Building a real-time spatio-temporal forecasting system is a challenging problem which has many practical applications such as trafic and road network management. Most forecasting research typically focuses on the average quality of predictive models, with much less attention paid to building a practical pipeline and achieving timely and accurate forecasts when the network is under heavy load. Additionally, transport authorities face the issue of how to efectively leverage various dynamic data sources, such as urban events (e.g., scheduled roadworks on the road network, cultural events) and vehicle-level flow data. In this paper, we investigate the practical challenges of real-time forecasting, and present Foresight, a cloud-based system for spatio-temporal forecasting developed in collaboration with Transport for the West Midlands (TfWM). Foresight can ingest, aggregate and process streamed trafic data to produce road network forecasts continuously. We adapt spatio-temporal machine learning methods to incorporate dynamic urban events and vehicle-level flow data, and experimentally evaluate a variety of predictive models in our setting. We employ a data-driven approach to identify peak times in the network, and provide insights on how the performance of forecasting solutions varies for these times when accurate forecasts are most important. We observe that incorporating roadworks into a Graph Neural Network (GNN) model can provide up to a 29.1% performance improvement (MAPE) at a 60-minute forecasting horizon. Further, modelling trafic propagation using vehicle-level flow data in order to support graph-based learning can yield performance gains of 8.8% (MAE) at peak times.
ods such as ARIMA [
A wide range of forecasting approaches have been ap- practical trafic forecasting system. First, there are chalplied to the trafic prediction task, from statistical meth- lenges around the scalable handling and pre-processing of the streaming trafic data, as well as in its use for realProceedings of the Workshop on Big Mobility Data Analytics (BMDA) time forecasting. Typically, most forecasting models are co-located with EDBT/ICDT 2023 Joint Conference (March 28-31, 2023), developed ofline, without considering the challenges of Ioannina, Greece producing forecasts on streaming data. The real-time ⋆ WThairswpiuckb,lipcraitoirotno dGeusncrdiubzesVewhobrikDpemerifrocri mjoeindinagt tImheagUinnaivtieornsiTtyecohf- forecasting problem requires that the forecasting process nologies, Alexandros Sfyridis joining Imperial College London, and takes place continuously within a given time lag of each Hakan Ferhatosmanoglu joining Amazon Web Services. real-world trafic event occurring. This is an important † These authors contributed equally. problem to study for practical data-driven systems, as ‡Also with Amazon Web Services. transport managers need to be able to take action based $ Chris.Conlan@warwick.ac.uk (C. Conlan); on responsive short-term forecasts. It has also been idenJ.Oakley@warwick.ac.uk (J. Oakley); Gunduz.Demirci@imgtec.com tified as an open research issue, and entails significant (HGa.kVa.nD.Fe@mwircair)w;Aic.kS.faycr.iudkis(@Hi.mFperehriaatlo.ascm.uakno(Agl.uS)fyridis); data management challenges, particularly when DL mod© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 els are employed [8]. Second, the focus of many previous ICntEernUatRionWal(CoCrBkYs4h.0o).p Proceedings (CEUR-WS.org) works is the minimization of the average error across models across both normal and peak trafic conditions. We discover that LSTM is often a viable alternative to a GNN based approach; although LSTM produces poorer predictions on average, it can achieve lower MAPE during crucial peak time hours, which is typically more important in practice. This indicates that LSTM yields fewer large outlier errors, and as such may be better at capturing unusual trafic patterns.
2 presents related work. Section 3 formalizes the trafic forecasting problem, and describes its real-time extensions. Section 4 illustrates Dynamic Urban Events. Section 5 describes the Flow-based GNN Adjacency Matrix.
Section 6 introduces Foresight, our cloud-based real-time forecasting system. Section 7 covers our experimental analysis. Finally, Section 8 concludes the paper. 2. Related Work all test samples. In practice, however, accurate forecasts are most important when the network is under heavy load, and/or when the trafic patterns on the network are unusual compared with historical norms. Finally, in addition to data captured at roadside sensors, dynamic urban events (DUE) and vehicle-level flow data should also be incorporated dynamically into forecasting models to improve predictive performance.
Towards addressing these challenges, we present Foresight, a cloud-based spatio-temporal forecasting system developed in collaboration with Transport for the West Midlands (Tf WM). Foresight ingests real-time trafic data, and constructs a Flow Aggregated Adjacency Matrix (FAAM) based on the observed vehicle-level flow between the network sensors, which supports graph-based learning. To ensure timely inference results, it leverages an automated ingestion, aggregation, and MLOps pipeline. To focus on the times when forecasting is most impactful, we develop a data-driven approach to examine the performance of models at peak times. Finally, we incorporate roadworks/road closures in Foresight. While previous works incorporate roadwork information into predictive models [9, 5], this is usually not done as part of a real-time pipeline. The dynamic processing of these DUEs into a format suitable for continuous inference presents non-trivial challenges.
The contributions of this work are as follows:
Numerous forecasting methods have been applied in the
trafic prediction domain. Forecasting is typically
undertaken with the use of statistical and machine learning
models. The Autoregressive Integrated Moving
Average (ARIMA) and its variations are the most widely used
time-series models [
Experiments demonstrate performance improvements of up to 29.1%. 2.1. Dynamic Urban Events • We present Foresight, a cloud-based system for addressing the real-time trafic forecasting prob- Urban events such as roadworks have been shown to siglem, which can continuously stream trafic data, nificantly impact trafic flow [ 22, 23]. Hence, the incorleverage up-to-date roadwork information, and poration of auxiliary information about such events can exploit trafic flow patterns to enhance forecast- further improve trafic forecasting performance. For exing performance. ample, roadwork and accident information has been uti• We perform experimental analysis of a variety of lized in trafic simulation systems, ML models and GNNs time series forecasting methods in a new environ- [24, 9, 5]. A combination of roadworks and weather conment. We compare the performance of multiple ditions have also been added to a bi-directional LSTM Autoencoder for short-term trafic prediction [25]. attracted relatively little attention in the large body of research on the topic.
In GNN models, the underlying graph structures are usu- We first present the definition of the trafic forecasting ally represented with an adjacency matrix which repre- problem, where the goal is to predict the future state sents the spatial relationships between the nodes of a of the road network, given a sequence of previously obgraph [4]. Although GNN adjacency matrices are typi- served time series readings. Trafic information is typically binary [26], multiple variations have been proposed cally obtained from roadside sensors, which can capture [21]. For example, a real-valued distance-based adja- features such as trafic flow or average speed, to form a cency matrix is a common alternative for representing (multivariate) time series. Given a set of sensors , we the spatial dependencies between nodes, and has been ap- denote the trafic information observed across all senplied in numerous trafic forecasting studies with GNNs sors as ∈ R||× , where is the total number of [27, 28, 29, 30, 31]. The travel time between nodes has predictive features used. Let () ∈ R||× denote the also been considered as an alternative to distance-based trafic signal observed at time , and (′) ∈ R||× metrics [32]. More recently, the integration of dynamic denote the trafic signal to be predicted at time ′. Note matrices has been introduced, that captures the dynamic that the number of target features may be diferent to changes in spatial dependencies of the graph and tends to . We aim to learn a function (· ) which maps from ′ improve forecasting [33, 34]. Coarse origin-destination historical trafic signals to future trafic signals: (OD) data has been applied as a substitute for a distancebased adjacency matrix [35]. However, to the best of our knowledge, no previous work on GNN based forecasting [(− ′+1), . . . , ()→]−− (· ) [ (+1), . . . , (+ )] has leveraged granular vehicle-level flow data to model (1) inter-sensor relationships.
In addition to statistical and ML/DL modelling ap- adds the constraint that all processing takes place within proaches, forecasting systems have also been developed a specified duration following the end of each time bin. as general tools for time series prediction and road man- In Foresight, anonymized streaming data is collected at agement optimization. For example, the AutoAI for Time road cameras and ingested into the platform via an API Series Forecasting (AUTOAI-TS) [36] automates fore- endpoint. Further details of this procedure are illustrated casting techniques and addresses specific requirements in Section 6.1. for time series data. DeepTRANS [37] combines the The real-time forecasting inference routine begins at DeepTTE system [38] with DCRNN [7] for bus travel the end of each time bin, which are each minutes long. time estimation. The system uses archive information First, the raw vehicle-level data (held in cloud storage) about bus and trafic flow from sensor data, and DCRNN is aggregated for the most recent time bin (i.e., the is used to estimate trafic speed at buses’ locations. The minutes from (− 1) to ()). We denote the time taken TraficStream forecasting system leverages GNNs and for this aggregation as . Next, the aggregated data is Continual Learning (CL) [39]. It constructs a sub-graph to pre-processed so that it is in the correct format for model capture network expansion, and constraints are applied inference. This includes fetching and processing the agon the current training model to integrate information gregated trafic count information for the last ′ time from historical data. bins, as well as retrieving any additional model-specific data used for inference (e.g., roadwork time series, adja3. Real-Time Spatio-Temporal cency matrix). The time taken for this phase is referred to as . Once the required data have been proForecasting duced, the inference API endpoint is invoked to perform the forecast. The time taken for inference processing to In this section, we first describe the trafic forecasting occur, as in Equation 1, is denoted by . problem, before introducing its real-time variant. A key We require the following expression to be satisfied for requirement of this procedure is that the aggregation, a system to be capable of real-time forecasting: pre-processing and inference of the trafic data must take place within a certain time lag of the real trafic events occurring. These practical aspects of forecasting have (2) = + + ≤
︂[ ]︂ Combining and ˆ, a new matrix ˜ = ˆ is
constructed, which is the new feature vector passed to the forecasting models. We evaluate these approaches within the context of a GNN model in Section 7.
A value of ≤ ensures that the shortest forecasting horizon still pertains to information that is yet to be aggregated in the system, and is therefore relevant to network managers.
Foresight is able to leverage DUE data dynamically to improve the accuracy of its forecasts. We use roadworks data as an illustrative example, but other such informa- Graph Neural Networks (GNNs) are popularly used in tion (e.g., social event data) could readily be applied in state-of-the-art forecasting models [27, 28, 29, 30, 31, 3, a similar fashion. In the context of trafic forecasting, 34, 7]. These methods typically represent the trafic senplanned and unplanned roadworks frequently influence sor network as a graph structure, whose adjacency matrix the volume and nature of trafic propagation through the aims to capture spatial relationships between the sensors. road network [22, 23], and so incorporating information The principle of GNN message passing and node aggregaabout them into predictive models is important for ac- tion approaches in the context of trafic forecasting, such curate predictions. Foresight automatically ingests DUE as difusion convolution [ 7], is to simulate trafic propadata and processes it into a format which forecasting gation in the network. This method of extracting features models can easily exploit. is typically embedded into a wider learning structure so
Roadworks data is ingested into Foresight via the Street that temporal features can be learnt along with spatial
Manager API1, which is invoked daily to receive a feed features in an integrated fashion.
of planned roadwork events. We denote the set of all The graph structure which models the trafic sensor
roadworks listed by a given daily API call as . For network is described by an ||×| | (weighted) adjacency
each roadwork ∈ , we obtain its latitude/longitude, matrix. The value at position (, ) approximates the
as well as its start and end dates and . In order strength of the relationship between sensor and sensor
to associate the live roadworks on a given day with . A popular method to assign weights in the adjacency
the road sensor network , we first select only those matrix is to calculate pairwise sensor distances measured
roadworks where ≤ ≤ . Next, we calculate the in the road network [
To incorporate this roadwork-to-camera influence in- co-located, trafic might rarely pass between them consecformation into the forecasting models, we convert utively, or may flow in one direction significantly more into a time series format at the same temporal granu- than the other; these properties cannot be easily captured larity as the observed trafic data. This has been shown by this approach. to be an efective method for adding roadwork data to We therefore develop a method for computing the adforecasting models [5]. We define this as a new feature jacency matrix weights which uses vehicle-level flow set with the same dimensions as , formally ˆ ∈ R||. data to more accurately determine the relationships beEach entry ˆ ∈ ˆ() has a value between 0 and 1 which tween sensors. By leveraging the properties of granular denotes the strength of the influence of the nearest active ANPR (Automatic Number Plate Recognition) data, our roadwork to sensor at time . method can anonymously capture (in order) the sequence
We consider two approaches to approximate this influ- of sensors which the cars pass as they traverse the road
ence. The first is a binary thresholding approach, where network. By aggregating this information at the network
entries are activated if there is a roadwork within thresh- level, we are able to determine actual flows within the
old distance metres of the sensor. The second method network. The new adjacency matrix is designed to
reinvolves first calculating the distance from each sensor tain the same dimensions used in most GNN methods for
to its nearest live roadwork, before normalizing these dis- spatio-temporal forecasting, so it can be directly
applicatances into [
Input Data Traffic Data Event Data
Ingestion & Aggregation
Kinesis Data Firehose Athena (SQL) Lambda CloudWatch
Glue
Scalable Cloud
Storage
S3
ML Inference SageMaker Endpoint
Lambda Conditional
Registration ML Experiments
MLOps Pipeline Processing
Training
Evaluation
1 unit of flow is recorded between cameras and when
a car is observed at camera ∈ at time , and is
then next observed ∈ no later than + , where
is a parameter given in seconds which denotes the
acceptable transition period. To construct , each entry
, is incremented by 1 for each observed unit of flow.
, is then averaged over all the time periods during
which flow was observed, before being normalized into
[
system, as illustrated in Figure 1. The overall goal of Foresight is to provide continuous forecasts for transport managers by leveraging streaming trafic data as well as dynamic urban event and flow information. We will ifrst describe how streaming trafic data is ingested and aggregated, before presenting the MLOps pipeline and forecasting inference procedure. Details of how DUE data and flow information are processed are given in Sections 4 and 5 respectively.
vehicle capture information in the West Midlands road network managed by Tf WM. This data flows into Foresight using a POST request to an API endpoint, before being forwarded to a streaming ETL service (Kinesis Data Firehose2). Individual vehicle captures (including a timestamp, salted hash of vehicle registration, camera/lane of observation and vehicle type) are bufered using this service, and are periodically flushed to object storage (once the bufer fills, or a short time period elapses). The bufered file is also converted to a columnar format (Apache Parquet3) for improved query performance.
We next use a serverless data integration ofering (AWS Glue4), to crawl the object storage buckets containing these intermediate files periodically. This enables the use of serverless SQL queries (via AWS Athena5) over the columnar Parquet data. These queries generate ag2https://aws.amazon.com/kinesis/data-firehose/ 3https://parquet.apache.org 4https://aws.amazon.com/glue/ 5https://aws.amazon.com/athena/ gregated trafic count data, illustrating the total number of vehicles of each type (e.g., petrol car, HGV) that have passed each roadside camera within the current time bin, i.e., the last minutes. We use scheduling functionality in a cloud monitoring service (AWS CloudWatch6) to trigger the SQL processing (via lightweight serverless functions) for the current time bin. This procedure writes a single file to object storage (AWS S3 7) per the current time bin, which can later be used as an input to ML workflows.
are then written to object storage, where they can be retrieved for downstream visualization.
In this section we present the results of our experiments to test the efectiveness of popular trafic forecasting methods in a new setting. We then evaluate the impact of incorporating DUE data as an additional dimension to the input feature vector. We also consider the performance impact of using the FAAM, in place of a distance-based adjacency matrix, in a GNN forecasting model. Finally, we explore the error profiles of our models, and their eficiency within Foresight.
We leverage an AWS SageMaker8 MLOps pipeline to create and deploy forecasting models. Data scientists can run experiments (e.g., in SageMaker Studio Notebooks) over data held in object storage, using standard libraries 7.0.1. Road Camera Dataset such as NumPy, PyTorch, TensorFlow, etc. Once a model The anonymized and aggregated data used for the exhas successfully been designed, its source code can be periments is from a set of ANPR cameras in the West pushed to one of two Git repositories (test, production) Midlands region of the UK, covering several large conurhosted in AWS CodeCommit9. bations including Birmingham and Coventry. The precise
Once a code update is performed in either reposi- locations of cameras remain private. The set of cameras tory, the MLOps pipeline provisions a compute instance are spread over a variety of diferent road types, including (whose size is specified by the data scientist) to perform many roads from inner city locations and smaller conthe necessary pre-processing and training of the model. necting roads. This is diferent to many prior datasets, The trained model is then deployed to a SageMaker end- such as METR-LA [40], where road sensors are typically point (which resides on a provisioned compute instance), located on freeways where one can expect a high volume where it can first be tested in a ‘staging’ environment of free-flowing trafic. The quality of this data is high; the before being made available for live inference (if the pro- rate of missingness is only 2.3%, compared with 8.1% for duction repository was updated). The MLOps pipeline METR-LA. We use linear interpolation to impute these can be configured to re-train the model periodically, e.g., missing values. once per week, to continually incorporate the latest trafifc data. 7.0.2. Experimental Setup
As described in Section 6.1, the ANPR trafic data is aggregated in periodic -minute time bins. We configure a serverless function (AWS Lambda10) to be triggered each time a new per-bin trafic file arrives in the specified S3 location. Once the serverless function is invoked, it first retrieves the latest ′ historical trafic files (see Section 3) and executes the required pre-processing logic. Note that while this serverless function is lightweight, the small data volume makes this processing eficient. Next, any auxiliary data (e.g., adjacency matrices, roadworks time series) required for inference is also fetched. The resultant payload is sent to the live inference endpoint described above, where trafic predictions for the next time bins over all sensors are made. These predictions
7https://aws.amazon.com/s3/ 8https://aws.amazon.com/sagemaker/ 9https://aws.amazon.com/codecommit/ 10https://aws.amazon.com/lambda/ The vehicle count data used in the experiments was collected between August 5th and December 5th 2021 (inclusive), and was aggregated at 15 minute intervals. DUE data was collected for the same period. The flow was measured between August and November 2021 in order to compute the FAAM. The data was split into training, validation and test sets in a 70/10/20 ratio. We evaluate performance using mean absolute error (MAE) and mean absolute percentage error (MAPE). We also calculate the error distribution’s coeficient of variation, which we refer to as the error coeficient of variation (ECV). We refer to the set of absolute errors across all test samples as ℰ , and hence = ((ℰℰ)) . The ECV allows us to compare the dispersion of the error terms across diferent distributions (i.e., the sets of errors made by diferent models), as it normalizes by the mean error. A high ECV indicates that predictions are inconsistent.
We evaluate the results firstly over all time periods in the test data, which we refer to as ‘Any Time’ (AT) experiments. We also perform evaluation focusing only on ‘Peak Times’ (PT). We identify peak times as those that have historically shown high average trafic counts, but also high levels of variability. High average trafic counts indicate heavy load on the network, which we assume are periods of interest for transport managers. High levels of variability are a sign of challenging forecasting conditions, and may denote periods of unusual trafic conditions on the network. We identify these periods of interest by first dividing the dataset into weekends and weekdays, and then further splitting each of these into hourly subsets. The mean and coeficient of variation of each subset is then calculated. Any of these subsets with both mean and coeficient of variation in the upper two quartiles is classified as peak time. The only time periods which satisfy this are 7am-8am, and 8am-9am on weekdays, hence we select these as our peak times. This selection also conforms closely to the domain knowledge of our partners at Tf WM.
The following forecasting models have been evaluated on the road camera dataset.
• Historical Average (HA): We produce a historical average matrix based on the training set. The average reading over the training set is calculated at each sensor in for each of the 672 (4x24x7) weekly time steps. To perform inference, we give the historical average value of the target time period as our prediction (the notion of ′ historical trafic signals is not applicable to this method). • ARIMA: We iterate over all sensors and all test examples. In each iteration, we train an ARIMA model11, using the previous ′ = 100 values as 11 = 1, = 0, = 1 the training input. • Feed Forward Neural Network (FFNN): We implement an FFNN, where the input consists of the previous ′ readings across all sensors ∈ . The model produces predictions for the next forecasting horizons. The network is constructed with two hidden linear layers, with ReLU activation functions. Model parameters are learned using backpropagation, with an L1 loss function. • Long Short Term Memory (LSTM): This is implemented similarly to FFNN, except using LSTM layers in place of linear layers. Within the LSTM layers, input data is treated as a sequence and temporal patterns are learnt using an additional hidden layer to capture the cell state, which passes information along the sequence. • Difusion Convolutional Recurrent Neural Network (DCRNN): We select DCRNN [7] as an illustrative example of an efective GNN method. This method has been previously identified as one of the best-performing (GNN) approaches for the trafic forecasting on benchmark datasets [ 8]. The model utilizes a distance-based adjacency matrix to model the spatial relationships between road sensors, and employs difusion convolution and bidirectional random walks to simulate trafifc propagation in the network. We utilize the PyTorch implementation of DCRNN [7]. • DCRNN-RW-T / DCRNN-RW-G: DCRNN with DUE adaption to include roadwork data. DCRNN-RW-T associates live roadworks to all sensors within a 1000m distance threshold. DCRNN-RW-G uses thresholded Gaussian kernel normalization (threshold = 0.1). • DCRNN-F: DCRNN with the FAAM representing
using Python 3.6, on a ml.g4dn.xlarge instance. We use PyTorch 1.8 to implement FFNN, LSTM, and DCRNN (including all variants). Unless stated otherwise, ′ = = 4, and = 15 minutes. In practice, we make predictions over horizons of 15, 30, 45 and 60 minutes (henceforth referred to as 15m, 30m, 45m, 60m). The more distant forecasting horizons (i.e., 45m, 60m) ofer transport managers more time to implement pre-emptive interventions on the road network. Hence, performance gains here are particularly valuable.
the underlying graph structure. An acceptable than LSTM across all forecasting horizons during the AT transition period between sensors is given as experiments (MAPE degradation - 15m: 22%, 30m: 25.8%, 3600 seconds and thresholded Gaussian kernel 45m: 21.3%, 60m: 11.3%); these discrepancies are furnormalization ( = 0.1) is applied on the matrix. ther exacerbated in PT experiments (MAPE degradation • DCRNN-RW-F: DCRNN with roadworks (using - 15m: 37.7%, 30m: 36.6%, 45m: 41.2%, 60m: 18.3%). This Gaussian kernel method) and FAAM. is an interesting result as it suggests that while LSTM makes poorer predictions on average (i.e., MAE), it also makes fewer mistakes of a significant margin, leading to a lower MAPE (this metric is highly sensitive to outliers in the error term). It may therefore be inferred that LSTM is better than DCRNN at predicting unusual trafic patterns, especially at peak times. In terms of MAPE, ARIMA was shown to be a highly competitive model across all forecasting horizons, outperforming DCRNN in all cases, with more pronounced gains in PT experiments. As ARIMA is retrained on the most recent data when evaluating each test sample (see Section 7.1), it will naturally be more responsive to unusual trafic patterns than models trained using a conventional train/test split. LSTM still largely outperforms ARIMA in regards to MAPE. HA performs particularly poorly on this metric, due to its inability to dynamically respond to current network conditions.
We describe the key findings from our experimental results, which are presented in Table 1. First, we compare the performance of several existing forecasting approaches in our new data setting. We then consider the impact of incorporating roadworks as an exogenous input feature, as well as using flow to determine edge weights in the adjacency matrix. Next, we discuss our findings pertaining to prediction reliability using ECV. Finally, we analyze the eficiency of Foresight. 7.2.1. Analysis of Existing Approaches We first consider the performance of several existing spatio-temporal forecasting approaches in our new data setting. During the AT experiments it can be observed that DCRNN makes more accurate predictions across all four time horizons (MAE improvements - 15m: 20.9%, 30m: 20.6%, 45m: 25.3%, 60m: 22.7%) compared to the next closest model (LSTM), with the largest improvements seen at the longest forecasting horizons. Similarly, during the PT experiments DCRNN remains the most accurate model. However, it is interesting to note that the improvements compared to LSTM are now much smaller (MAE improvements - 15m: 18.5%, 30m: 15.1%, 45m: 14.2%, 60m: 8.3%), and the trend at longer horizons is reversed where we see the smallest MAE improvements.
ARIMA tends to be a competitive model for shorter horizons, during both PT and AT experiments, however the performance deteriorates quickly at longer forecasting horizons, which indicates that this model requires fresh data to support accurate predictions. HA and FFNN make the least accurate predictions across all forecasting horizons.
Diferent trends emerge when MAPE performance is considered. DCRNN now exhibits poorer performance 7.2.2. DUE Analysis
events to GNN models. Mixed results are achieved when MAE is considered. DCRNN-RW-G, which associates roadworks using a thresholded Gaussian kernel, generally yields higher MAE than DCRNN across both AT and PT experiments. These discrepancies in MAE are particularly pronounced for long forecasting horizons during peak times (MAE degradation - 45m: 5.4%, 60m: 11.4%).
On the other hand, DCRNN-RW-T (binary thresholding) achieves lower MAE compared to DCRNN over all AT experiments. However, it still yields inferior performance at more distant forecasting horizons at peak times (MAE degradation - 45m: 1.4%, 60m: 2.1%).
The results for MAPE present a contrasting picture, where DCRNN-RW-G outperforms DCRNN-RW-T across all experiments. During AT experiments (especially at longer horizons), DCRNN-RW-G achieves significant improvements compared to DCRNN (MAE improvements - 45m: 29.8%, 60m: 29.1%). We observe a similar pattern during peak times. These findings indicate that using a thresholded Gaussian kernel during the construction of a FAAM yields a reduction in large outlier errors (likely resulting in improved performance under unusual road network conditions). 7.2.3. FAAM Analysis Our experimental results indicate that using vehicle-level lfow data to model inter-sensor relationships is an efective strategy. For AT experiments, DCRNN-F achieves utilize this system to develop methods for the incorpolower MAE than DCRNN across all time horizons, and is ration of Dynamic Urban Event (DUE) and vehicle-level particularly efective at long forecasting horizons (MAE lfow information into predictive models. We consider improvement - 60m: 3.2%). Further, we observe even several approaches for associating roadworks to the roadlarger MAE gains for DCRNN-F compared to DCRNN side sensors which they impact, and present a FAAM at peak times (MAE improvement - 60m: 8.8%). These based on granular and anonymized vehicle-level flow ifndings support the inclusion of vehicle-level flow data data. We implement and evaluate a range of time series into GNN models for improved predictive performance. forecasting models in a new urban data setting, enabled
We note that leveraging the FAAM in place of a by ANPR infrastructure in the West Midlands region. We distance-based adjacency matrix (i.e., DCRNN) yields observe performance improvements of up to 29.1% for MAPE improvements in all cases. However, the most GNN models when DUE and flow data are leveraged. Our significant MAPE gains are still experienced by DCRNN- experimental results provide further insights on the foreRW-G, indicating that incorporating roadworks is a more casting accuracy during peak times when accurate results efective strategy for minimizing outlier errors. It should are more critical, compared to the traditional approach be noted that DCRNN-F mitigates much of the degrada- of targeting the average accuracy. Further work may tion in MAPE performance at peak times that DCRNN apply our approach for handling DUEs to more varied sufers in comparison to LSTM, while also ofering lead- data sources beyond planned roadworks, such as weather ing MAE results. or cultural event information. Our data-driven method for identifying peak times could be compared to a rele7.2.4. Error Coeficient of Variation vant ground truth. Foresight’s response time could be improved, particularly via acceleration of . Finally, As illustrated in Table 1, DL models, particularly those an additional temporal dimension could be added to our which have been enhanced by DUE data or the FAAM, flow-based adjacency matrix. experience the highest ECV (especially at longer forecasting horizons). As shown above, it is at these more distant horizons that the biggest performance improve- Acknowledgments ments (MAE/MAPE) are observed for our augmented models. This suggests that while these solutions produce the best forecasts on average, their errors are the least consistent. This finding is noteworthy, and we would recommend further investigation to better understand its implications.
orators there, particularly Tim Katheru, Andrew Burns and Stuart Lester in the Data Insights team. This research is also supported in part by the Feuer International Scholarship in Artificial Intelligence, WM5G, and the UK Engineering and Physical Sciences Research Council under Grant No. EP/L016400/1. 7.2.5. Eficiency Analysis As discussed in Section 3.2, the real-time forecasting task requires that = + + ≤ . In the current version of Foresight, we allow for ≤ 40 seconds. For all of the implemented forecasting models, ≤ 6 seconds. Each model except ARIMA achieves ≤ 2 seconds. As discussed above, at inference time we train an ARIMA model over the previous ′ = 100 values for each ∈ . For ARIMA, ≤ 16 seconds. Hence, all of the presented models achieve ≈ 1 minute, satisfying Equation 2 with significant headroom for = 15 minutes. Further, these results conform to alternative notions of real-time forecasting [41], where predictions were produced in a single-digit order of minutes.
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