.9 per km, secondary 13.4, tertiary 8.2, primary only 6.0. Density does not rise steadily with road class.
• The top three roads for rollovers are all through arterials: Fengxiangkou Bridge section 33, Wuda Line 28, Hangtian Avenue 27.
• Intersections: Hangtian Avenue × Shengli South Road, 77 crashes, ranks first, with 42 angle and 33 rear-end. Second place has only 36. The top 15 intersections hold 47% of crashes that could be located to an intersection.

Limitations: the network is from 2026. The 12.9% intersection-related share comes from how addresses were geocoded. Roads that share a name dilute the per-km density. For example, the merged OSM length of Hangtian Avenue is 58.6 km.

Negative binomial regression: method

Crash counts are overdispersed: the variance exceeds the mean. So a Poisson model does not fit. I used a negative binomial model:

Results

• On a 500 m grid, Spearman ρ = 0.82. The densest quintile has 87 crashes per cell. The sparsest has 1.7.
• But crashes per unit of activity fall as density rises: crashes per 100 POIs drop from 113 in Q1 to 23 in Q5. Density is a positive externality for safety, because speeds are lower. Total activity hides this effect.
• NB results: β₁ = 0.65 (s.e. 0.04), α = 2.0. There are 33 excess cells with z > 2. They have 1,484 observed crashes against 204 expected. The top 8 excess cells are almost all on through arterials: Wuda Line, Dangui Bridge, First Ring Road and Hangtian Avenue. One Wuda Line cell has 77 crashes, 2 POIs, 2.2 expected and z = 21.3.
• Hubs: within 1 km of the coach stations, density is 10 times that of the 2–3 km band. But crashes per 100 POIs are flat across bands (25–35). So activity intensity fully explains the high density near coach stations. The rail station is different. In the 0–0.5 km band there are 52 crashes per 100 POIs. This falls steadily to 27 farther out. So the station forecourt area carries its own risk. The cause is taxis, three-wheelers, pedestrians and pick-up/drop-off cars mixing.

Global CLQ

This card gives the definition and the sources. Leslie & Kronenfeld (2011) proposed the global CLQ. Cromley, Hanink & Bentley (2014) proposed a geographically weighted version. Wang et al. (2017) proposed the local CLQ with a permutation test. The ArcGIS Pro "Colocation Analysis" tool is based on the Wang version.

Local LCLQ (one value per A point)

How the ArcGIS Pro tool works

1. Neighborhood: K nearest neighbors (default 8), a distance band, or a spatial weights matrix.
2. Kernel: with a Gaussian kernel, weights decay with distance. A box kernel gives equal weights.
3. Significance: a local permutation test, 99 permutations by default. Each permutation shuffles the B labels and recomputes the LCLQ. This gives the p-value.
4. Output fields: LCLQ, p-value, LCLQTYPE. LCLQTYPE has five classes: Colocated–Significant, Colocated–Not Significant, Isolated–Significant, Isolated–Not Significant, Undefined. Undefined means no B point falls in the neighborhood, so the LCLQ cannot be computed. The global CLQ table also gives a p-value for each pair of categories.

Terminology: the 2023 Chinese report called this measure "location entropy". The defense reviewers pointed out that it is a quotient, not an entropy. The rebuilt report uses "colocation quotient (CLQ)" throughout.

① Between crash types: all 3.5–8.6, far above 1

Near any crash type, the share of every other type is 3–4 times its global share. Crash types show no spatial division of labor. They all respond to traffic volume and conflict-point density. Rollover self-colocation (8.63) is the highest. "Other" self-colocation (6.36) is second. These two types are strongly site-specific (curves, grades, road surface). They suit engineering "spot treatment" best.

② POI → crash: almost all < 1 (0.35–0.95)

Catering 0.36–0.46, shopping 0.35–0.46, daily services 0.39–0.51, and so on. Only three pairs are slightly > 1: government × rollover 1.24 (p = 0.02, the only significant one), business-residential × other 1.21, and education × other 1.04.

③ Local LCLQ: 80–90% of points are not significant

Net colocation = % significantly colocated − % significantly isolated. Results: government +2.2, business-residential +2.2, education +1.6, sports +1.2, healthcare +0.7; accommodation 0; daily services −0.9, companies −1.6, catering −1.6, shopping −5.4.

④ A better explanation: from "police attention" to "speed environment"

The 2023 report explained the isolation of shopping and company POIs as "heavy traffic, a police priority, alert drivers". It explained the colocation of residential and government POIs as "a relaxed setting that makes drivers careless". In 2026 I changed the explanation to speed environment. Shopping and catering streets are the most congested and the slowest. Low speed suppresses the crashes that get reported to police. Roads past government offices, schools and business-residential blocks are wider and faster. Three other findings support this: crashes per unit of activity fall as density rises; negative binomial (NB) residuals concentrate on through arterials; and the railway station area shows excess crashes.

Gradient boosted decision trees (GBDT): the prediction is the sum of T regression trees, f(x) = Σ_t h_t(x). Each new tree fits the negative gradient of the current loss, that is, the residual. The trees "correct errors" one after another.

LightGBM (Ke et al., NIPS 2017, Microsoft) is faster and uses less memory than XGBoost. It handles categorical variables natively and is robust to collinearity. It relies on three techniques:

1. GOSS (gradient-based one-side sampling): keep the top a × 100% of samples by absolute gradient. Randomly draw b × (1 − a) × 100% of the rest, and scale their weights up by (1 − a)/b. A large gradient means the current model fits poorly, so the sample carries more information. These samples must be kept.
2. EFB (exclusive feature bundling): bundle mutually exclusive sparse features into one feature. Mutually exclusive means they are never nonzero at the same time. This reduces dimensionality.
3. Histogram algorithm + leaf-wise growth: bin continuous features. Grow the tree at the leaf with the largest gain, not level by level.

Why this model: segment crash counts are overdispersed counts. The features are highly collinear, for example lane count and road class, or office density and night lights. The features also have thresholds and interactions. GBDT handles nonlinearity and interactions automatically and is robust to collinearity. Its weakness is interpretability, so it is paired with SHAP.

SHAP (SHapley Additive exPlanations, Lundberg & Lee 2017) splits each prediction into additive contributions:

Intuition: think of the 13 features as 13 teammates. Together they "produce" the crash count of a segment. A feature's SHAP value is how many crashes it contributes on average, positive or negative. The average runs over all joining orders, so it is fair.

Data: 2,847 segments. The dependent variable is the segment crash count (a count, not a rate). The 13 features fall into three groups. Land use: office / commercial / residential POI counts, WorldPop population density, night lights. Hubs: distance to the railway station / airport / long-distance bus station. Road: administrative class, lane count, road form, median type, direction of flow.

Mean |SHAP| falls into three tiers. Tier 1, > 4: office land use 7.3, railway station distance 4.5, administrative class 4.4, lane count 4.2. Tier 2, 2.5–3.5: commercial, airport distance, residential, population density, bus station distance, night lights. Tier 3, < 1.6: road form, median type, direction of flow.

Direction: all land-use features are positive. All hub distances are negative: nearer means more crashes. Higher class and more lanes mean more crashes. Segments with a physical median have almost all negative SHAP. It is the only road attribute in the model that lowers crashes systematically.

Seven patterns in the dependence plots

1. Below 50 office POIs, SHAP ≈ 0. Above 50 it rises roughly exponentially. The densest segments reach +40 to +50 crashes. This is a threshold effect.
2. Residential density has a kink at about 100. It interacts with road class: at the same density, higher-class roads have more crashes.
3. Night lights below 20 give all-negative SHAP. Above 50, SHAP rises clearly.
4. Commercial land use is nonlinear but rises overall. Where commercial and office uses are both dense, SHAP is clearly higher.
5. Hub effects are local. SHAP is positive and volatile within 3 km of the railway station, 5–7 km of the airport, and 1–2 km of the bus station. Beyond that it returns to zero. Segments near hubs are also dense commercial segments. Hubs act through the activity around them.
6. ≤ 3 lanes: all negative. ≥ 4 lanes: all positive. ≥ 8 lanes: another jump. This is the cleanest design signal: "wide roads are more dangerous", in the sense of crash burden.
7. Divided two-way roads have the highest SHAP in economically active areas. Frontage roads are also in active areas, but they contribute very little. This suggests that separating through traffic from local traffic works in itself.

Economic reading: land use and hubs act mainly through exposure. Road class and lane count act on both exposure (more vehicles) and risk (higher design speed, more complex lane changes). This is risk compensation in reverse: "the safer the road looks, the faster people drive". A physical median does not depend on driver discipline. It is central to the Safe System approach. International evidence: physical medians on urban arterials can cut injury crashes by 20–40%. The office threshold effect suggests that land-use approvals should include a traffic impact assessment to internalize the externality.

Principle

Bayes' theorem: P(A|B) = P(B|A)·P(A) / P(B). A Bayesian network is a directed acyclic graph (DAG). Nodes = random variables, edges = conditional dependence, no edge = conditional independence. The joint distribution is P(X₁…X_n) = Π_i P(X_i | parents(X_i)). Experts can set the structure, or it can be learned from data. Learning methods come in two kinds: score-based (such as BIC / K2) and constraint-based (such as PC). The parameters are conditional probability tables (CPTs), learned from data by EM or maximum likelihood. Strengths: it handles uncertainty and missing data, and it supports scenario inference. Example: "with rain + night + poor street lighting, what is the probability of a severe crash?"

Mutual information is used for feature selection: I(X;Y) = Σ p(x,y) log[p(x,y) / (p(x)p(y))] = H(Y) − H(Y|X). It measures how much knowing X reduces the uncertainty about Y.

How far this project got

The tool was GeNIe. In 2023 the team first discretized the variables and computed marginal distributions (N = 19,990). Severity: minor 77% / moderate 20% / severe 3%. Visibility: good 41 / fair 34 / poor 25. Street lighting: good 59 / fair 26 / poor 14. Day 79 / night 21. Weather: clear 38 / cloudy 13 / light rain 41 / moderate rain 6 / heavy rain 2. Road surface: dry 51 / wet 49. The network structure came from the literature and experience: weather → road surface, visibility; lighting + street lights → visibility; participants → collision type; road surface + visibility + collision type → severity. Parameter learning and validation were not completed.

Only descriptive conclusions are possible. Severity is highly skewed: 3% ≈ 600 "severe" crashes, almost all in combinations of vulnerable road users (VRU) and heavy vehicles. "Poor" visibility is 25%, while night is only 21%. So poor visibility also comes from rain and fog. Most of the variance in severity comes from "who hit whom", not from weather or lighting.

The identity

The marginal benefit of an intervention = the term it changes × the other three terms. Hot-spot corridors already have high exposure and high risk. Cutting severity there gives the largest product.

Collision energy ∝ v². A pedestrian hit at 30 km/h has about a 10% fatality risk. At 50 km/h the risk is > 80% (Elvik 2013; ITF 2016). Nilsson's power model: injury crashes ∝ v², fatal crashes ∝ v⁴. A 10% speed cut → about −19% injury crashes. A 30 km/h limit in VRU-dense areas changes both "whether a crash happens" and "how severe it is". It is the only measure that does both.

Principle: crash cost = injury cost + property damage and administrative cost + indirect costs such as congestion (Elvik 2009; Viscusi & Aldy 2003). Injury cost covers VSL, medical care, lost work and pain. VSL is the value of a statistical life, estimated from willingness-to-pay studies. China has no official VSL standard. Values in the literature range from several hundred thousand to several million yuan.

Result: RMB 0.6–1.7 billion, ≈ 1–3% of GDP. This matches the WHO benchmark of "about 3%". Severe crashes are only 3% of crashes but account for more than half the cost. Crashes involving vulnerable road users are a quarter of crashes but account for about three quarters of the cost.

Limitations: the unit costs are scenario assumptions, not Xichang measurements. The GDP of RMB 56 billion is approximate. The result shows only the order of magnitude and the structure. Do not cite it as a precise figure.

There are three kinds of internalization tools. Prices: insurance premiums tied to exposure or risk, distance-based charges, truck entry fees. Prices are optimal in theory but hardest to apply at the local level. Regulation: speed limits, truck restrictions, right of way. Regulation depends on enforcement. Environment: narrower lanes, physical medians, raised crossings, tighter intersections. The environment needs one investment and works for a long time. It is the core of the Safe System approach. A fourth tool acts on future externalities: traffic impact assessment in land-use approvals. The seven recommendations are ranked by expected crash cost avoided / implementation cost. Effect sizes come from international handbooks.

1. Make the high-density core cells (top 10%, about 5 km²) a 30 km/h zone, with raised crossings, tighter intersections and refuge islands. Basis: vulnerable road users account for 79% of casualties; Gi* hot-spot cells (13% of cells) hold 65% of crashes. Effect: speed −10% → injury crashes −19%.
2. Heavy-vehicle management and station-area traffic organization: truck time windows and routes in the core, right-turn blind-spot treatment, and pedestrian–vehicle separation in front of the railway station. Basis: heavy vehicle × pedestrian, 2.04 casualties per crash; within 0.5 km of the railway station, crashes per unit of activity are twice the city average.
3. Physical medians, access management and speed limits on through arterials; intersection channelization on secondary roads in the old city. Basis: a physical median is the only attribute in the model that lowers crashes systematically. Revised after Phase 2: invest first in the Wuda Line, Heyan Road Section 2 and the Chang'an Road family, not in the full length of Hangtian Avenue. Effect: injury crashes −20–40%.
4. Add traffic safety assessment and development conditions to land-use approvals. Basis: office density shows a threshold effect; crashes concentrate within 1–3 km of hubs.
5. Treat physical risk under heavy rain: drainage, skid-resistant pavement, signs at ponding points, and arterial control during rainstorm warnings. Basis: heavy rain RR 1.15 (1.03–1.29).
6. Curve and grade engineering on the rollover corridors (G5 Jingjiu section, G348 Heyan section): speed limits, roadside barriers, markings. Basis: rollover self-colocation CLQ 8.63; rollovers cluster on their own outside the city.
7. Build the exposure denominator: traffic volumes, an injury severity scale, and geocoded police reports. Use EB for network screening. Phase 2 has partly done this with a sketch-level model.

Not recommended, three things: general rainy-day publicity campaigns; "safety awareness" campaigns aimed at pedestrians and cyclists; and new wide arterials in the low-density periphery. The last one would copy the "wide roads are more dangerous" pattern.

The core identity

Without E, you cannot tell the two problems below apart. They call for completely different responses:

US practice is set out in Chapter 4 (network screening) of the Highway Safety Manual (HSM). It first builds a safety performance function (SPF) with AADT as exposure. An SPF predicts how many crashes a road should have, given its traffic volume. Then it screens the network with Empirical Bayes (EB). Recommendation 7 of the Phase 1 report was "build the exposure denominator and use EB for network screening". But at the time this was not possible.

Method

Trip generation estimates each zone's productions P_i (home end) and attractions A_j (non-home end). Productions usually come from a trip rate: population × daily trips per person × purpose share. Cross-classification is another option. Attractions come from employment or floor area × an attraction rate. For each purpose, ΣP must equal ΣA. So attractions are balanced to the production total, because home-end data are more reliable. For NHB neither end is at home, so P = A, distributed by non-residential activity.

This project

There are two sets of attraction weights w_pc. HBO / NHB use the median peak-hour person trips per 100 m² of floor area from CJJ/T 141-2010 (retail 15, restaurants 10, schools 12, hospitals 7.5, offices 3, residential 1.6). HBW uses employment proxy weights (offices 1.0, health / education 1.5, retail / restaurants / services 0.3, residential 0).

External travel has three parts. First, hinterland trips into the city: hinterland population × r × city-bound share 0.25. Second, road traffic at external stations: G5 through traffic + through traffic across the city + traffic into and out of the city, balanced with IPF. Third, ground access to the airport and railway stations.

Result: 1.174 million person trips per day (HBW 470,000 / HBO 587,000 / NHB 117,000). Hinterland residents make 38,700 vehicle trips into the city per day. External and hub traffic adds 57,800 vehicle trips.

Limitation: the POI weights are defined per floor area but applied to POI counts. This assumes POIs of each type have similar average size. As a result, large employers are underestimated and dense clusters of small shops are overestimated. The trip-purpose split is borrowed from Yixing / Guilin.

Method

Trip distribution turns P_i and A_j into an OD matrix T_ij. The gravity model is an analogy to Newton's law of gravity. Trips are proportional to the size of both ends and decline with impedance c_ij. A doubly constrained model requires row sums = P_i and column sums = A_j:

There are three common friction (deterrence) functions: negative exponential f = e^−βc, power f = c^−γ, and gamma f = a·c^b·e^c₀c (NCHRP 716). Calibration usually targets the trip length frequency distribution (TLFD) or the mean trip length. Without a survey, only the mean can be targeted.

This project

• Impedance c_ij = zone-to-zone congested car travel time (minutes). All modes share this one impedance. This is a sketch-level simplification. Intrazonal impedance = 0.5 × the time to the nearest neighboring zone. AequilibraE computes the skim matrix by shortest path. Paths may not pass through centroids.
• f = e^−βt. There is no observed TLFD. So I solved for β by bisection, so that the mean trip distance equals a target. Targets: HBW 4.5 km, HBO 3 km, NHB 3 km. The HBW target comes from GB/T 51328: in cities of 0.5–1 million people, the mean commute distance is ≤ 5 km. Note that impedance is in time but the target is in distance. That is because the standards and surveys give distances.
• Calibrated values: β_HBW = 0.0375 /min, β_HBO = 0.230, β_NHB = 0.220. Non-work trips are about 6 times more sensitive to time, so they are shorter.

Result: 54% of trips are shorter than 3 km, and 9% are longer than 8 km. Intrazonal trips are 7.5%. The mean HBW car time is 8.4 minutes.

Limitation: the negative exponential function fixes the "shape" of the distribution. Only the mean is constrained. Walk and bike trips use car time as impedance, which understates their cost.

Method

The standard approach is a discrete choice model (multinomial or nested logit): P_m = e^V_m / Σ e^V_k. The utility V_m combines time, cost and a mode constant. Estimating the coefficients needs a travel survey. Without a survey, the fallback is fixed mode shares or shares by distance band.

Why not logit

Xichang has no household travel survey. No utility coefficient can be estimated. Coefficients borrowed from other cities cannot have their constants calibrated either. So I used "fixed total shares + allocation by distance":

So the total shares are a scenario input. The model only decides where each mode is used. Vehicle trips = car person trips / 1.4 occupancy + taxi person trips / 1.4 × 1.3 empty-running factor. E-bike OD is output separately and not assigned to the motor-vehicle network. Transit is not assigned either.

Result: within 1 km, 73% of trips walk. From 2 to 6 km, e-bikes carry 40%. The car share is 7% within 2 km and 42% above 8 km. The e-bike share of one third matches the 33.2% in the Guilin 2017 survey. The 65% walk-and-bike share meets the GB/T 51328 target of "≥ 60% for medium-sized cities".

Limitation: mode shares are the least certain parameters in the model (car 11%–26%). Guilin is the only reference in southwest China. So I use scenarios instead of estimates.

Time of day

I assign only the AM peak hour. I build the AM peak OD from the daily PA matrices with departure-from-home and return-home peak factors (HBW from home 0.30, HBO from home 0.12, …). Then I scale everything so that the person-trip-weighted AM peak share = 0.15. References: Yixing 20.1% for 7–8 a.m.; the US 7.9%. Daily volume = AM peak / K. K is the ratio of network-wide AM peak VKT to daily VKT. This assumes every link has the same daily profile.

User equilibrium (UE)

Wardrop's first principle: at equilibrium, all used paths between an OD pair have equal travel time. That time is no greater than the time on any unused path. No traveler can cut their own time by switching routes alone. Beckmann showed this is equivalent to a convex optimization problem:

Frank–Wolfe and bi-conjugate Frank–Wolfe

1. Compute t_a(xⁿ) at the current volumes xⁿ. Run an all-or-nothing (AON) shortest-path assignment to get the auxiliary flow yⁿ.
2. Line-search λ ∈ [0,1] to minimize Z(xⁿ + λ(yⁿ − xⁿ)).
3. xⁿ⁺¹ = xⁿ + λ(yⁿ − xⁿ).

Classic FW zigzags near the optimum and converges slowly. Bi-conjugate FW (BFW) combines the descent direction with the previous two directions as conjugates. This speeds up convergence greatly. AequilibraE's bfw reaches 1e-4 in 41 iterations. The classic FW in TransCAD 4.5 ran about 300 iterations and stopped at 1.6e-4.

Relative gap

Feedback

The times used in distribution should equal the congested times after assignment. So I loop 3 times. Round 1: free-flow skim → gravity → mode → time of day → UE → congested skim. The congested skim is averaged with the previous round by MSA (method of successive averages), then round 2 starts. And so on. The RMSE change in the AM peak car OD falls from 4.0% in round 2 to 1.2% in round 3.

Assignment settings

There are 4 vehicle classes (multi-class): car, hinterland, ext_hub (pce 1) and ext_road (pce 1.5, many trucks). They share one volume-delay function, so the equilibrium in total pcu is unique. The algorithm is bfw with an rgap target of 1e-4.

One command, tc45_run.py --scenario now, runs five steps:

1. prep: write links.shp with 1,500 links + 133 centroid connectors. Fields include T_AB / T_BA, CAP_AB / CAP_BA, ALPHA, BETA and others. Also write pa.dbf and od_fixed.dbf (66 × 66 cells) and generate a parameter macro. One-way links get T_BA = 9,999 min and CAP_BA = 99,999. The reason: GISDK 4.5 cannot write the topological Dir field.
2. compile: RSCC.EXE compiles the GISDK macro into a UI database.
3. assign: run tcw.exe -q -a xc_ui -ai "XC Assign Only". It takes about 30 seconds and exits on its own.
4. full: run "XC Full Chain". TransCAD runs gravity + mode + assignment itself.
5. collect: gather the CSVs. Join the link ID crosswalk. Produce comparison charts and a numbers macro.

What the GISDK macro does

• Build Network: ImportArcViewShape imports the shapefile. Centroid nodes are identified from the connectors. CreateNetwork includes time, capacity, α and β fields. ChangeNetworkSettings turns on Centroids.
• Skim: Multiple Paths minimizes free-flow time. Checked against Python: difference ≤ 0.005 min.
• Assign: TCB Run Procedure "Assignment". Load Method 5 = UE, Convergence 0.0001, Iterations 500.
• Full Chain: Gravity is called once per purpose. The reason: in 4.5, running all three purposes in one call left HBO empty. Testing found this. Settings: Double constraint, Exponential impedance, c set to the Python calibrated value. TransposeMatrix gives the return trips. Matrix Fill builds the AM peak car OD, then UE runs.

Why assignment only gives 0.9999 but the full chain only 0.963

1. Assignment only: both sides use identical OD, network and volume-delay functions. Differences come only from the algorithm and convergence. TransCAD's classic FW stops at 1.6e-4. AequilibraE's BFW reaches 0.9e-4. The differences sit on low-volume links. Three intermediate checks agree: free-flow skims differ by ≤ 0.005 min; no flow passes through centroids; one-way links carry zero reverse flow.
2. Full chain: the TransCAD version has two deliberate simplifications. First, mode choice uses one flat share instead of distance bands. Second, there is no distribution–assignment feedback. The flat share cuts AM peak car trips by 7% and raises the share of short trips. So pcu-km is 13.8% lower.
3. Another technical cause lies in the skim matrix. The exported skim is the one after the last feedback MSA averaging. Python's final distribution used the skim before averaging. HBO / NHB have a large β and are sensitive to impedance, so their trip tables differ by 20%. HBW differs by only 1%. I checked TransCAD's gravity model against a numpy Furness run with the same skim and the same β. Cell by cell, they differ by ≤ 0.005 trips. So the gravity model implementations agree.
4. Conclusion: the results do not depend on the software implementation. The distance-banded mode choice and the feedback in the Python model change link volumes materially. They are not negligible details. I documented the causes of the gap in the report instead of reporting only 0.9999.

Three concepts from the FHWA manual

The Travel Model Validation and Reasonableness Checking Manual, 2nd ed. (Cambridge Systematics for FHWA / TMIP, 2010) separates three concepts:

Xichang has no counts and no surveys. So this project does only the last two. I do not call it validation.

13 parameters: trip rate, purpose split, car mode share, peak-hour share, through-traffic share, BPR α, BPR β, capacity level, external volume, trip-length target, vehicle occupancy, share of G5 traffic that exits into the city, and hinterland city-bound share.

• OAT (one-at-a-time): change one parameter to its low or high value. Keep the rest at base. That gives 13 × 2 = 26 runs. They show the direction and size of each parameter's effect (tornado chart).
• LHS (Latin hypercube sampling): sample all 13 parameters together, 20 times. Each dimension is split into n strata. One point is drawn at random within each stratum. The strata are then paired at random. LHS covers the parameter space with fewer samples than simple random sampling. It shows the range of results when parameters move together.
• With the base run, that makes 47 full four-step runs, including feedback. They ran on 4 parallel workers.

Spearman rank correlation

Results

• The largest effects on total VKT: external volume −15% / +19%, car share −15% / +16%, hinterland city-bound share ±12%. Trip rate and trip length come next. Under LHS, the 5–95% range of total VKT is 2.59–3.71 million (−19% / +16%). Two of the top three parameters concern traffic from outside the study area. That is exactly where the data are weakest.
• The largest effects on congestion (share of links with V/C > 1): capacity (13.8%–2.4%) and peak-hour share. They barely change VKT. BPR parameters and through-traffic share have small effects on both.
• Rank stability: of the 25 busiest links in the base run, 14 stay in the top 20 in ≥ 80% of runs. Of the top 15 corridors, 14 stay in the top 15 in ≥ 80% of runs.
• Policy implication: the best way to narrow exposure uncertainty is classified counts. Place them at the entry points and the main corridors into the city. Together they form a cordon line around the study area. They constrain external volume, hinterland share and car share at once.

Without counts, travel time is the only free independent observation. The AMap traffic-status API is closed to new users. So I use the AMap driving-route API to probe 40 two-way routes, 1.2–4 km long. Routes include the G5, Hangtian Avenue, Wuda Line, Haibin Middle Road and Nanshan Avenue. Each day has 24 time slots: every 15 minutes in the AM and PM peaks, plus 14:00 and 23:00 as controls. The plan is 14 days.

The test is fixed in advance: the Spearman rank correlation between the observed peak / late-night travel-time ratio and model V/C. I also check whether Hangtian Avenue, Nanshan Avenue and Chang'an Road are among the slowest observed. Pass criteria: ρ ≳ 0.4, p < 0.05, and the high-V/C corridors are the most congested in the observations. Then the relative congestion ranking passes. Otherwise the V/C ranking is unreliable. This is still not volume validation. It checks relative congestion only.

Principle: the safety performance function (SPF) is the core of the HSM. Given the road type and exposure, it predicts the expected number of crashes. Crash counts are overdispersed, so I use negative binomial regression (NB2):

The elasticities are far below 1 for three reasons. I cannot separate them. First, model volumes have measurement error, which biases the elasticity toward zero (attenuation bias). Second, crash coordinates are coarse, so many crashes land on the link next to a landmark. Third, the true relationship is nonlinear. So I do not interpret the size of β₁. I use the SPF only as an expected baseline for the same class and the same traffic.

Principle (Hauer 1997; HSM Chapter 4): observed crash counts fluctuate at random. They also show regression to the mean: a site with many crashes one year tends to have fewer the next. EB weights the observed count and the SPF prediction by their reliability:

Three screening measures

This card tests whether "through arterials are dangerous" holds. First I reproduced the Phase 1 model exactly on the 250 m grid (619 cells): crashes ~ ln(1 + POI). The coefficients and the 33 excess cells match exactly. Then I added two variables: ln(1 + daily VKT / 1000) and a dummy for "no model link in the cell." Finally I added a through-arterial dummy and checked its IRR (incidence rate ratio):

Three findings: (1) Traffic volume itself has strong explanatory power. The POI elasticity drops. Part of what Phase 1 credited to "activity" was actually traffic. (2) "Through arterial" as a category is no longer significant. It is not significant in any of the 47 runs. (3) The excess at specific sites remains. Examples are several cells on Wuda Line, Hangtian Avenue and Dangui Bridge. The risk belongs to sites, not to a road category.

Scenario setup

Three population levels

Central city of 600,000 / 700,000 / 850,000 residents. The 850,000 figure: development boundary of 85.79 km² ÷ 100 m² per person. Today's population is 470,000. So growth is 130,000 / 230,000 / 380,000 residents.

Allocation rule: "water-filling"

1. The plan's growth directions are "expand west, expand south, lift the north, hold the east, refine the center." I split zones into five groups and weight each. West 1.0 (including the new zone 53 for the high-speed-rail town, 9.9 km²). North 1.0 (the Anning corridor). South 0.8. Center 0.5 (old city). East 0.25.
2. Capacity: growth areas are capped at a gross density of 10,000 residents/km². Old city +10%. East +5%.
3. Added residents ∝ weight × remaining capacity. Overflow is reallocated. Base case result: west 54%, north 31%, south 10%, old city 5%, east 0%. The high case uses 92% of total capacity. So 850,000 is close to the limit.

Other assumptions

• Attractions: POIs grow with population, at today's POIs per person by category. The jobs–housing ratio of each area stays the same. I do not model industrial parks as separate job centers.
• Network: most municipal roads in the 14th Five-Year Plan are already built. The real addition is the ring expressway. Its geometry comes from the OSM construction layer: four lanes (two per direction), 49.7 km, 4 interchanges. Three planned grade separations: capacity × 1.3 on 34 links within 300 m.
• Car mode share 18% → 20 / 24 / 28%. External traffic grows 1.5 / 2.5 / 3.5% per year for 10 years.
• Policy test: on top of the 2035 base, car share drops 5 percentage points (24 → 19%). Half shifts to transit, half to e-bikes.

• Spatial pattern: growth goes west and north. Caizishan Avenue rises from 11,000 to 23,000 vehicles/day. The Ningyuan Avenue west extension goes from ≈ 0 to 6,500. The G5 rises 55% along its length. Wuda Line rises 40%. Old-city corridors stay flat or fall. Chang'an Road, Sanchakou South Road and First Ring Road change by less than ±5%. Hangtian Avenue +9%. Heyan Road Section 2 −3%. There are two reasons. New residents live outside the old city. And the western section of the ring expressway (about 11,000 vehicles/day) takes traffic that now crosses the north of the old city.
• In the low case, mileage with V/C > 1 is lower than today (28 vs 34 km). The reason: the ring expressway and the added capacity at grade separations offset the demand growth. Three new bottlenecks appear: where the Ningyuan Avenue west extension enters the old city, the G5 Xichang North ramps, and the north section of Hangtian Avenue.
• Policy scenario: car share drops 5 percentage points. VKT growth falls from 42% to 28%. Mileage with V/C > 1 is 32 km, back to today's level. Hangtian Avenue +9% → +1%. Nanshan Avenue +19% → +6%. About 48% of the added arterial crashes are avoided. Avoided crash cost is RMB 14–88 million per year.

Crash conversion method: I use the class-specific SPFs from Section 11 (β₁ 0.31–0.45). I compute expected crashes on the 626 arterial links that carry volume today. I give two bounds: the fitted elasticity, and β₁ = 1 (proportional). Cost: Phase 1 crash cost for 2019 of RMB 0.58–1.73 billion/yr × arterial crash share of 37% × percent change.

This card explains the choice. The site meets three conditions at once:

1. It ranks first among intersections in Phase 1, with 77 crashes: 42 angle and 33 rear-end. The second-ranked site has only 36.
2. Exposure does not explain it away. Its south-east approach link has an EB excess of +70 crashes. That is about 13 times the SPF prediction. It ranks 6th among 640 links with volumes. Yet the Hangtian Avenue corridor as a whole has a negative excess. So the risk is concentrated at this node, not along the corridor.
3. It is an at-grade signalized intersection in the central city. Engineers can act on it.

This closes the "macro → meso → micro" chain. The demand model says Hangtian Avenue as a whole just carries a lot of traffic. EB says: except at this intersection. VISSIM answers: how can this intersection be changed?

Microsimulation

Microsimulation models each vehicle at each time step, here 10 steps per second. It models each vehicle's acceleration, deceleration, lane changes and yielding. It can show bottlenecks such as signals, queues and weaving. A static macroscopic model cannot see these. So the two complement each other.

Wiedemann car-following model (psycho-physical model)

A car-following model describes how a driver follows the vehicle ahead. The driver switches among four states based on distance and speed difference: free driving, approaching, following and braking. Drivers cannot hold an exact distance. They drift between perception thresholds. This is called car-following oscillation.

• Wiedemann 74 (urban): three parameters. ax is the average standstill distance, default 2 m. bx_add is the additive safety distance, set to 2. bx_mult is the multiplicative part, set to 3. Desired safety distance d = ax + (bx_add + bx_mult · z) · √v. These three parameters mainly set the saturation flow rate. You can tune them to 1,600–1,800 pcu/h/lane.
• Wiedemann 99 (freeway / interurban): 10 parameters, more detailed. For example, CC0 is standstill distance, CC1 is headway time, CC2 is following variation.
• In this project, motor vehicles use W74 "Urban (motorized)". E-bike links use "Cycle-Track (free overtaking)," which allows side-by-side passing.

Lane changes

There are two kinds. A necessary lane change follows the route. A free lane change seeks a faster lane. Parameters: maximum deceleration, accepted deceleration, waiting time, and safety distance factors front and rear. Waiting time defaults to 60 s. After that, the vehicle is removed from the network. This is why 17 vehicles were removed under the existing plan.

Conflict areas vs priority rules

Signals, seeds, evaluation

• Fixed-time signals: a VisSig .sig file defines signal groups, phases, cycle length and green splits. Signal heads sit at the stop line of each lane. The student edition cannot connect external actuated control.
• Random seeds: arrivals, desired speeds and driver parameters are all drawn at random. So one run is only one sample. This project runs 20 seeds per plan. I use seeds as samples in the statistical tests. The first 120 s are warm-up and are not counted.
• Evaluation outputs: node evaluation gives volume, average delay, stops and queues for each turning movement. There are also travel-time sections, delay segments and data collection points.
• Webster timing: cycle C₀ = (1.5 L + 5) / (1 − Y). Y = Σ y_i, the sum of critical lane flow ratios q/s for each phase. L is total lost time. Effective green g_i = (C − L) · y_i / Y. This project uses a saturation flow of 1,700 pcu/h/lane and 4 s lost time per phase.

SSAM is the Surrogate Safety Assessment Model. FHWA developed it (Gettman & Head 2008). It reads the microsimulation trajectory file (.trj), finds conflict events between vehicle pairs, and computes surrogate safety measures. The logic: crashes are rare, and simulated vehicles do not crash. So near misses stand in for crashes.

• TTC (time to collision): assume both vehicles keep their current speed and heading. TTC is the time until they collide. A minimum TTC at or below a threshold counts as a conflict. The default threshold is 1.5 s.
• PET (post-encroachment time): the time between the first vehicle leaving the conflict point and the second vehicle arriving there. Threshold ≤ 5 s.
• Other severity measures include MaxS, DeltaS, DR and MaxDeltaV.
• Classification by conflict angle: based on the angle between the two headings. < 30° is rear-end. 30–85° is lane-change. > 85° is crossing. The SSAM default crossing threshold is 80°. This project uses 85°.
• Standard cleaning: remove records with TTC = 0. These are simulation artifacts where vehicle outlines already overlap. They make up 84–88% of records. Remove the warm-up period. Normalize per 1,000 entering vehicles.

SSAM conflicts are not crashes. Their use here: check whether the conflict types a plan reduces match the main crash types at this intersection.

Software: VISSIM 5.30 student edition. Limits: network ≤ 1 km × 1 km, ≤ 600 s per run, ≤ 10 signal controllers, no pedestrians, no COM interface, and a watermark. Without COM, Python cannot drive VISSIM. But the .inp file is plain text. So a script generates the entire network.

Reasonableness check first

The improved plan passes. Motor-vehicle throughput is 96% of demand. None of the 12 turning movements has GEH > 5. The existing plan fails. Throughput is only 63%. 7 movements have GEH > 5, up to 17.4 on the Hangtian Avenue north-west left turn. 17 vehicles waited more than 60 s to change lanes and were removed. About 1/3 of demand never entered the intersection. So the comparison is biased in favor of the existing plan. Its measured disadvantage is a lower bound.

Delay

Average motor-vehicle delay fell from 62.7 to 38.5 s/veh (−39%, p < 0.001). At the same time, the improved plan served 52% more motor vehicles. Left-turn delay fell from 120–170 s to about 50 s. The cost is a small rise in delay for the north-east through movement on Shengli South Road.

Conflicts

Interpretation: protected left turns remove the main crash type at this intersection. Of 77 crashes, 42 were angle crashes, which match crossing conflicts. Crossing risk per vehicle falls by about four-fifths. Rear-end conflicts are over 90% of the total. They grow in step with throughput, so the rate per 1,000 vehicles stays the same. So signal phasing changes the type of conflict, not the rear-end exposure from queues. Reducing rear-end conflicts needs queue measures: longer left-turn bays, queue warning or coordinated control.