Organizations: Aix-Marseille University, CNRS, LIS, Marseille, France · Machine Learning Group, Université Libre de Bruxelles, Brussels, Belgium · WEL Research Institute, Wavre, Belgium · School of Computer Science, University of Leeds, UK
Urban traffic management relies on sensor networks whose spatial coverage is limited by deployment costs and privacy regulations. Machine learning models trained on such sparse data cannot generalize to unmonitored locations and must be retrained whenever the sensor infrastructure changes. We propose a simulation-based methodology that addresses this problem by generating augmented traffic count datasets in which each physical sensor is replaced by a virtual sensor placed at a surrogate location in the road network. Virtual sensors are selected by a graph-search heuristic that jointly maximises vehicle-flow continuity and traffic-metric similarity between the original and surrogate locations, while enforcing a minimum spatial displacement to ensure diversity of observed traffic conditions. We validate the method on two Belgian cities: Brussels, using a calibrated model, and Namur, using synthetic models. The augmented datasets preserve the bimodal daily demand profile and the dynamics of traffic at the observed locations.
Figures & tables
Figure 1: Example of traffic data augmentation on a part of the Brussels road network. Physical sensors (red) provide sparse coverage. Our method places virtual sensors (green) at locations with similar traffic dynamics within a limited topological distance, improving spatial coverage while preserving statistical consistency. Random placements (blue) may not capture representative traffic conditions.
Symbol
Description
E
Set of all edges in the road network (with and without physical sensors).
Es⊆E
Subset of edges equipped with physical sensors.
[hmin,hmax]
Integer interval bounding the hop distance of a virtual sensor from its paired physical sensor. Candidate locations closer than hmin hops are excluded as locally redundant; those beyond hmax hops are excluded as likely uncorrelated with the physical sensor.
dhop(e,e′)
Hop distance between two edges: the minimum number of directed edges traversed along any path from the downstream junction of e to the upstream junction of e′ . Returns 0 when e=e′ and +∞ when no directed path exists.
Tt(e,e′)
Simulated turn-count from edge e to adjacent downstream edge e′ during hourly interval t : the number of vehicles observed in simulation transitioning from e to e′ within interval t .
Mt(e)
Scalar traffic metric for edge e in interval t (e.g. average speed, travel time, or occupancy), as produced by the micro-simulation.
Table 1: Symbols and notation used in the proposed method.
Figure 2: Road networks of the two case-study Belgian cities. Only edges accessible to private vehicles are shown.
Hop Range
Simfree
Simbased
Avg #Hops
RMSE
STD
Avg #Hops
RMSE
STD
[1,5]
2.72
70.34
12.42
2.81
96.81
18.50
[1,10]
5.22
96.87
20.74
5.15
131.19
11.03
[3,10]
6.37
101.46
19.27
6.30
138.83
12.70
Table 2: Augmentation error by hop range, averaged over all (α,metric) combinations. Lower RMSE and standard deviation indicate better virtual sensors placement.
α
Metric
Simfree
Simbased
MAE
RMSE
Avg #Hops
MAE
RMSE
Avg #Hops
0.0
occupancy
22.7
59.4
3.00
43.4
118.5
3.06
speed
22.7
59.4
3.00
43.4
118.5
3.06
traveltime
22.5
55.0
3.23
41.5
117.2
3.11
0.2
occupancy
14.6
50.1
1.86
14.5
58.2
1.92
speed
17.4
53.5
2.24
20.7
71.0
2.26
Table 3: Augmentation error grouped by α and simulation metric for hop range [1,5] . Bold rows indicate the best configuration per strategy.
Figure 3: Average hourly vehicle count across all sensors for the input ground-truth, the simfree, and the simbased augmented models, at the best configuration ( α=0.2 , occupancy, hop range [1,5] ). Both augmented profiles reproduce the characteristic bimodal demand pattern of Brussels, with morning and evening peaks.
Figure 4: Distribution and cumulative percentage of the absolute count error per sensor (in vehicles per hour) between the augmented (simfree) and ground-truth datasets. The majority of sensor–interval pairs exhibit errors below 20 vehicles.
Figure 5: Spatial regions of 3000m2 used for the spatiotemporal error analysis.
Figure 6: Signed error (augmented − real) per spatial region and hour of day for the best simfree configuration ( α=0.2 , occupancy, hop range [1,5] ) for Brussels scenario. Negative values (dark blue) indicate underestimation; positive values (red to yellow) indicate overestimation.
Figure 7: Network-wide average speed (m/s) per hour for the input ground-truth, simfree and simbased augmented models for Brussels scenario.
Calibration
Hop Range
Proposed
QR-Pivot
Random
Simfree
[1,5]
70.34
172.43
170.99
[1,10]
96.87
173.72
181.45
[3,10]
101.46
87.67
83.48
Simbased
[1,5]
96.81
185.11
192.63
[1,10]
131.19
191.42
187.18
[3,10]
138.83
173.81
147.45
Table 4: RMSE for the proposed method and baseline placement strategies, across hop ranges and calibration strategies. Lower is better. The proposed method consistently outperforms both baselines for the two best-performing hop ranges [1,5] and [1,10] . Note that in Proposed column we refer to the results of the best configuration (hop range [1,5], α=0.2 , occupancy metric).
Demand
Metric
h1 – h2 : 1–5
h1 – h2 : 1–10
h1 – h2 : 3–10
50k
Occupancy
0.296±0.017 ( α =0.2)
0.521±0.020 ( α =0.2)
0.753±0.109 ( α =0.0)
Speed
0.231±0.020 ( α =0.2)
0.640±0.059 ( α =0.2)
0.660±0.013 ( α =0.0)
Travel time
0.558±0.084 ( α =1.0)
0.739±0.109 ( α =0.0)
0.815±0.111 ( α =0.0)
100k
Occupancy
0.287±0.023 ( α =0.2)
0.521±0.056 ( α =0.2)
0.681±0.076 ( α =0.0)
Speed
0.228±0.041 ( α =0.2)
0.604±0.068 ( α =0.2)
0.661±0.023 ( α =0.0)
Travel time
0.521±0.043 ( α =1.0)
0.728±0.147 ( α =0.0)
0.816±0.122 ( α =0.0)
Table 5: Best RMAE (mean ± std, lower is better) for each demand level and augmentation metric across the three evaluation windows (hop interval h1 – h2 ) for the Namur scenario, with the optimal α in parentheses. Bold highlights the best result per row.
Figure 8: Cumulative mean RMAE across the 30 independent runs for the three demand levels (50k, 100k, 150k vehicles).
Aix Marseille University, CNRS, LIS, Marseille, France · Université Libre de Bruxelles, Machine Learning Group, Brussels, Belgium · WEL Research Institute, Wavre, Belgium