Chapter 17.3: SUMO-Canyon Coupling

17.3.1 Bridging Microsimulation and Canyon Physics

The key insight connecting SUMO (Chapter 17.1) with street canyon pollution (Module 16) is the spatial emission density. SUMO’s Floating Car Data (FCD) provides per-vehicle speed $v_i$ and acceleration $a_i$ at each timestep. These feed into HBEFA to produce individual emission rates $E_{\text{NOx}}(v_i, a_i)$. Aggregating over all vehicles on an edge of length $L_e$ gives the line source strength:

$$S_e(t) = \frac{1}{L_e} \sum_{i \in \text{edge}} E_{\text{NOx}}(v_i(t),\, a_i(t))$$

This $S_e(t)$ is the source term $q_L$ in the OSPM model (Chapter 16.2). Each street segment now has a time-varying pollution field driven by the actual traffic state.

17.3.2 Two-Way Feedback Loop

The coupling is not one-directional. When pollution concentrations are fed back into the MFG routing framework (Module 12), drivers reroute to avoid polluted streets. This changes the traffic distribution, which changes emissions, which changes concentrations:

$$\text{SUMO} \xrightarrow{v_i, a_i} \text{HBEFA} \xrightarrow{E_{\text{NOx}}} \text{OSPM} \xrightarrow{C_{\text{street}}} \text{MFG} \xrightarrow{\text{routes}} \text{TraCI} \xrightarrow{\text{reroute}} \text{SUMO}$$

The integration diagram connects all preceding modules:

┌──────────────────────────────────────────────────────────────┐
│                    Integration Architecture                    │
│                                                                │
│  OSMnx (Mod 6) ──→ netconvert ──→ SUMO (.net.xml)           │
│                                        │                      │
│                                    TraCI (TCP)                │
│                                    ↕        ↕                 │
│                              FCD output   Route updates       │
│                                 │              ↑              │
│                            HBEFA (17.1)   MFG Router (12)    │
│                                 │              ↑              │
│                           E_NOx(v,a)     Pollution cost       │
│                                 │              ↑              │
│                          OSPM (16.2) ──→ C_street(x,t)       │
│                                                               │
│  Signal Control (13) ──→ TraCI ──→ TLS updates               │
└──────────────────────────────────────────────────────────────┘

17.3.3 Traffic Load Scenarios

We analyse three traffic scenarios to understand how load affects canyon pollution:

Scenario	Flow (veh/hr)	Density (veh/km)	Mean Speed	Emission Factor
Light	200	5	40 km/h	1.0x
Moderate	800	30	25 km/h	1.8x
Congested	600 (capacity drop)	80	8 km/h	4.2x

The emission factor increase from light to congested is nonlinear because stop-and-go driving involves repeated high-acceleration events, each producing a spike in NOₓ emissions.

17.3.4 Signal Control Impact on Pollution

Three signal control strategies from Module 13 are compared by their pollution outcomes:

Fixed-time: pre-set green splits, no adaptation. Produces predictable but suboptimal emission patterns.
Actuated: extends green based on detector occupancy. Reduces idling at low-demand approaches, cutting emissions by 10–20%.
PMP (Pontryagin): optimal control from Module 13 with pollution-augmented cost. Can reduce peak concentrations by 25–40% through coordinated green waves.

The key mechanism: green waves reduce the number of stop-start cycles. Each avoided stop eliminates one acceleration event, preventing the associated emission spike.

17.3.5 Mean-Field Limit: Krauss to LWR

As the number of vehicles $N \to \infty$, the Krauss car-following model converges to the Lighthill-Whitham-Richards (LWR) macroscopic model from Module 10. The correspondence is:

$$\text{Krauss: } v_i(t+\Delta t) = \min(v_{\max}, v_{\text{safe},i}) \quad \xrightarrow{N \to \infty} \quad \text{LWR: } \frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x}[\rho \, V(\rho)] = 0$$

The equilibrium speed-density relation $V(\rho)$ of the LWR model is the deterministic limit of the Krauss safe-velocity function. Setting $\sigma = 0$ (no dawdling) and computing the equilibrium spacing at each speed:

$$s_{\text{eq}}(v) = v\,\tau + \frac{v^2}{2b} + s_0 \quad \Longrightarrow \quad \rho(v) = \frac{1}{L_{\text{veh}} + s_{\text{eq}}(v)}$$

This provides a rigorous bridge between the microscopic SUMO simulation and the macroscopic PDE models used in Modules 10–12.

17.3.6 Python: SUMO-Canyon Coupling Simulation

SUMO-Canyon Coupling: Emissions, OSPM, Signal Control

Python

script.py200 lines

import numpy as np
import matplotlib.pyplot as plt

# ─── SUMOCanyonCoupling class ───
class SUMOCanyonCoupling:
    """Simulates the SUMO-OSPM coupling for a single street segment."""

def __init__(self, H=20, W=20, L=200, u_H=5.0):
        self.H = H
        self.W = W
        self.L = L
        self.u_H = u_H
        self.alpha = H / W
        self.kappa = 0.41
        self.C_D = 0.005
        self.C_B = 25.0  # background NO2 (ug/m3)

# Vortex velocity
        self.u_v = self.C_D * u_H / ((1 + self.alpha) * self.kappa)

def hbefa_nox(self, speed, accel):
        """Simplified HBEFA NOx emission (mg/s) for a single vehicle."""
        # Normalised power
        m = 1400  # kg (passenger car)
        c_r = 0.01
        c_d = 0.3
        A_f = 2.2  # m^2
        rho_air = 1.225
        g = 9.81

F_roll = c_r * m * g
        F_air = 0.5 * rho_air * c_d * A_f * speed**2
        F_accel = m * max(accel, 0)  # only positive for emission
        P_norm = speed * (F_roll + F_air + F_accel) / 100000  # normalised

# Emission map (simplified piecewise)
        if P_norm < 0:
            return 0.5  # idle
        elif P_norm < 0.3:
            return 0.5 + 5.0 * P_norm
        else:
            return 2.0 + 8.0 * P_norm  # high load

def emission_density(self, vehicles):
        """Compute S_e (mg/m/s) from list of (speed, accel) tuples."""
        if not vehicles:
            return 0.0
        total = sum(self.hbefa_nox(v, a) for v, a in vehicles)
        return total / self.L

def ospm_concentration(self, S_e):
        """OSPM model: returns NO2 concentration in ug/m3."""
        q_L = S_e * 1e-3  # convert mg to g

# Direct component
        sigma_w = 0.8
        u_s = max(self.u_v * 0.5, 0.3)
        C_D_conc = (q_L / (np.sqrt(2*np.pi) * sigma_w * u_s)) * 1e6

# Recirculation
        L_R = min(self.W, self.H)
        C_R = (q_L * L_R / (self.u_v * self.W * self.H)) * 2.0 * 1e6

return C_D_conc + C_R + self.C_B

def who_threshold_check(self, concentration):
        """Check against WHO guidelines."""
        if concentration > 40:
            return "EXCEEDS WHO (40 μg/m³)"
        elif concentration > 25:
            return "Exceeds WHO 24h (25 μg/m³)"
        else:
            return "Within limits"

# ─── Simulate three traffic scenarios ───
np.random.seed(42)
dt = 1.0  # s
T_sim = 600  # 10 minutes
time = np.arange(0, T_sim, dt)

scenarios = {
    "Light (200 veh/hr)": {"n_veh": 11, "mean_speed": 11.1, "speed_std": 2.0, "accel_std": 0.5},
    "Moderate (800 veh/hr)": {"n_veh": 44, "mean_speed": 6.9, "speed_std": 3.0, "accel_std": 1.5},
    "Congested (capacity)": {"n_veh": 80, "mean_speed": 2.2, "speed_std": 2.0, "accel_std": 2.5},
}

canyon = SUMOCanyonCoupling(H=20, W=20, L=200)
results = {}

for name, params in scenarios.items():
    S_e_series = []
    C_series = []

for t_step in time:
        n = params["n_veh"]
        speeds = np.maximum(0, np.random.normal(params["mean_speed"], params["speed_std"], n))
        accels = np.random.normal(0, params["accel_std"], n)
        vehicles = list(zip(speeds, accels))

S_e = canyon.emission_density(vehicles)
        C = canyon.ospm_concentration(S_e)
        S_e_series.append(S_e)
        C_series.append(C)

results[name] = {
        "S_e": np.array(S_e_series),
        "C": np.array(C_series)
    }

# ─── Figure 1: Emission density and concentration time series ───
fig, axes = plt.subplots(2, 1, figsize=(14, 8))
fig.patch.set_facecolor("#0f172a")

colors = {"Light (200 veh/hr)": "#22c55e", "Moderate (800 veh/hr)": "#eab308", "Congested (capacity)": "#ef4444"}

for name, data in results.items():
    axes[0].plot(time, data["S_e"], color=colors[name], linewidth=1.5, alpha=0.8, label=name)
    axes[1].plot(time, data["C"], color=colors[name], linewidth=1.5, alpha=0.8, label=name)

axes[0].set_ylabel("Emission Density S_e (mg/m/s)", color="white", fontsize=12)
axes[0].set_title("SUMO → HBEFA Emission Density", color="white", fontsize=13, fontweight="bold")
axes[1].set_ylabel("NO₂ Concentration (μg/m³)", color="white", fontsize=12)
axes[1].set_xlabel("Time (s)", color="white", fontsize=12)
axes[1].set_title("OSPM Street-Level Concentration", color="white", fontsize=13, fontweight="bold")

# WHO limits
axes[1].axhline(40, color="#ef4444", linestyle="--", alpha=0.7, linewidth=1, label="WHO annual (40 μg/m³)")
axes[1].axhline(25, color="#f59e0b", linestyle="--", alpha=0.7, linewidth=1, label="WHO 24h (25 μg/m³)")

for ax in axes:
    ax.legend(fontsize=9, facecolor="#1e293b", edgecolor="#334155", labelcolor="white")
    ax.set_facecolor("#0f172a")
    ax.tick_params(colors="gray")
    ax.grid(True, alpha=0.2, color="#334155")
    for spine in ax.spines.values():
        spine.set_color("#334155")

plt.tight_layout()
plt.savefig("output.png", dpi=120, bbox_inches="tight", facecolor="#0f172a")
plt.close()

# ─── Figure 2: Signal control comparison ───
fig2, ax = plt.subplots(1, 1, figsize=(12, 6))
fig2.patch.set_facecolor("#0f172a")

# Simulated concentration reductions from signal control
base_C = results["Moderate (800 veh/hr)"]["C"].mean()
controls = {
    "Fixed-Time": {"factor": 1.0, "color": "#94a3b8"},
    "Actuated": {"factor": 0.85, "color": "#eab308"},
    "PMP (Module 13)": {"factor": 0.65, "color": "#10b981"},
}

x_pos = np.arange(len(controls))
bars = ax.bar(x_pos, [base_C * c["factor"] for c in controls.values()],
              color=[c["color"] for c in controls.values()], width=0.5, edgecolor="#1e293b", linewidth=2)
ax.axhline(40, color="#ef4444", linestyle="--", linewidth=1.5, label="WHO limit")
ax.set_xticks(x_pos)
ax.set_xticklabels(controls.keys(), color="white", fontsize=11)
ax.set_ylabel("Mean NO₂ (μg/m³)", color="white", fontsize=12)
ax.set_title("Signal Control Impact on Canyon Pollution (Moderate Traffic)", color="white", fontsize=13, fontweight="bold")
ax.legend(fontsize=10, facecolor="#1e293b", edgecolor="#334155", labelcolor="white")
ax.set_facecolor("#0f172a")
ax.tick_params(colors="gray")
ax.grid(True, alpha=0.2, color="#334155", axis="y")
for spine in ax.spines.values():
    spine.set_color("#334155")

# Annotate bars
for bar, (name, ctrl) in zip(bars, controls.items()):
    val = base_C * ctrl["factor"]
    reduction = (1 - ctrl["factor"]) * 100
    ax.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.5,
            f"{val:.1f} μg/m³\n(-{reduction:.0f}%)", ha="center", va="bottom",
            color="white", fontsize=10)

plt.tight_layout()
plt.savefig("output.png", dpi=120, bbox_inches="tight", facecolor="#0f172a")
plt.close()

# ─── Summary ───
print("=== SUMO-Canyon Coupling Results ===")
print(f"Canyon: H={canyon.H}m, W={canyon.W}m, α={canyon.alpha:.1f}, L={canyon.L}m")
print(f"Wind: u_H={canyon.u_H} m/s, u_v={canyon.u_v:.4f} m/s\n")

for name, data in results.items():
    C_mean = data["C"].mean()
    C_max = data["C"].max()
    status = canyon.who_threshold_check(C_mean)
    print(f"─── {name} ───")
    print(f"  Mean S_e: {data['S_e'].mean():.3f} mg/m/s")
    print(f"  Mean C:   {C_mean:.1f} μg/m³  ({status})")
    print(f"  Max  C:   {C_max:.1f} μg/m³")
    print(f"  Time > WHO (40): {(data['C'] > 40).mean()*100:.1f}%")
print()
print("─── Signal Control (Moderate Traffic) ───")
for name, ctrl in controls.items():
    val = base_C * ctrl["factor"]
    print(f"  {name:>20s}: {val:.1f} μg/m³ ({(1-ctrl['factor'])*100:.0f}% reduction)")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

17.3.7 Key Takeaways

SUMO FCD provides (v, a) per vehicle, which HBEFA converts to emission rates; spatial aggregation gives the OSPM line source strength $S_e = (1/L_e)\sum E_{\text{NOx}}$.
The two-way feedback loop (emissions → MFG rerouting → TraCI → emissions) creates a coupled system where traffic and pollution co-evolve.
Congested traffic produces 4x the emissions of light traffic due to stop-and-go acceleration events.
PMP signal control from Module 13 can reduce peak canyon concentrations by 25–40% by smoothing traffic flow and reducing acceleration events.
In the mean-field limit ($N \to \infty$), Krauss car-following converges to LWR (Module 10), providing a rigorous micro-macro bridge.

← OSMnx → SUMO Pipeline Module 18: Integration Architecture →