ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal
Regular Issue, Vol. 13 (2024), e31866
eISSN: 2255-2863
DOI: https://doi.org/10.14201/adcaij.31866

Bus Ridership Prediction and Scenario Analysis through ML and Multi-Agent Simulations

Pasqual Martí^a, Alejandro Ibáñez^a, Vicente Julian^a,b, Paulo Novais^c and Jaume Jordán^a

^a Valencian Research Institute for Artificial Intelligence (VRAIN), Universitat Politècnica de València, Valencia, Spain

^b Valencian Graduate School and Research Network of Artificial Intelligence, Universitat Politècnica de València,
Valencia, Spain

^c ALGORITMI Centre, Universidade do Minho, Braga, Portugal

✉ pasmargi@vrain.upv.es, alejandro.ibapen@gmail.com, vjulian@upv.es, pjon@di.uminho.pt, jjordan@dsic.upv.es

ABSTRACT

KEYWORDS

1. Introduction

Public transportation is a crucial necessity globally. According to statistics¹, in the United States, 12 % of the population relies on public transport daily, while countries such as South Korea have reached 40 %. Accurately predicting bus occupancy levels is key to optimising routes, enhancing reliability, and reducing waiting times. Historical data allows to proactively identify issues such as bottlenecks, rush hour shortages, and resource wastage. Modifying route planning and resource allocation based on these insights can prevent problems and improve public transportation systems.

This paper aims to establish a benchmark for public transportation systems, to analyse their performance across various environments and identify long-term challenges through experimental simulation. The main contribution of this work is the creation of an initial passenger demand with a specific environmental setup, its load to a fleet simulator, and the analysis of the simulations themselves. To achieve this, traditional and machine learning (ML) techniques were employed to develop models that accurately predict bus occupancy levels, whereas multi-agent simulation was used to validate the predictions. Our approach’s performance was evaluated using a real-world bus system dataset.

Bus passenger flow optimisation has been a widely discussed topic in recent years. Studies by (Baghbani et al., 2023) and (Nagaraj et al., 2022) achieve a real-time passenger prediction task using a final Long Short-Term Memory (LSTM) model layer (Schmidhuber and Hochreiter, 1997). Such a technique can not be directly applied to the current work since the simulation requires an atemporal prediction, but it may be useful for our study to use a modification. Similarly, the study by (Liyanage et al., 2022) employed a bidirectional LSTM model for atemporal prediction, obtaining satisfactory results. Nevertheless, the technique is unsuitable for our purpose, as in a real-scenario application of a simulation, future data would not be available, thus sticking to the unidirectional part of the model.

Moreover, research by (Ming et al., 2014) used a combination of ARIMA-SVM models, where the first one captured the linearity of the data, while the other, the non-linearity. Lastly, (Zhang et al., 2017) used a Grey Prediction Model (GM) (Julong et al., 1989). GM models are widely used in passenger prediction since they capture two types of patterns: normal trends (from day to day) and cyclic trends (between the same weekday at different weeks). More traditional ML techniques can also be adequate for the passenger prediction task. Thus, techniques such as Random Forest (RF), Support Vector Machine for Regression (SVR), and Neural Network (NN) can produce good results depending on the context.

Recently, passenger ridership prediction has been used in transportation optimisation research to help decision- making for mass-transportation operators. The study by (Santanam et al., 2024) focuses on post-event (sports, concerts, etc.) ridership prediction combined. Their approach combines ML with historical trends to forecast the passenger flow curve at stations near the event, finally estimating transport frequencies to serve as many customers as possible. Similarly, the study of (AlKhereibi et al., 2023), approaches the same issue but adds the urban land use information and the built environment around the stations to enrich their prediction. Most recent studies use a variety of ML and traditional statistical techniques, such as the work by (Nair et al., 2023), thus maximising their optimisation options. RF and linear regression models provide, in general, good results in this area. However, more modern hybrid predictors may overcome traditional models for specific issues, as demonstrated by the experimentation of (Lv et al., 2024). Finally, it is worth mentioning that ridership prediction is often combined with anomaly detection, as exemplified by (He et al., 2022), better exploiting data to create more useful solutions.

In the specific context of bus passenger demand prediction, there are primarily two simulation methodologies that stand out for their effectiveness and applicability. The first is agent-based modelling (Hajinasab et al., 2016), which is an intricate approach where each bus and passenger is represented as an individual agent. These agents interact within a simulated environment, mirroring real-world dynamics. This method excels in capturing the complex behaviours and interactions among buses, passengers, and their surroundings. However, the detailed nature of agent-based models often makes them computationally intensive and reliant on extensive data inputs and careful parameter tuning.

The second notable methodology is discrete event simulation (Gunawan et al., 2014). This approach views the bus system’s operations as a series of discrete, time-stamped events. Each event represents a significant change within the system, such as a bus arriving at a stop or passengers boarding and alighting. Discrete event simulation is particularly adept at handling large-scale systems, offering a more streamlined and efficient way to model processes compared to agent-based models. However, its main limitation lies in potentially not capturing the full dynamic behaviour of bus systems, especially the nuanced interactions between the different elements of the system.

In our research, we have chosen to utilise agent-based simulation. This decision is grounded in the method’s superior ability to replicate the intricate dynamics of urban bus systems. By leveraging agent-based models combined with advanced machine learning techniques, we are able to generate realistic and detailed simulations of passenger demand and bus system operations. These simulations are crucial in analysing and understanding the performance and efficiency of the transportation service. Our application of agent-based simulation to a real-world urban bus service has provided valuable insights, demonstrating the model’s efficacy in informing decision-making processes for transportation providers and aiding in the development of optimised transportation services.

Our current research contributes to the development of practical applications for the analysis and enhancement of transportation services. On the one hand, the developed ML prediction models allow us to realistically generalise demand data for the studied transportation system. On the other hand, the predicted demand can be used to create realistic simulation scenarios that reproduce the transportation service in motion. The analysis of such simulations permits the discovery of trends in the performance of the transportation service. Our experimentation on a real-world urban bus service and the subsequent result analysis proves the usefulness of our approach when it comes to guiding the decision-making process of transportation providers, helping the configuration of an optimised service. This paper significantly extends the work presented by (Ibáñez et al., 2023) and builds on the earlier ideas set out in that work.

The rest of the paper is organised as follows: Section 2 describes the data and its treatment. Section 3 presents the training of the demand prediction models. The simulation data generation is described, alongside experimental results, in Section 4. Then, Section 5 goes over the contribution of the paper and the limitations of the chosen techniques. Lastly, Section 6 presents the conclusions and the future line of work.

2. Data

Over the past years, significant endeavours have been made to enhance public transportation systems. These endeavours often involve collecting and analysingvarious data sources to uncover patterns, trends, and valuable insights to support decision-making. This section describes the data fed to the ML techniques and the transformations applied to it for proper learning. A dataset provided by the Ames Transit Agency in Ames, Iowa, has been chosen, as it offers the most comprehensive information available on bus transportation in urban areas.

2.1. Data Sourcing

The bus occupancy data utilised in this study was obtained from multiple routes operated by the Ames Transit Agency in the metropolitan area of Ames, Iowa, spanning from October 2021 to June 2022 (Wilbur, 2022). In total, the dataset comprises 4,577,930 records. The data was collected using automatic passenger counters (APCs), ensuring that each entry in the database corresponds to the number of passengers boarding and alighting at each bus stop.

In addition to passenger counts, each record includes information about the route, scheduled and actual arrival and departure times, and the vehicle’s capacity. The bus routes consist of nine circular routes, three linear routes (with separate routes for outward and inward journeys), and one hybrid route (linear during the school year and circular during summer). Among these routes, four exhibit operational inconsistencies: one undergoes changes in its itinerary on weekdays and weekends, one has limited service resulting in periods of missing data, and two do not operate or have altered routes during the summer season. Therefore, in this study, we only considered nine routes that have consistent data, two of them being round-trip routes, so we will finally refer to the following eleven routes: 1E, 1W, 2E, 2W, 3, 5, 7, 9, 11, 14, and 23.

The dataset covers five different bus types, categorised according to passenger capacity. These types, ranked by usage frequency, are as follows: 60 passengers (70.02 %), 65 passengers (23.16 %), 90 passengers (4.84 %), 40 passengers (1.63 %), and 20 passengers (0.35 %).

2.2. Pre-Processing

Several steps were taken to unify the dataset for training. Firstly, routes displaying inconsistencies were excluded, preserving two linear (round-trip) routes and seven circular routes, as commented before. Also, during the data collection period, the stops of some routes were modified. To adapt the dataset, stops that no longer existed were removed, while new stops were disregarded. Finally, some routes had multiple patterns, as temporary alterations occurred during certain events. However, due to the time-sensitive nature of these cases, they were omitted from the dataset.

Since the aim of prediction is to estimate the number of passengers requiring bus services within a specific time range and area, the data, presented as individual records, needed to be aggregated into flows. This involved defining sections by grouping stops and establishing time ranges. Each route was divided using Ames neighbourhoods as a reference and then subdivided considering changes in the surroundings of a bus stop, such as transitioning from residential to commercial zones. The black rectangles in Figure 1 provide a visual representation of the section divisions.

Regarding time zones, the schedule of Iowa State University² served as the basis for creating 7 time periods to account for fluctuations in passenger occupancy. Table 1, under «Time period division», describes each period. The night periods from the previous and current day were aggregated into a single period.

As the occupancy rate in public transportation follows weekly trends (Liu et al., 2019), two additional variables were created to keep that context: «ons_yesterday» and «ons_last_week». «ons_yesterday» stores the total onboardings during the previous day at the same route, section and hour range, whereas «ons_last_week» does the same but for the previous week, on the same weekday. With this, both a general trend and a particular trend for each weekday were procured. Variables for offboarding were also created analogously.

The environmental conditions have some effect on the behaviour of passenger traffic in public transport (Wang et al., 2020). Therefore, in order to enhance the data analysis and investigate the impact of different weather conditions, a weather dataset was incorporated from the Iowa Environmental Mesonet³. The specific weather station selected for this study was AMES 5 SE, identified by the code IA0203. The weather data, however, had a different level of granularity compared to the existing dataset, as it provided daily information instead of hourly data. To overcome this disparity, weather values for each hour range were inferred by considering the adjacent days as a moving window. Rather than simply retaining the daily value or using a fraction of it, this approach ensured a more accurate estimation. Such a value was derived from a sixth of the weighted total data from the previous and current day. This methodology, as outlined in Table 1, under «Precipitation», accounted for precipitation trends and mitigated the impact of intense downpours.

On the other hand, for the snow depth variable, we considered the gradual melting of snow over time. A weighted average of the current day and the following day was calculated to estimate the snow depth value for each hour range. This approach is depicted in Table 1, under «Snow depth».

By incorporating the weather dataset and employing these inference techniques, the analysis could capture the influence of various meteorological conditions on the bus transportation system with greater accuracy and detail.

The final aggregation structure consists of the route as the first level, followed by the section, date, and time range, and includes the aforementioned information on onboadings, offboardings and weather conditions. Hence, the dataset and the description of each field can be seen in Table 2.

3. Model Training and Evaluation

The individuals in our data are treated as independent blocks without the context of previous time steps. However, considering real-world trends, we incorporate the daily and weekly boarding variables such as «ons_yesterday» and «ons_last_week» to provide contextual information on normal and periodic trends, respectively. The same process has been done for the offboarding models. We create separate models for each route to optimise efficiency rather than using a generalised model with a route variable decision-maker. This approach reduces convergence and prediction time.

For our approach, we employ Random Forest (RF), Support Vector Machine for Regression (SVR), and Neural Network (NN) techniques. It is also important to note that we also made tests with LSTM and GM models. However, the results are significantly worse than those of the other models, and we do not show them here. This is because the aggregations by time periods and sectors cause the data to lose autocorrelation. The selection of these three techniques over others was influenced by their proven track records in handling similar predictive modeling tasks across various domains, their ability to process and learn from large volumes of data, and their flexibility in modeling complex, nonlinear relationships inherent in public transportation systems. Additionally, these techniques were chosen because they demonstrated the best results in preliminary tests conducted before the full experimentation, leading to the exclusion of other methods like GM and LSTM networks from the final experimentation. These methods provide a comprehensive approach to accurately forecasting bus ridership, thus aiding in optimising bus routes and schedules to meet passenger demand efficiently. The main characteristics of each of these methods are summarised below.

Random Forest (Breiman, 2001; Liaw et al., 2002) stands out as an effective and flexible ensemble learning technique applicable for both regression and classification tasks. It builds numerous decision trees during the training phase and determines the outcome based on the most frequent class (classification) or the average prediction (regression) across all trees. This method addresses the tendency of decision trees to overfit their training data, enhancing its reliability and accuracy. A distinctive attribute of Random Forest is its proficiency in processing large datasets with extensive dimensionality, capable of handling thousands of variables without the need for variable elimination. By averaging or aggregating the predictions from various decision trees, it minimizes the likelihood of overfitting.

The Support Vector Machine for Regression (Cortes and Vapnik, 1995; Drucker et al., 1996) represents an advanced machine learning technique that expands upon the foundational concepts of Support Vector Machines (SVM) (Vapnik, 2013), adapting them from classification scenarios to regression contexts. Distinct from conventional regression approaches that focus solely on minimizing the discrepancy between forecasted and observed values, SVR endeavours to maintain prediction errors within a predefined limit. This strategy endows SVR with significant resilience to outlier data and the proficiency to manage non-linear dependencies via kernel functions.

Neural Networks (Bishop, 1995; Haykin, 2009; Goodfellow et al., 2016) are inspired by the human brain, constructed with layers of nodes or «neurons» that simulate how our brain processes information. These networks are composed of an input layer that receives data, multiple hidden layers that perform computations and feature extraction, and an output layer that produces the final decision or prediction. The real power of NNs lies in the hidden layers, which can adjust their interconnected weights through learning, and optimizing the network’s predictions. Activation functions, such as the Rectified Linear Unit (ReLU), play a crucial role by introducing non-linearity, allowing the network to learn complex and abstract patterns in the data. Our specific NN design incorporates a dense structure with six hidden layers of varying sizes (64, 64, 32, 32, 16, 8), employing ReLU activation functions for the hidden layers and a linear function for the output layer. This configuration is tailored for tasks requiring continuous variable predictions, leveraging the dense connections and ReLU’s properties to efficiently model intricate data relationships and deliver accurate, nuanced outputs. The linear output layer ensures the network’s ability to produce a range of continuous values, making it versatile for various regression tasks and beyond.

The Grey Prediction Model (GM) (Liu and Forrest, 2010), particularly the GM(1,1) model, is a unique forecasting technique within the Grey System Theory framework (Julong et al., 1989), designed to handle systems with incomplete or uncertain information. Its strength lies in its ability to make accurate predictions with minimal and imprecise data, setting it apart from traditional statistical models that require large datasets to be effective. The core idea of GM revolves around the concept of «grey», which signifies the partial knowledge about a system, and it utilises this knowledge to model and predict future behaviour. GM operates by first converting the original sequence of data into a new sequence that reveals the inherent pattern of the system. This is achieved through an accumulation process, which smoothens the randomness in the data and highlights the underlying trend. Once the sequence is transformed, the GM (1,1) model applies a first-order differential equation to predict the future values. This approach makes GM particularly suitable for forecasting in fields where data is scarce or highly uncertain. Long Short-Term Memory (LSTM) (Schmidhuber and Hochreiter, 1997; Gers et al., 2000) networks are a specialised form of Recurrent Neural Networks (RNNs) (Elman, 1990) designed to address the challenge of long-term dependencies in sequence data. LSTMs are particularly adept at tasks where understanding the context and relationships over extended sequences is crucial, such as natural language processing, speech recognition, and time series analysis. Unlike traditional RNNs that struggle with vanishing or exploding gradients—problems that make it difficult to learn and retain information over long sequences—LSTMs incorporate a unique architecture featuring gates that regulate the flow of information. These gates—namely, the input gate, output gate, and forget gate—allow the network to selectively remember or forget information, making LSTMs capable of capturing long-range dependencies with greater precision. This gating mechanism enables LSTMs to maintain a balance between remembering important past information and forgetting irrelevant data, thus enhancing their learning

capability and efficiency across tasks involving sequential data.

The experimental objective is to compare the performance of each model across different routes, regardless of the route’s specific context, as they may vary in magnitude. To address this, the R2 score evaluation metric has been developed, which measures the similarity between the predicted values and the actual values of the test set. The R2 score ranges from minus infinity to one, with a higher value indicating a better fit of the model to its route.

When comparing models, it is preferable to use an absolute metric to gauge the overall performance. For this, the mean absolute error (MAE) has been chosen since it calculates the absolute difference between each predicted value and its actual value and then takes the average of all these errors. This provides a comprehensive assessment of the model’s performance in terms of the absolute deviation from the actual values.

The performance results for the onboarding models are summarised in Table 3, with the best model for each route highlighted in green. There is no clear winner among the regression models, as the best model varies depending on the criteria used. However, if both metrics agree on a specific model for a route, that should be the preferred choice. Routes 1 Red West, 2 Green East, 2 Green West, 3 Blue, 5 Yellow, 7 Purple, 9 Plum, and 23 Orange exhibit R2 scores above 82 %, except for 5 Yellow, which stands at 70.2 %. For routes with similar R2 and MAE values, there is little difference in the metrics among the top models. So, it is better to select the model with the lowest MAE value. Routes 1 Red East and 14 Peach show negligible improvements (0.001 and 0.021, respectively), while route 11 Cherry exhibits a significant difference of 0.504. Regarding overall performance, RF is the top model, achieving the most wins in both R2 score (8 wins) and MAE (7 wins). NN comes in second with 3 wins in R2 score and 2 wins in MAE. SVR only emerges as the best model twice for the MAE metric.

The results for the offboarding models are presented in Table 4, with the best model for each route highlighted in green. Similar to Table 3, some routes exhibit different best models based on different criteria. However, there are routes where both metrics agree on the same model, including 1 Red East, 1 Red West, 2 Green East, 2 Green West, 3 Blue, 5 Yellow, 9 Plum, 14 Peach, and 23 Orange. These routes achieve R2 scores above 85 %, except for 5 Yellow and 14 Plum, which stand at 61.2 % and 67.6 %, respectively. For routes with multiple best models, such as 14 Peach, the difference in R2 score is negligible, making it preferable to consider the model with the lower MAE value. In terms of overall performance, the RF model surpasses the rest with 7 wins in R2 score and 9 wins in MAE. The NN comes in second, being the best model for 4 routes in R2 score and 2 routes in MAE. The SVR model is not the best model for any route.

4. Experimental Results

Sections 2 and 3 have characterised a series of ML prediction models tailored to the public bus transportation services of Ames, Iowa. In this section, the use of such models is illustrated through multi-agent simulation. The combination of ML prediction and agent-based simulation provides a system that enables the evaluation and tuning of transportation systems. The experimentation shown below analyses the performance of Ames’ bus routes. From the results of the different simulations, we can adjust the amount of resources dedicated to each route, thus achieving an improved operation of the service.

Following, Section 4.1 presents the simulation software employed in this research and describes the creation of the simulation scenarios taking into account the ML models’ outputs. Then, Section 4.2 presents the baseline simulations, assessing the performance of the bus service in each of its routes and according to the predicted demand. Finally, Section 4.3 extends the experimentation focusing on three of the bus routes that present certain particularities.

4.1. Simulation Environment

To illustrate the use of the ML prediction models, different simulation scenarios are built and executed with the SimFleet (Palanca et al., 2019) multi-agent simulator. SimFleet is a transportation simulation platform that focuses on the creation and evaluation of agent strategic behaviours. SimFleet’s simulations are set on real-world road networks, allowing for a faithful reproduction of already existing transportation services. One of SimFleet’s key advantages is its ability to generate dynamic scenarios based on real-time traffic information and passenger demand, making it valuable for testing new technologies and algorithms in data-driven settings. Finally, it is worth noting that SimFleet allows its users to define the metrics to be quantified during the simulation and exported upon its finishing, thus easing simulation data visualisation and analysis.

For the current work, the simulator was adapted to reproduce a public bus service, as depicted by Figure 2. That included the encoding of the behaviour of three different agents: bus stop agents, transport agents representing buses, and customer agents representing passengers.