This web page was created programmatically, to learn the article in its authentic location you may go to the hyperlink bellow:
https://journals.plos.org/plosone/article%3Fid%3D10.1371/journal.pone.0345576
and if you wish to take away this text from our web site please contact us
Abstract
Accurate visitors quantity prediction is crucial for managing congestion, enhancing highway security, mitigating environmental impacts, and supporting long-term transportation planning. The conventional four-step journey demand mannequin (FSM) is a well-established framework, however it depends on static survey information, substantial calibration effort, and simplified behavioural assumptions that will not adequately seize advanced journey patterns. In distinction, data-driven fashions are able to studying nonlinear relationships from massive datasets, but they’re usually designed for short-term forecasting and sometimes don’t goal the long-term, segment-level quantity estimation duties required for strategic planning. This examine proposes Mukara, a deep studying framework that instantly approximates the mapping from exterior socioeconomic and community options to noticed visitors volumes on freeway trunk highway segments. The mannequin is educated on eight years of knowledge from England and Wales and incorporates inhabitants, employment, land use, highway community traits, and factors of curiosity as inputs. Mukara achieves a imply GEH of fifty.74, a imply absolute error of 8,989 autos per day, and an R2 of 0.583 underneath random cross-validation, outperforming baseline fashions and current research underneath comparable settings. Under a extra stringent region-based spatial cross-validation scheme, efficiency stays sturdy, demonstrating robust spatial transferability. Ablation experiments additional exhibit the robustness of the proposed structure and reveal the relative significance of various enter function teams for prediction.
Citation: Li Y, Chen S, Jin Y (2026) Mukara: A deep studying different to the four-step journey demand mannequin with a case examine on interurban freeway visitors prediction within the UK. PLoS One 21(4):
e0345576.
https://doi.org/10.1371/journal.pone.0345576
Editor: Gianluca Genovese, University of Salerno: Universita degli Studi di Salerno, ITALY
Received: April 29, 2025; Accepted: March 6, 2026; Published: April 16, 2026
Copyright: © 2026 Li et al. This is an open entry article distributed underneath the phrases of the Creative Commons Attribution License, which allows unrestricted use, distribution, and copy in any medium, supplied the unique creator and supply are credited.
Data Availability: All python scripts and recordsdata can be found from the GitHub repository https://github.com/yueli901/mukara.
Funding: The creator(s) obtained no particular funding for this work.
Competing pursuits: The authors have declared that no competing pursuits exist.
Introduction
Traffic prediction performs a pivotal function in addressing vital challenges corresponding to lowering congestion, mitigating carbon emissions and air pollution, and enhancing highway security and public well being [1–5]. In the United Kingdom, highway transport is the predominant mode of journey, accounting for 86% of all passenger kilometres in 2022 [6]. This development is per many OECD international locations, the place highway transport equally dominates passenger journey [7]. Simultaneously, automobile possession is quickly growing within the Global South, with projections indicating that by 2030, 56% of the world’s autos shall be owned by non-OECD international locations, in comparison with 24% in 2002 [8]. A sturdy visitors prediction system may also help travellers plan routes successfully, help visitors operators in knowledgeable decision-making, and improve total visitors administration effectivity [9].
Despite developments in visitors prediction, analysis has predominantly targeted on city visitors, leaving interurban visitors networks comparatively underexplored [10]. Interurban settings, nonetheless, current a novel alternative for testing novel visitors prediction fashions as a result of abundance of high-quality information and the comparatively decrease complexity of visitors patterns in comparison with city areas. Urban visitors is commonly influenced by localised elements corresponding to pedestrian exercise, public transit techniques, and extremely variable demand patterns, making it noisier and more difficult to mannequin. In distinction, interurban visitors information sometimes displays extra steady and predictable patterns, making it ultimate for evaluating the feasibility of modern approaches like Mukara.
As proven in Table 1, visitors prediction has historically relied on two fundamental approaches: the four-step journey demand mannequin (FSM) and deep learning-based fashions. The FSM has lengthy served as a foundational framework in transportation planning [11]. It decomposes journey behaviour into journey era and attraction, journey distribution, mode alternative, and visitors project. A concise overview of the FSM construction and its sequential elements is supplied in Appendix S1 (S1 File). In precept, the FSM supplies a transparent mapping from zonal socioeconomic inputs to an origin-destination (OD) matrix after which to link-level flows. Its modular construction and behavioural grounding have made it a cornerstone of planning follow for many years. In follow, nonetheless, FSM implementations usually depend on restrictive practical varieties and oversimplified assumptions. The sequential construction of the FSM additionally treats its steps as largely unbiased, regardless that vacation spot alternative, mode alternative, and route alternative are intently interrelated in actuality [12]. As a consequence, FSM-based workflows sometimes require repeated calibration of the OD matrix and project parameters, which is labour-intensive and more and more tough at massive spatial scales or underneath novel planning eventualities [13]. A case examine in Istanbul discovered large discrepancies between each day visitors predicted by FSM and the precise noticed each day visitors quantity [14].
On the opposite hand, deep studying fashions have emerged as highly effective alternate options because of their capacity to mannequin advanced spatial-temporal dependencies in visitors information [10,15]. Architectures corresponding to Convolutional Neural Networks (CNNs) [16], Recurrent Neural Networks (RNNs) [17], Long Short-Term Memory networks (LSTMs) [18], and Gated Recurrent Units (GRUs) [19] have considerably improved the modelling of temporal developments, whereas current developments like Transformers [20], Graph Neural Networks (GNNs) [21], and Graph Attention Networks (GATs) [22] additional allow spatial reasoning inside graph-structured networks. State-of-the-art fashions corresponding to ST-ResInternet [23], DCRNN [24], ConvLSTM [25], PFNet [26], and STGAT [27] incorporate these methods to supply extremely correct short-term predictions. However, most of those fashions deal with visitors prediction as a time-series forecasting process based mostly on historic sensor readings. As such, their outputs usually replicate patterns seen previously slightly than insights into the determinants of visitors dynamics. This is illustrated in current work corresponding to ST-MetaInternet [28,29], the place the predictions strongly mirror enter developments. While some fashions incorporate exterior options corresponding to factors of curiosity (POIs), highway varieties, and occasion information [23,30], these are sometimes used as auxiliary inputs slightly than as main determinants.
Motivated by these limitations, current research have explored machine studying fashions as alternate options for particular person steps of the FSM. Deep studying–based mostly gravity fashions have been proposed as predictive alternate options to conventional journey distribution formulations, instantly estimating OD flows from zonal attributes [31]. Other work has targeted on zone-to-zone journey demand forecasting utilizing data-driven fashions [32], mode alternative prediction utilizing machine studying classifiers [33], or approximating visitors project and equilibrium behaviour utilizing graph neural networks [34]. These research exhibit that machine studying can enhance flexibility and predictive efficiency for particular elements of the demand modelling pipeline. However, most current approaches deal with approximating particular person elements of the FSM in isolation, are sometimes tough to interpret, and infrequently produce link-level visitors volumes in a totally built-in and scalable method.
These observations spotlight complementary strengths and limitations throughout modelling paradigms. FSM presents interpretability and theoretical construction however might be restricted in flexibility, scalability, and calibration effectivity. Data-driven fashions provide the potential to enhance prediction accuracy by uncovering non-linear relationships and leveraging various information sources, however they’re usually not designed for long-term planning functions and infrequently goal full segment-level demand estimation. There stays a necessity for a modelling framework that preserves the strategic planning orientation of the FSM whereas leveraging trendy machine studying to instantly estimate segment-level visitors volumes.
In this examine, we suggest Mukara, a deep studying framework that approximates the mixture relationship between exterior demand-related and community options and noticed freeway visitors volumes. The goals are threefold: (1) to develop a data-driven mannequin that instantly estimates national-scale freeway visitors volumes from socioeconomic traits and highway community construction; (2) to judge its predictive efficiency and spatial generalisability by benchmarking it in opposition to baseline fashions; and (3) to look at the contribution of various function teams to prediction accuracy via ablation evaluation. We title our mannequin “Mukara”, derived from the Japanese time period which means “from nothing”, reflecting its goal of predicting visitors with out counting on historic sensor readings.
Materials and strategies
Overview
We now introduce the workflow of this examine. First, we assemble a freeway trunk highway community, the place the graph construction encodes connectivity data related to journey distribution throughout OD pairs. Each highway section is enriched with attributes corresponding to driving distance and driving period, which correspond to the generalised journey price inputs sometimes used within the project step of FSM. Next, we combine rasterised geographic datasets together with inhabitants density, employment statistics, land use areas, the variety of numerous forms of POIs, and aggregated measures of native highway infrastructure. These inputs serve to approximate key components of journey era and mode alternative, capturing the spatial and socioeconomic determinants of journey demand which can be historically modelled utilizing regression and discrete alternative fashions inside FSM [11]. They have additionally been proven to be basic determinants of journey demand throughout the broader transport and concrete economics literature, constantly shaping journey frequencies, spatial interplay patterns, and community flows [35–38]. Ground fact visitors quantity information is aligned with corresponding highway segments to allow supervised studying.
Mukara is educated utilizing sensor-labelled highway segments within the coaching set and evaluated on spatially distinct check segments to evaluate spatial generalisability. By structuring inputs across the core elements of FSM and studying end-to-end mappings to noticed visitors volumes, Mukara supplies a data-driven predictive approximation of the general demand-to-flow course of with out explicitly modelling intermediate behavioural levels. Fig 1 illustrates the entire methodological pipeline. Table 2 is a abstract of all symbols used on this examine. Table 3 supplies a abstract of all information sources, together with the supply company, time protection, spatial decision, and meant utilization inside the examine.
Data
Highway community.
To examine interurban visitors dynamics, a freeway community graph overlaying your complete area of England was constructed based mostly on the National Highways Strategic Road Network [39]. This graph serves because the spine for data propagation in Mukara. The community consists of 181 nodes (), representing freeway trunk highway junctions, sometimes situated close to main cities, and 498 edges (
), akin to 249 freeway trunk highway segments in each instructions. Each edge is assigned a sensor from the National Highway Traffic Information System (TRIS) [40], leading to a complete of 498 sensors. Nodes and edges have been chosen to seize visitors stream alongside trunk roads connecting main cities and cities, whereas avoiding bypasses and freeway exits. Details of the sensor choice process and the representativeness analysis of the chosen sensors are included in Appendix S2-S3 (S1 File).
Features on freeway trunk highway segments in each instructions have been collected utilizing the Google Routes Application Programming Interface (API). The extracted edge options embody driving period, driving distance, straight-line distance, common driving pace, and detour issue. Together, these edge options, , are structured right into a tensor with dimensions
, the place
is the full variety of edges and
is the variety of options. All edge options are normalised earlier than being enter into the mannequin. Fig 2 supplies a visible abstract of the distributions of those edge options.
Population and employment.
Population information was sourced from the Population Estimates – Small Area dataset [41], supplied by the Office for National Statistics (ONS) via the National Online Manpower Information System (NOMIS) service. This dataset supplies annual inhabitants estimates for England and Wales on the Lower Layer Super Output Area (LSOA) stage, stratified by age group and intercourse. Employment information was obtained from the Business Register and Employment Survey (BRES) [42], additionally supplied by ONS via NOMIS. This dataset contains employment counts, overlaying full-time, part-time, and self-employed staff throughout all industries inside England and Wales.
For each datasets, information from the years 2015–2022 have been chosen. The LSOA-based information was rasterised right into a 1 km x 1 km grid utilizing LSOA boundaries supplied by ONS [43,44]. This course of resulted in a grid tensor with dimensions
, the place
is the variety of years,
and
are the peak and width of the grid, and
represents the variety of grid channels for inhabitants and employment.
To account for variations in journey behaviour throughout demographic teams, separate channels have been created for inhabitants and employment strata. The enter information have been stratified accordingly, and Table 4 summarises the ensuing enter channels. In every coaching process, all channels or a subset of those channels have been chosen to analyse the mannequin’s efficiency underneath completely different ranges of stratification of the enter information. Fig 3 visualises the aggregated inhabitants and employment information in 2022 as warmth maps.
Land use, highway community, and POI.
Land use, highway community, and POI information have been sourced from OpenStreetMap (OSM) and downloaded by way of Geofabrik’s free obtain server [45]. The information have been extracted from a historic snapshot of the England subregions and Wales .osm.pbf recordsdata with the timestamp 2023-01-01. This static snapshot was chosen for all years from 2015 to 2022 to make sure consistency and completeness, as land use and POI information are comparatively steady over time. To assess robustness to OSM information classic, we carried out a further sensitivity evaluation utilizing another historic OSM snapshot (timestamp: 2019-01-01), chosen to be temporally nearer to the early portion of the examine interval. Results of this evaluation are reported in Appendix S4 (S1 File).
The tags used to extract the info are summarised in Table 5. These embody land use classifications (e.g., residential, industrial), highway community hierarchies from high-level motorways to low-level residential roads, and a various set of POI classes corresponding to transport, meals, well being, schooling, and retail services. The collection of these tags was based mostly on the Deep Gravity mannequin [31] and their availability within the OSM database.
For every grid cell, the next metrics have been calculated: complete space of every land use kind, complete size of roads for every hierarchical stage, and complete variety of POIs for every class. These metrics have been then aggregated right into a grid tensor, , with dimensions
, the place
and
signify the peak and width of the grid, and
is the variety of grid channels akin to the land use and POI classes. Fig 4 visualises these options as warmth maps. To assemble the ultimate grid options
, the tensor
was broadcast on the time axis leading to
, which was then concatenated with the inhabitants and employment tensor
alongside the channel dimension:
.
Traffic quantity.
The floor fact visitors quantity information have been sourced from the Traffic Information System (TRIS), managed by National Highways [47]. TRIS supplies complete information on visitors pace and quantity, collected in 15-minute intervals utilizing loop sensors. Across England, 19,364 sensors are built-in into this community, which has been operational since 2014. The information used on this examine have been accessed and downloaded via the API supplied by TRIS [40].
To align the visitors quantity information with the enter options, we used 8 years of visitors quantity data from 1 January 2015 to 31 December 2022, for every of the 498 sensors included within the established freeway community. The imply weekday each day visitors quantity was calculated for every year and every sensor to generate the bottom fact tensor , with dimensions
. Weekends and financial institution holidays are excluded to deal with common visitors patterns. A sensitivity evaluation of together with weekends and holidays is supplied in Appendix S5 (S1 File). This mean-based aggregation serves to clean out each day variability and scale back noise brought on by anomalous or irregular visitors days. The ensuing common displays the everyday structural demand for freeway utilization underneath regular situations, aligning with the planning-level nature of our examine. Fig 5 reveals a histogram of the typical visitors volumes throughout the 498 sensors over the 8-year interval, illustrating the variability in visitors ranges. Fig 6 supplies a spatial visualisation of those volumes, averaged over each instructions.
Mukara mannequin
The aim of the Mukara mannequin is to foretell weekday each day visitors volumes for all freeway segments in a given yr, utilizing solely exterior options. The mannequin leverages three main inputs: the graph construction of the freeway community, edge-level traits, and grid-based contextual options for the corresponding yr. The prediction process for yr t is formally outlined as:
the place denotes the set of predicted visitors volumes for all edges in yr t;
represents the freeway community graph, the place
is the set of nodes and
is the set of directed edges;
is the set of uncooked function vectors for every edge
; and
is the rasterised grid-based enter tensor for yr t. For notational simplicity, we omit the time subscript t within the the rest of this part the place the context is evident.
To effectively move data from inputs to outputs, the Mukara mannequin consists of two fundamental constructing blocks: a CNN block for processing spatial grid options, and a GAT block for capturing topological and relational data from the community. An overview of those blocks is supplied in Figs 7 and 8.
Fig 7. A visual representation of the CNN block in the Mukara model.
The block processes grid features () by extracting regions of interest (ROIs) around each node, applying convolutional and pooling layers, and generating node embeddings (
) for subsequent graph attention processing.
Fig 8. An overview of the GAT block in the Mukara model.
Initial node embeddings () are refined through multiple GAT layers, incorporating edge embeddings (
). The final embeddings are concatenated and passed through an MLP to predict traffic volumes for edges. Solid and dashed lines represent training and test edges, respectively.
The CNN block is accountable for processing the grid options to generate node-specific embeddings by extracting and encoding data from a fixed-size Region of Interest (ROI) centred round every node. CNNs are significantly appropriate for this process, as they not solely flatten the grid right into a usable vector but in addition extract wealthy spatial patterns (e.g., density gradients, clustering results) which can be usually misplaced in easy aggregations. This permits extra nuanced illustration of native environmental context. For every node
, its geographic coordinates are used to find the corresponding centre pixel in
. A sq. ROI of fastened measurement that’s aligned with the pixel grid and centred at this location is extracted to signify the spatial context across the node. If the ROI extends past the boundaries of the grid, zero-padding is utilized to take care of constant enter dimensions. The ROI measurement, outlined in pixel models, corresponds to a real-world spatial space (e.g., 25 km × 25 km) and is handled as a tunable hyperparameter. The extracted ROIs are additionally three-dimensional tensors, with the primary two dimensions representing the spatial extent (peak and width), and the third dimension representing the variety of function channels in
.
Each ROI is handed via a sequence of convolutional layers with depth LCNN, adopted by Rectified Linear Unit (ReLU) activations and max-pooling operations. The closing convolutional output is flattened right into a one-dimensional vector, producing the preliminary node embedding . The complete CNN transformation might be expressed as:
the place is the preliminary embedding of node
produced by the CNN block; LCNN is the variety of convolutional layers, ∘ denotes operate composition; and
is the area of curiosity centred at node
extracted from the grid enter
.
This preliminary node embedding captures the spatial and socioeconomic context surrounding every node, which is expounded to the journey era course of, and serves as the place to begin for graph-based reasoning.
Following the CNN block, the GAT block refines the node embeddings by integrating data from neighbouring nodes and the attributes of the connecting edges. Each edge embedding is generated by making use of a Multi-Layer Perceptron (MLP) to the uncooked edge function vector
:
the place is the uncooked function vector related to edge
, and
denotes the shared edge embedding layer utilized throughout all edges. The output of this layer is the sting embedding
.
The GAT block operates over a number of layers, every performing an attention-based message passing step. At every layer l, the node embeddings are up to date by attending to their neighbours and the options of the connecting edges, based mostly on the graph construction:
the place is the embedding of node
at layer l;
is the embedding from the earlier layer;
is the embedding of the sting connecting
and its neighbour
; and
is the enter graph. The operate
represents the graph consideration operation of the l-th GAT layer.
The consideration mechanism computes unnormalised scores that quantify the significance of node
to node
, based mostly on their respective embeddings and the sting connecting them:
the place and
are learnable linear projection matrices utilized to node and edge embeddings, respectively;
is a learnable consideration vector; and
denotes vector concatenation. To explicitly incorporate edge data, the sting embedding
is included within the consideration mechanism. This permits the mannequin to modulate consideration weights not solely based mostly on node content material but in addition on attributes of the sting (e.g., distance, pace, or detour issue), that are extremely related for visitors stream. As a consequence, the edge-aware consideration improves the flexibility of the mannequin to seize significant spatial interactions within the freeway community. For readability, we omit the eye head index ok within the notation for
and
, though in follow, separate units of consideration parameters are discovered for every of the Okay consideration heads at every layer.
Within every layer, the eye coefficients are computed by normalising the eye scores
throughout the neighbouring nodes
of node
:
Using these consideration coefficients, every node updates its embedding for consideration head ok by aggregating the remodeled embeddings of its neighbours:
the place denotes a non-linear activation operate corresponding to ReLU, and
indexes completely different consideration heads.
The outputs from all Okay consideration heads are concatenated and handed via a MLP to supply the up to date embedding for node at layer l:
The GAT block sequentially updates node embeddings by calculating consideration scores, normalising these scores, and aggregating neighbour data throughout LGAT layers. By the tip of the method, the node embeddings encapsulate each native contexts and wider community data.
Finally, visitors quantity predictions for every edge are obtained by concatenating the ultimate embeddings of the origin node (), the vacation spot node (
), and the sting embedding (
), and passing the consequence via a prediction MLP:
This structured design permits Mukara to successfully seize spatial, relational, and feature-based dependencies, resulting in correct predictions of visitors volumes throughout the freeway community.
Model coaching and experimental settings
Loss operate and analysis metrics.
The Mukara mannequin is educated utilizing the imply of the Geoffrey E. Havers (GEH) statistic [48]—hereafter known as MGEH—a metric extensively used to judge the goodness-of-fit of visitors fashions. The GEH statistic accounts for each absolutely the distinction and the share distinction between the modelled and noticed flows, making it significantly appropriate for visitors quantity prediction duties. Unlike the generally used Mean Squared Error (MSE), GEH emphasises proportionality, permitting errors to be evaluated relative to the magnitude of the noticed volumes. A current examine has proven that the GEH loss operate is constant and outperforms Mean Absolute Error (MAE) and MSE normally [49].
The GEH statistic for a person edge is outlined as:
the place is the noticed visitors quantity and
is the anticipated visitors quantity for edge
. The time subscript t on this equation and the equations for MAE and MSE are omitted for simplicity.
For analysis, along with MGEH, we report the Mean Absolute Error (MAE) and the coefficient of dedication R2. MAE, MSE, and the coefficient of dedication R2 are outlined as follows:
the place denotes the imply noticed visitors quantity throughout all evaluated edges.
The MGEH loss operate used for coaching is the imply of the GEH statistics throughout all edges:
To assess the robustness of this alternative of goal operate, we carried out a loss-function sensitivity evaluation (Appendix S6, S1 File), during which Mukara was re-trained utilizing different goals (MSE, MAE, and Huber loss) underneath the identical spatially blocked cross-validation protocol. The outcomes point out that combination predictive efficiency stays broadly constant throughout loss specs.
Training algorithm.
Model coaching and analysis have been carried out utilizing each random cross-validation (CV) and spatial CV. For CV, a five-fold scheme was adopted. In every iteration, one fold was held out because the check set, whereas the remaining 4 folds have been used for mannequin coaching. This course of was repeated 5 occasions so that every subset served because the check set as soon as. For spatial CV, the 498 freeway trunk-road segments have been grouped in accordance with the 9 official areas of England. A nine-fold spatial CV process was then applied, during which all segments inside one area have been held out because the check set in every fold, whereas the remaining eight areas constituted the coaching set. Ground truths for segments within the check area have been used completely for analysis and weren’t accessed throughout mannequin coaching. This analysis design is per the examine’s goal of assessing the feasibility of predicting visitors volumes for geographically unobserved freeway segments, thereby offering a stringent check of spatial transferability.
As proven in Algorithm 1, the coaching course of entails iteratively deciding on one yr of grid options from the coaching information, performing a ahead move to make predictions, calculating the loss to measure prediction errors, and conducting a backward move to compute gradients. The parameters are up to date after every batch, and this cycle is repeated for a predefined variety of epochs. While utilizing your complete yr of coaching samples as a batch is kind of computationally beneficiant, it ensures that the mannequin learns from all sensors concurrently. Experiments confirmed that this method achieves decrease loss in comparison with splitting the samples into smaller batches.
Algorithm 1 Training algorithm for the Mukara mannequin
Input: Highway community graph , edge options
, grid options
.
Output: Predicted visitors volumes .
1: Split sensors into 5 folds, and choose one fold because the check set.
2: Initialise mannequin parameters .
3: for epoch = 1 to Nepochs do
4: for every year t in coaching information do
5: Extract grid options from
.
6: Extract floor fact visitors volumes from
for all sensors.
7: Perform a ahead move via the Mukara mannequin:
8: Compute the coaching loss:
9: Compute gradients: .
10: Update parameters utilizing gradient descent with studying charge :
11: finish for
12: finish for
13: Return: Trained Mukara mannequin and predicted visitors volumes .
Experimental settings.
For the default grid options, we use aggregated inhabitants, aggregated employment, all land use, highway community, and POI options, leading to a complete of channels for the grid tensor. The default mannequin hyperparameters are as follows: The ROI measurement is ready to 25, akin to 25 km, which covers typical spatial extents of small to medium-sized UK cities and aligns with noticed city exercise ranges corresponding to commuting distances and financial catchment areas. This alternative ensures that the mannequin captures adequate spatial context with out introducing extreme noise from distant, unrelated areas. The CNN block consists of LCNN = 3 layers with channel sizes of 16, 32, and 64 for every layer. The kernel measurement is ready to three, strides are set to 1, and max pooling is utilized with a pool measurement of two and strides of two, successfully lowering spatial dimensions whereas preserving related function patterns. The output dense layer of the CNN block, which additionally serves because the node embedding measurement within the GAT block, is ready to 16 to stability representational capability and computational effectivity. The GAT block consists of LGAT = 5 layers, every using 3 consideration heads to seize various relational patterns amongst neighbouring nodes and edges. All MLPs used within the mannequin have a hidden measurement of 16 with ReLU because the activation operate and an output measurement of 16. Each batch corresponds to at least one yr of knowledge; subsequently, there are 8 batches in a single epoch.
Training is carried out utilizing the Adam optimiser with a studying charge of 0.001 and gradient clipping at 5 to make sure stability. The experiments have been carried out on a system geared up with an Intel i7 CPU, 16 GB of RAM, and a single NVIDIA RTX 4060 Ti GPU. The software program surroundings included Windows 11 because the working system, Python 3.9.18, TensorFlow 2.10.1, and Deep Graph Library (DGL) model 1.1.2 with CUDA 11.8 assist.
Following greatest practices in empirical forecasting and utilized machine studying [50–53], we introduce three commensurate benchmark fashions evaluated underneath equivalent CV protocols and efficiency metrics: (1) Ridge regression (L2 regularised linear regression) utilizing the identical segment-level function set as Mukara; (2) a gravity-interaction baseline, a classical distance-decay formulation based mostly on aggregated inhabitants and employment “masses” linked to noticed visitors volumes by way of log-linear regression; (3) Random forest regressor, a non-linear ensemble mannequin educated utilizing the equivalent function set. All baseline fashions are educated and evaluated underneath each random CV and spatial CV. Hyperparameters are tuned strictly inside coaching folds to forestall leakage. Full methodological particulars for these baselines are supplied in Appendix S7 (S1 File).
Results
Ablation examine and tuning
In the primary experiment, we carried out a grid search to establish optimum settings for the Mukara mannequin. As proven in Table 6, the tuned hyperparameters included the variety of channels in every CNN layer, the ROI measurement, the depth of the GAT block LGAT, the variety of consideration heads, and the size of the node embeddings. Each mannequin was educated for a most of fifty epochs, and the bottom MGEH and MAE losses have been recorded.
The studying curve for the default mannequin is proven in Fig 9. The curve demonstrates that the mannequin learns successfully, with the bottom loss occurring across the twenty seventh epoch. After this level, the mannequin begins to overfit, as indicated by a gradual improve in check loss. Other fashions additionally have a tendency to achieve their greatest efficiency round this level, suggesting that fifty epochs are adequate for the training process. An early stopping mechanism was additionally examined, with a persistence of 10 epochs and a studying charge decay schedule ranging from 0.01 and decaying by an element of 10 right down to 0.00001. The greatest efficiency achieved underneath this new setting matches the height efficiency with out the mechanism.
The outcomes of the hyperparameter tuning are offered in Fig 10. The optimum settings have been discovered to be CNN channels of [16, 32, 64], an ROI measurement of 21 km x 21 km, 4 consideration heads, a GAT depth (LGAT) of 5, and a node embedding measurement of 16. Based on these findings, the default mannequin was up to date to incorporate 4 consideration heads whereas retaining the opposite hyperparameter settings.
Several observations might be drawn from these experiments. First, the best mannequin, which depends solely on edge options for prediction and doesn’t use grid options or node embeddings, ends in excessive loss. This discovering emphasises that geographic and contextual data captured within the node embeddings is crucial, as edge embeddings alone are inadequate for correct predictions. A barely extra advanced mannequin that comes with OD node embeddings along with edge options, however excludes GAT layers (LGAT = 0), additionally yields excessive loss. This demonstrates that including solely origin and vacation spot embeddings to the sting illustration is just not adequate for efficient predictions. Models with a GAT depth of 5 or 6 achieved the bottom losses, suggesting that incorporating data from nodes as much as 5 or 6 levels away considerably enhances the mannequin’s predictive functionality. However, growing the depth past this level led to overfitting.
The inclusion of a number of consideration heads additionally improved efficiency, highlighting the good thing about passing a number of channels of data via the community. This impact is analogous to growing the variety of function maps in CNNs, enhancing the mannequin’s capacity to seize various patterns and relationships.
Finally, the size of the CNN channels and node embeddings have been simplest when balanced. Channels and embeddings that have been too small resulted in underfitting, because the mannequin did not seize adequate data. Conversely, excessively massive dimensions led to overfitting, the place the mannequin struggled to generalise because of capturing irrelevant or noisy options.
Performance analysis
We evaluated the Mukara mannequin utilizing the optimum configuration recognized via hyperparameter tuning. For every cross-validation scheme, the mannequin was retrained inside the coaching folds and evaluated completely on held-out information. The configuration reaching the bottom MGEH inside the validation process was retained. The educated fashions have been then used to generate visitors quantity estimates for all eight years throughout the 498 freeway trunk-road sensors. The corresponding outcomes are offered in Figs 11 and 12.
Fig 11. Prediction performance of the Mukara model.
(Left) Scatter plot comparing predicted traffic volumes with ground truth values for all sensor-year points, with GEH boundaries for reference. (Upper right) Histogram of mean GEH for each sensor, averaged over 8 years. (Lower right) Bar plots of MGEH and MAE for sensors grouped by traffic volume quartiles. Results are for the first fold of the cross-validation. Metrics shown are mean and standard deviation across folds.
Fig 12. Error maps showing signed MGEH values for northbound and southbound traffic.
Positive values (red) indicate overestimation, while negative values (blue) indicate underestimation. The maps reveal localised errors, particularly around areas such as Manchester, but no clear geographical trends overall.
Table 7 summarises comparative efficiency throughout fashions and validation schemes. Under random 5-fold CV, Mukara achieves a imply check MGEH of fifty.74 (1.51), a check MAE of 8,989 (236) autos per day, and an R2 of 0.583 (0.027). These outcomes considerably outperform all baseline fashions. The gravity mannequin yields an MGEH of 84.23 (2.47) and an MAE of 14,836 (419), whereas ridge regression and random forest scale back errors additional however stay clearly inferior to Mukara. The international imply predictor performs worst, as anticipated.
Under spatial CV, total efficiency decreases modestly for all fashions, reflecting the extra stringent analysis setting. Mukara attains a imply MGEH of 57.63 (3.42), an MAE of 9,955 (612), and an R2 of 0.521 (0.072). Importantly, the relative efficiency rating stays unchanged, and no systematic degradation is noticed throughout areas. Slightly larger errors are noticed in folds akin to London and the South West, which seemingly replicate distinct visitors regimes (extraordinarily high-volume city segments and lower-volume rural segments, respectively). The constant benefit of Mukara underneath spatial CV demonstrates that the mannequin generalises to geographically unseen areas. The efficiency of ridge regression and random forest underneath spatial CV is corresponding to that of the Mukara variant with GAT depth of 0, indicating that fashions relying solely on native link-level and endpoint options obtain comparable predictive capability. The extra beneficial properties noticed within the full Mukara configuration subsequently come up from multi-hop message passing and structural context propagation throughout the highway community. This confirms that incorporating non-local relational data supplies measurable advantages over purely native fashions.
Fig 11 illustrates detailed prediction efficiency. The left panel presents a scatter plot evaluating predicted visitors volumes with grounds throughout all sensor–yr observations, with GEH reference thresholds overlaid. The upper-right panel reveals the distribution of imply GEH values for every sensor averaged over eight years. The lower-right panel reviews MGEH and MAE grouped by visitors quantity quartiles. Consistent with Table 7, errors are bigger for sensors with extraordinarily low or extraordinarily excessive visitors volumes, suggesting that excessive visitors regimes stay more difficult to mannequin than medium-range volumes.
GEH reference ranges are generally used as diagnostic tips slightly than formal acceptance standards. Because the GEH statistic scales with stream magnitude, larger reference ranges are sometimes utilized when evaluating each day imply visitors volumes in comparison with hourly counts. Following established follow in large-scale project validation [48,54], values beneath 16 are handled as indicative of shut settlement and values between 16 and 32 as reflecting reasonable deviation for each day volumes. In the check units underneath random CV, 18% of sensors obtain a MGEH beneath 16, and 49% fall beneath 32. The empirical distribution of MGEH throughout sensors additional signifies a right-skewed sample, with the twenty fifth, fiftieth (median), and seventy fifth percentiles equal to 23.88, 32.10, and 72.51, respectively.
Fig 12 presents spatial error maps displaying signed MGEH values averaged over eight years. Positive values point out overestimation and detrimental values point out underestimation, with separate panels for northbound and southbound visitors. No robust large-scale geographic bias is noticed. Errors seem localised slightly than regionally systematic, additional supporting the mannequin’s spatial robustness.
In addition, we additionally present detailed hierarchical aggregation ends in Appendix S8 (S1 File), together with region-level and national-level noticed versus predicted totals underneath each random and spatial cross-validation. These supplementary tables report absolute and share deviations for every area, providing a complementary planning-scale analysis of aggregation coherence past edge-level metrics.
Feature significance
In this part, we discover the relative significance of varied enter options within the Mukara mannequin. First, we analyse how completely different ranges of stratification in inhabitants and employment have an effect on the mannequin’s efficiency. As detailed within the inhabitants and employment subsection, stage 1 stratification contains 7 channels for inhabitants (2 for intercourse and 5 for age) and 21 channels for employment (3 for work kind and 18 for sector). Level 2 stratification expands to 10 channels for inhabitants and 54 channels for employment.
The outcomes are illustrated in Fig 13. When inhabitants is the only grid function, growing the extent of stratification doesn’t considerably scale back the loss. However, for employment, the introduction of stratified channels results in a marked lower in loss, significantly for stage 2 stratification. Furthermore, when each inhabitants and employment are included, the mannequin achieves its lowest loss values with larger stratification ranges, surpassing the efficiency of both function alone. This signifies that stratification permits the mannequin to seize nuanced patterns within the grid options and leverage interactions between demographic and employment strata, corresponding to age, intercourse, part-time/full-time employment, and sectors.
Next, we conduct a function ablation examine to judge the significance of every function set. The full mannequin, which makes use of all options, serves because the baseline. Six extra fashions are examined, every omitting one of many following options: inhabitants, employment, land use, highway community, POI, and edge options. The share change in MGEH and MAE loss values is calculated relative to the baseline, revealing the significance of every function. Fig 14 presents the radar plots summarising these modifications throughout sensors grouped by total efficiency and visitors quantity tertiles (low, medium, and excessive ranges).
Fig 14. Radar plots showing the percentage change in MGEH (red) and MAE (blue) when individual feature sets are removed.
The analysis is presented for overall performance and traffic volume tertiles (low, medium, high). Negative changes indicate a reduction in loss, suggesting possible overfitting or redundancy.
The outcomes present that the removing of any function usually will increase the loss, highlighting their contribution to the mannequin. Notably, land use emerges as essentially the most vital function, with its removing resulting in the biggest loss improve throughout all tertiles. Interestingly, eradicating employment ends in a slight lower in loss, suggesting potential redundancy or correlation with different options. For sensors with low and medium visitors volumes, employment, land use, POI, and edge options are significantly vital, whereas high-traffic sensors exhibit much less sensitivity to those options. In reality, for high-volume sensors, the loss discount upon function removing suggests potential overfitting or deceptive patterns within the coaching information that fail to generalise to the check set.
These findings underscore the significance of fastidiously deciding on and incorporating options within the Mukara mannequin, in addition to the necessity to account for variations of their relevance throughout completely different visitors quantity ranges. The outcomes additionally spotlight the worth of stratifying options to enhance the mannequin’s capacity to seize advanced interactions within the information.
Discussion
This examine proposes a methodological shift in visitors quantity prediction by modelling weekday each day freeway visitors volumes utilizing an end-to-end deep studying framework that depends completely on exterior socioeconomic and spatial inputs obtainable from official statistics and OSM, with out utilizing historic visitors sequence as mannequin inputs. Using the UK strategic highway community as a case examine, Mukara achieves a imply check MAE of 8,989 autos per day in opposition to a mean each day visitors quantity of 33,734.9 autos (relative error 26.6%) and a imply check R2 of 0.583 underneath random 5-fold CV. Under a extra stringent nine-fold spatially blocked CV scheme based mostly on England’s official areas, efficiency stays steady, with an MAE of 9,955 autos per day and an R2 of 0.521. Mukara outperforms all baseline fashions in each CV settings. The modest discount in accuracy underneath geographic hold-out means that the mannequin generalises successfully to spatially unseen areas. In comparability, a standard FSM analysis on an Istanbul case examine reported a best-case %RMSE of roughly 100.92% [14]. Related work additionally reviews decrease or comparable efficiency underneath completely different settings and information sources: Das and Tsapakis [55] reported a imply R2 of 0.36 when predicting annual common each day visitors on low-volume roads utilizing census and survey information, whereas Ganji et al. [56] achieved R2 = 0.58 utilizing aerial imagery for city roads. Narayanan et al. [57] reported larger R2 values in a metropolitan case examine, however relied on artificial visitors information slightly than real-world observations, which generally include higher noise and heterogeneity.
Importantly, Mukara constantly outperforms all commensurate baseline fashions evaluated underneath equivalent information splits and metrics. Under random CV, the gravity-interaction baseline achieves an R2 of 0.342, ridge regression 0.463, and random forest 0.504, all considerably beneath Mukara’s 0.583. Under spatial cross-validation, efficiency gaps widen additional: the gravity mannequin attains an R2 of 0.201, ridge regression 0.302, and random forest 0.361, in comparison with Mukara’s 0.521. Similar developments are noticed for MAE and MGEH. The baseline fashions exhibit bigger variance and stronger degradation underneath spatial blocking, indicating higher sensitivity to geographic distribution shifts. These outcomes exhibit that fashions relying solely on native link-level and endpoint options—or easy distance-decay formulations—have restricted capability to generalise throughout areas. By distinction, Mukara’s graph consideration structure with a number of depths captures structural context past speedy nodes, enabling data propagation throughout the community and yielding measurable efficiency beneficial properties underneath each random and strictly spatial analysis settings.
From an applied-econometrics perspective [50,51,53], Mukara is framed explicitly as a predictive demand-approximation software slightly than a structural causal estimator. All efficiency claims are restricted to out-of-sample predictive accuracy underneath defensible validation protocols, and enhancements are demonstrated relative to clear, commensurate baseline fashions evaluated underneath equivalent spatially blocked cross-validation splits. This benchmarking technique aligns with forecasting follow as mentioned in Barkan et al. [52], the place beneficial properties have to be proven in opposition to easy and interpretable baselines whereas guaranteeing coherence throughout aggregation ranges. In this examine, we subsequently consider efficiency on the edge stage (main goal), look at regional aggregation underneath spatial cross-validation, and confirm that enhancements on the section stage translate into constant combination patterns.
The framework has a number of sensible implications. By substituting hand-specified, rule-based calculations with a data-driven predictive mapping, Mukara captures nonlinear interactions between exterior determinants and noticed visitors volumes inside a unified end-to-end modelling framework. At the identical time, its enter construction is aligned with the FSM custom, which helps planning use instances the place exterior eventualities (e.g., modifications in inhabitants, employment, or land use) can be found however historic visitors measurements could also be sparse or unavailable. Although not examined outdoors the UK on this examine, the design helps prediction on highway segments with no prior stream observations, supplied that comparable exterior options and community representations might be constructed. This property is related for data-sparse contexts. More usually, fashions that rely purely on historic information can wrestle to anticipate community modifications pushed by new infrastructure, as illustrated by the Shenzhen–Zhongshan Link: whereas it alleviated congestion on the Humen and Nansha Bridges, it was related to extreme congestion inside Shenzhen because of elevated inflows to the town community [58].
Several limitations needs to be acknowledged. First, whereas Mukara is conceptually aligned with FSM logic, we didn’t embody exterior fashions for direct comparability underneath equivalent information and assumptions. No current deep studying methodology instantly matches the current process setting—predicting highway-level each day volumes utilizing exterior drivers in an FSM-like enter format with out historic visitors sequence—and implementing a standard FSM on the UK community would require OD estimation and intensive calibration past the uncooked inputs used right here. Without such tuning, FSM implementations can carry out poorly in follow and wouldn’t present a significant benchmark underneath the identical assumptions. For this purpose, we focus benchmarking on each statistical baselines and inner neural ablation variants evaluated underneath equivalent information splits and metrics, and on comparisons with printed outcomes that use completely different information, examine designs, and analysis settings.
Second, the examine is predictive slightly than causal. It doesn’t try and establish exogenous results of inhabitants, employment, land use, or community traits, and it doesn’t resolve econometric identification issues corresponding to simultaneity, omitted variables, or reverse causality [59–61]. These variables co-evolve with transport techniques over very long time horizons, and Mukara needs to be interpreted as predicting realised visitors volumes conditional on noticed spatial and socioeconomic configurations. Relatedly, using a static OSM snapshot for a multi-year visitors panel introduces temporal misalignment and potential measurement error. Although main highway hierarchies and national-scale land-use constructions within the UK evolve comparatively slowly, this alternative stays a realistic trade-off, and time-varying land-use and infrastructure datasets can be preferable the place out there.
Third, a number of modelling and information selections constrain efficiency and generalisability. Errors are larger for sensors with very low or very excessive volumes, which can replicate measurement noise, capability constraints, junction results, and the absence of time-varying operational drivers (e.g., incidents, climate, roadworks) that may be influential for extremes. In addition, sensor choice was designed to signify interurban trunk-road situations with dependable protection, together with prioritising sensors close to section midpoints to scale back native entry results. While this reduces noise, any choice technique could have an effect on representativeness, and increasing protection by matching extra sensors to segments could enhance coaching sign. Although the efficient pattern contains repeated edge–yr observations, the variety of distinct monitored segments stays a constraint when studying generalisable network-wide representations.
Finally, whereas Mukara helps spatial switch to unmonitored hyperlinks and areas inside the studied community, exterior validation in a distinct geographic area or institutional context was not carried out. Transfer to areas with completely different modal constructions, land-use patterns, highway hierarchies, or information high quality subsequently stays an open empirical query on this paper.
These limitations inspire a number of instructions for future analysis. A primary sensible step is to increase coaching protection by mechanically matching all out there sensors to highway segments slightly than manually deciding on a single consultant sensor per section, thereby growing the variety of targets and capturing within-segment variability. A second path is to diagnose which components of the FSM the mannequin approximates effectively and the place the principle bottlenecks lie. For instance, Deep Gravity has proven that OD distribution might be predicted utilizing exterior determinants [31], suggesting that remaining challenges could also be extra associated to modal break up and assignment-like behaviour. Controlled experiments utilizing artificial or semi-synthetic information may assist systematic analysis of deep studying alternate options for particular person FSM steps, or mixtures of steps, underneath recognized floor fact. A 3rd path is architectural refinement. CNNs present a handy mechanism for aggregating gridded spatial context, however different spatial encoders (e.g., Vision Transformers) could higher signify multi-scale or long-range spatial construction. Likewise, whereas GNNs are efficient for data propagation, assignment-like behaviour could profit from architectures that permit extra interpretable interactions between embeddings, doubtlessly integrating specific impedance representations with structured consideration or routing-inspired modules.
A broader growth agenda contains (a) computational effectivity and suitability for real-time deployment, (b) extension to city contexts, (c) long-term forecasting, (d) finer temporal resolutions corresponding to each day or hourly prediction, (e) integration of uncertainty estimation via probabilistic modelling, and (f) transferability to completely new areas with minimal adaptation. The present implementation is computationally light-weight, with reminiscence utilization peaking at round 11 GB. Training takes roughly 2 minutes per epoch (or about 15 seconds per yearly time step), and inference over the complete community might be accomplished inside about 5 seconds underneath the present setup. This runtime profile helps sensible deployment and turns into more and more related if the mannequin is prolonged to larger temporal resolutions.
Extending Mukara to city contexts is theoretically possible however more difficult because of dense networks, frequent intersections, and stronger interactions with public transport techniques. Addressing these complexities could require extra datasets corresponding to public transport provide, sign timing, and richer operational data. For forecasting, the present annual-resolution mannequin can generate scenario-based projections if future exterior drivers (e.g., inhabitants and employment forecasts) can be found, however extrapolation far past the coaching vary needs to be interpreted cautiously. Refining the temporal decision to each day or hourly predictions would require modelling temporal dynamics (seasonal, weekly, diurnal cycles) and incorporating dynamic drivers corresponding to climate, holidays, particular occasions, and highway upkeep logs. Adding static modal context (e.g., public transport availability, schedules, and prices) could additional enhance realism in multimodal settings.
We additionally examined an uncertainty-aware extension utilizing heteroscedastic regression with a Gaussian detrimental log-likelihood loss to estimate each imply and variance. This variant produced weaker level prediction efficiency and fewer steady convergence, with minimal MAE growing from roughly 9,000 to round 12,000. These outcomes have been subsequently not included in the principle analysis. Nonetheless, uncertainty estimation stays vital for planning and risk-aware functions, and different approaches corresponding to Bayesian neural networks or ensemble strategies could present better-calibrated predictive intervals whereas preserving level accuracy.
Regarding transferability, Mukara might be utilized to highway segments with no historic visitors observations as a result of it depends on exterior determinants slightly than lagged visitors states. The attention-based message passing helps generalisation throughout community constructions when comparable options can be found. In follow, a light-weight fine-tuning process utilizing a small quantity of native information could assist seize regional variations whereas retaining the benefits of minimal information necessities. However, full switch to areas with distinct cultural, infrastructural, or institutional contexts stays to be evaluated.
Finally, problems with welfare evaluation, financial effectivity, and market failure identification, whereas vital, fall outdoors the scope of this examine. Mukara is just not meant to judge optimality or effectivity of noticed visitors patterns, however to foretell realised visitors volumes conditional on current spatial and socioeconomic configurations. Extending the framework towards welfare-aware or policy-evaluative functions can be a beneficial path for future analysis.
Conclusion
This examine proposes Mukara, an end-to-end deep studying framework for predicting weekday each day visitors volumes on freeway trunk highway segments utilizing solely exterior socioeconomic, land-use, and network-related options. Using the UK trunk-road community as a case examine, Mukara achieved a imply check MGEH of fifty.74 and a imply check R2 of 0.583. These outcomes are corresponding to, and in some instances outperform, current research carried out underneath completely different settings, whereas addressing a extra restrictive prediction process that excludes historic visitors observations. Ablation experiments confirmed that correct prediction is determined by the joint modelling of spatial context and community construction, with land-use options enjoying a very vital function.
Mukara is meant as a predictive, planning-oriented framework. Within this scope, the outcomes exhibit that an built-in, representation-learning method can approximate key components of the demand-to-flow relationship with out explicitly modelling particular person steps of the four-step framework or requiring intensive calibration.
Future analysis may lengthen this framework by increasing sensor-to-segment matching to extend coaching protection, incorporating time-varying spatial and community attributes, and enhancing the remedy of very low and really excessive visitors volumes. Additional work can be wanted to judge transferability throughout completely different geographic and institutional contexts and to evaluate the efficiency of the method underneath different temporal resolutions or modelling assumptions.
Supporting data
S1 File. Supplementary appendix (PDF).
Contains Appendix S1–S8. Appendix S1 summarises the four-step travel demand model (FSM). Appendix S2 describes the sensor selection procedure, and Appendix S3 evaluates the representativeness of selected sensors. Appendix S4–S6 present robustness and sensitivity analyses, including the OSM vintage robustness test, weekend and holiday inclusion sensitivity, and GEH loss sensitivity analysis. Appendix S7 details the specification of baseline models, and Appendix S8 reports hierarchical aggregation consistency and planning-scale evaluation results.
https://doi.org/10.1371/journal.pone.0345576.s001
(PDF)
Acknowledgments
This analysis was supported by the Cambridge Commonwealth, European and International Trust. Additional assist was supplied by the Martin Centre for Architectural and Urban Studies. The authors gratefully acknowledge the Office for National Statistics, OpenStreetMap contributors, and National Highways for offering the info used on this examine. The authors additionally thank colleagues and exterior consultants for beneficial discussions and suggestions. The views expressed are these of the authors and don’t essentially replicate these of the supporting establishments. All code used on this examine is publicly out there at https://github.com/yueli901/mukara. All information used on this examine are obtained from publicly accessible sources. UK Office for National Statistics information are licensed underneath the Open Government Licence, and OpenStreetMap information are licensed underneath the Open Database License (ODbL).
References
- 1.
Wang J, Li H, Wang Y, Yang H. A novel evaluation and forecasting system for visitors accident financial loss brought on by air air pollution. Environ Sci Pollut Res Int. 2021;28(35):49042–62. pmid:33928504 - 2.
Zhao Z, Zhou D, Wang W, Dai J, Yang R, Hu Q. Research progress on highway visitors accident prediction based mostly on massive information strategies. In: Wang W, Guo H, Jiang X, Shi J, Sun D. Smart transportation and inexperienced mobility security. Singapore: Springer Nature Singapore. 2024. 121–43. - 3.
Mystakidis A, Koukaras P, Tjortjis C. Advances in Traffic Congestion Prediction: An Overview of Emerging Techniques and Methods. Smart Cities. 2025;8(1):25. - 4.
Afrin T, Yodo N. A Survey of Road Traffic Congestion Measures in the direction of a Sustainable and Resilient Transportation System. Sustainability. 2020;12(11):4660. - 5.
Chen S, Li Y, Jin Y. Social and environmental disparities in psychological well being advantages from energetic transport within the UK: a causal machine studying evaluation. Transportation Research Part A: Policy and Practice. 2026;204:104809. - 6.
UK Department for Transport. Transport Statistics Great Britain 2022: Domestic Travel. 2023. - 7.
Tikoudis I, Papu Carrone A, Mba Mebiame R, Lamhauge N, Hassett Okay, Bystrom O. Household transport selections: New empirical proof and coverage implications for sustainable behaviour. Paris: OECD Publishing. 2024. - 8.
Dargay J, Gately D, Sommer M. Vehicle Ownership and Income Growth, Worldwide: 1960-2030. The Energy Journal. 2007;28(4):143–70. - 9.
Boukerche A, Tao Y, Sun P. Artificial intelligence-based vehicular visitors stream prediction strategies for supporting clever transportation techniques. Computer Networks. 2020;182:107484. - 10.
Medina-Salgado B, Sánchez-DelaCruz E, Pozos-Parra P, Sierra JE. Urban visitors stream prediction methods: A evaluate. Sustainable Computing: Informatics and Systems. 2022;35:100739. - 11.
Ortúzar JdD, Willumsen LG. Modelling Transport. fifth ed. Chichester, UK: Wiley. 2011. - 12.
Mladenovic M, Trifunovic A. The Shortcomings of the Conventional Four Step Travel Demand Forecasting Process. Journal of Road and Traffic Engineering. 2014. - 13.
Najmi A, Rashidi TH, Vaughan J, Miller EJ. Calibration of large-scale transport planning fashions: a structured method. Transportation. 2019;47(4):1867–905. - 14.
Gachanja JN. Towards built-in land use and transport modelling: evaluating accuracy of the 4 step transport model- the case of Istanbul, Turkey. 2010. - 15.
Jiang W, Luo J. Graph neural community for visitors forecasting: A survey. Expert Systems with Applications. 2022;207:117921. - 16.
Lecun Y, Bottou L, Bengio Y, Haffner P. Gradient-based studying utilized to doc recognition. Proc IEEE. 1998;86(11):2278–324. - 17.
Hochreiter S, Schmidhuber J. Long Short-Term Memory. Neural Computation. 1997;9(8):1735–80. - 18.
Graves A, Schmidhuber J. Framewise phoneme classification with bidirectional LSTM and different neural community architectures. Neural Netw. 2005;18(5–6):602–10. pmid:16112549 - 19.
Cho Okay, van Merrienboer B, Gulcehre C, Bahdanau D, Bougares F, Schwenk H. Learning Phrase Representations Using RNN Encoder-Decoder for Statistical Machine Translation. 2014. - 20.
Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN. Attention is All You Need. In: Advances in Neural Information Processing Systems, 2017. - 21.
Scarselli F, Gori M, Tsoi AC, Hagenbuchner M, Monfardini G. The graph neural community mannequin. IEEE Trans Neural Netw. 2009;20(1):61–80. pmid:19068426 - 22.
Veličković P, Cucurull G, Casanova A, Romero A, Liò P, Bengio Y. Graph Attention Networks. 2018. - 23.
Zhang J, Zheng Y, Qi D. Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction. AAAI. 2017;31(1). - 24.
Li Y, Yu R, Shahabi C, Liu Y. Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting. In: 2018. - 25.
Yao H, Wu F, Ke J, Tang X, Jia Y, Lu S, et al. Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction. AAAI. 2018;32(1). - 26.
Wang C, Zuo Okay, Zhang S, Lei H, Hu P, Shen Z, et al. PFNet: Large-Scale Traffic Forecasting With Progressive Spatio-Temporal Fusion. IEEE Trans Intell Transport Syst. 2023;24(12):14580–97. - 27.
Kong X, Xing W, Wei X, Bao P, Zhang J, Lu W. STGAT: Spatial-Temporal Graph Attention Networks for Traffic Flow Forecasting. IEEE Access. 2020;8:134363–72. - 28.
Pan Z, Liang Y, Wang W, Yu Y, Zheng Y, Zhang J. Urban Traffic Prediction from Spatio-Temporal Data Using Deep Meta Learning. In: Proceedings of the twenty fifth ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2019. 1720–30. - 29.
Pan Z, Zhang W, Liang Y, Zhang W, Yu Y, Zhang J, et al. Spatio-Temporal Meta Learning for Urban Traffic Prediction. IEEE Trans Knowl Data Eng. 2022;34(3):1462–76. - 30.
Wang S, Lv Y, Peng Y, Piao X, Zhang Y. Metro Traffic Flow Prediction by way of Knowledge Graph and Spatiotemporal Graph Neural Network. Journal of Advanced Transportation. 2022;2022:1–13. - 31.
Simini F, Barlacchi G, Luca M, Pappalardo L. A deep gravity mannequin for mobility flows era. Nature Communications. 2021;12(1):6576. - 32.
Zhang X, Zhao X. Machine studying method for spatial modeling of ridesourcing demand. Journal of Transport Geography. 2022;100:103310. - 33.
Kalantari HA, Sabouri S, Brewer S, Ewing R, Tian G. Machine studying in mode alternative prediction as a part of MPOs’ regional journey demand fashions: is it time for change?. Sustainability. 2025;17(8). - 34.
Hu X, Xie C. Use of graph consideration networks for visitors project in a lot of community eventualities. Transportation Research Part C: Emerging Technologies. 2025;171:104997. - 35.
Cervero R, Kockelman Okay. Travel demand and the 3Ds: Density, variety, and design. Transportation Research Part D: Transport and Environment. 1997;2(3):199–219. - 36.
Duranton G, Turner MA. The Fundamental Law of Road Congestion: Evidence from US Cities. American Economic Review. 2011;101(6):2616–52. - 37.
Wilson AG. Entropy in Urban and Regional Modelling. 1st ed. Routledge: Routledge. 1970. - 38.
Wegener M. Overview of land use transport fashions. Journal of Discrete Algorithms. 2004;5. - 39.
National Highways. National Highways Strategic Road Network. National Highways. 2023. - 40.
National Highways. Traffic Information System (TRIS). 2024. - 41.
Office for National Statistics. Population Estimates – Small Area (2021 Based); 2011-2022. - 42.
Office for National Statistics. Business Register and Employment Survey (BRES). 2022. - 43.
Office for National Statistics. Lower Layer Super Output Areas (December 2011) Boundaries EW BFC (V3). 2011. - 44.
Office for National Statistics. Lower Layer Super Output Areas (December 2021) Boundaries EW BFC (V10). 2024. - 45.
Geofabrik GmbH, OpenStreetMap C. OpenStreetMap Data Extracts: United Kingdom. 2022. - 46.
Office for National Statistics. Countries (December 2023) Boundaries UK BFC. 2024. - 47.
National Highways. National Highways: Managing England’s Strategic Road Network. 2024. - 48.
Feldman O. The GEH Measure and Quality of the Highway Assignment Models. London, UK: Association for European Transport and Contributors. 2012. - 49.
Esugo M, Haas O, Lu Q, Havers GE. Hybrid deep-learning method with Geoffrey E. Havers-based loss operate and analysis metric for multilocation traffic-flow forecasting. Transportation Research Record. 2023;0(0):03611981241274645. - 50.
Varian HR. Big Data: New Tricks for Econometrics. Journal of Economic Perspectives. 2014;28(2):3–28. - 51.
Mullainathan S, Spiess J. Machine Learning: An Applied Econometric Approach. Journal of Economic Perspectives. 2017;31(2):87–106. - 52.
Barkan O, Benchimol J, Caspi I, Cohen E, Hammer A, Koenigstein N. Forecasting CPI inflation elements with Hierarchical Recurrent Neural Networks. International Journal of Forecasting. 2023;39(3):1145–62. - 53.
Bajari P, Nekipelov D, Ryan SP, Yang M. Machine Learning Methods for Demand Estimation. American Economic Review. 2015;105(5):481–5. - 54.
Friedrich M, Pestel E, Schiller C, Simon R. Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. Transportation Research Record: Journal of the Transportation Research Board. 2019;2673(4):722–32. - 55.
Das S, Tsapakis I. Interpretable machine studying method in estimating visitors quantity on low-volume roadways. International Journal of Transportation Science and Technology. 2020;9(1):76–88. - 56.
Ganji A, Zhang M, Hatzopoulou M. Traffic quantity prediction utilizing aerial imagery and sparse information from highway counts. Transportation Research Part C: Emerging Technologies. 2022;141:103739. - 57.
Narayanan S, Makarov N, Antoniou C. Graph neural networks as strategic transport modelling different – A proof of idea for a surrogate. IET Intelligent Transport Systems. 2024;18(11):2059–77. - 58.
Post SCM. Long visitors jams greet Hong Kong vacationers making an attempt out new Shenzhen-Zhongshan hyperlink. South China Morning Post. 2024. - 59.
Athey S, Imbens GW. The state of utilized econometrics: causality and coverage analysis. Journal of Economic Perspectives. 2017;31(2):3–32. - 60.
Athey S. The Impact of Machine Learning on Economics. University of Chicago Press. 2018. 507–47. - 61.
Anselin L. Thirty years of spatial econometrics. Papers in Regional Science. 2010;89(1):3–26.
This web page was created programmatically, to learn the article in its authentic location you may go to the hyperlink bellow:
https://journals.plos.org/plosone/article%3Fid%3D10.1371/journal.pone.0345576
and if you wish to take away this text from our web site please contact us
