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).
We propose a method for estimating time-varying traffic flow patterns from sparse aggregated vehicle counts. The method partitions the study area into spatial regions, constructs a set of feasible region-to-region routes, and solves a weighted least-squares optimization problem to determine the number of vehicles to allocate on each route. A weighted contribution matrix encodes sensor coverage, steering the optimizer toward flow configurations that are directly observable by sensors. Edge-level trajectories are then derived by scoring candidate routes against the temporal and volumetric profiles of aggregated regional sensor counts. The method is evaluated on the Brussels road network using real and synthetic traffic data. Results show that the proposed approach reproduces the daily traffic profile in the input data and outperforms the baseline methods at a fraction of the computational cost.
Davide Guastella, Gianluca Bontempi
Aix Marseille University, CNRS, LIS, Marseille, France · Université Libre de Bruxelles, Machine Learning Group, Brussels, Belgium · WEL Research Institute, Wavre, Belgium
Accurate measurement of traffic volumes and flows is vital for modern intelligent transportation. However, despite recent technological advances in sensor devices, it is still expensive to install and maintain fixed traffic counters. Therefore, it is restricted to a small portion of location points where the counters can be installed, which severely limits the possibility of grasping and predicting the total traffic volume at a city-wide level. By contrast, devices with location history such as smartphones and connected vehicles are now widely used and provide much wider spatial coverage. However, the data from these devices are usually partial and noisy, so they are not enough to directly estimate total traffic volumes and flows. In this paper, we use the information from these widely available devices to help decide where to place additional traffic counters, and we study how selecting new measurement locations can improve city-wide traffic estimation performance. To achieve this, we propose an algorithm that chooses additional counter locations to increase the diversity of observed traffic signal patterns, rather than simply spreading counters evenly over space. The goal is to capture traffic-pattern types that are rare in the current counter set and to make the collected observations more representative for later estimation and forecasting. We also present a real-world evaluation; in a target city, we select new locations expected to improve traffic prediction, and we then commissioned new field measurements at those locations at our expense. The resulting data led to an improvement in traffic volume estimation accuracy across different fidelities.
Masaaki Inoue, Akifumi Okuno, Shintaro Fukushima
1TOYOTA Motor Corporation · Institute of Statistical Mathematics · 3The Graduate University for Advanced Studies, SOKENDAI +1
Urban traffic simulation is a critical tool for infrastructure planning, including the placement of electric vehicle charging stations. However, realistic traffic simulation across many cities is hindered by two fundamental data limitations: detailed real-world traffic measurements are available for only a small fraction of road segments in most cities, and employment distribution data critical for modeling commuter traffic is rarely available at the resolution needed for simulation. This paper presents a genetic algorithm-based framework that directly addresses both limitations, calibrating urban traffic simulations from sparse road observations without requiring detailed job location data. Using the SUMO traffic simulation platform for Greensboro, North Carolina, our approach optimizes job distributions and gate-traffic parameters to align simulated traffic with a small sample of roads with known traffic-flow rates. We demonstrate that this approach produces simulated traffic that correlates well with real-world measurements, generalizes to road segments withheld from training, and produces job distributions that show promising qualitative agreement with census employment data despite never directly training on that employment data. This work demonstrates that realistic urban traffic simulation can be achieved from minimal real-world observations, offering a scalable and data-light approach to simulation calibration that reduces the barrier to deploying traffic models across diverse cities.
Hunter Sawyer, Jesse Roberts, Simon Matei
Department of Computer Science · Tennessee Technological University · Cookeville, TN