The management and analysis of massive trajectory data present significant challenges in storage scalability and computational eficiency. In this paper, we introduce TDWbench - a benchmark designed to assess and compare two alternative trajectory data warehouse schema designs, i.e., point-based and cell-based. TDWbench is based on a large-scale open maritime trajectory dataset provided by the Danish Maritime Authority The benchmark allows assessing trade-ofs between storage eficiency, query performance, and query accuracy. We provide experimental results that demonstrate how TDWbench supports the comparison of trajectory data warehouse models with realistic analytical workloads, for diferent spatial resolutions and scale factors.
In this section, we provide an overview of the related work spanning two complementary areas of
research: (
TDW designs. In [3], the authors present the design and implementation of a TDW called TWAREHOUSE. T-WAREHOUSE integrates all the necessary components for TDW management, encompassing trajectory reconstruction, ETL processing, and visual OLAP. In [4] the conceptual schema of a segment-based TDW is proposed, where the fact table contains trajectory segments and their attributes (like the geometry of a segment route, a distance traveled, speed, and duration). In [5], the authors use Cartesian grid systems with fixed x-y dimensions to map a regular lattice onto a spherical globe. [ 6] focuses on and end-to-end method for building a TDW, from data pre-processing, TDW loading, to building analytical solutions.
TDW benchmarks. BerlinMOD [7] is a benchmark based on human mobility data. It is
parameterized by: (
To conclude, benchmarks for spatial data storage and querying systems are essential for identifying the most appropriate logical and physical designs. However, to the best of our knowledge, no existing work proposes a fully-featured, ad hoc benchmark specifically tailored to TDWs. Such a benchmark would need to encompass multiple design schemas, varying scale factors, query workloads, and relevant performance metrics.
This section introduces TDWbench1 designed to compare spatio-temporal data models and systems that manage trajectory data. The benchmark is constructed from a real-world dataset of maritime voyages (Section 3.1) and enables the generation of TDWs with varying data volumes, in a manner analogous to well-known TPC benchmarks. The key characteristics of TDWbench are discussed below. • Scalability: the scale factor of the DW is represented by length of the observation period (the number of days). • Schema comparison: the benchmark supports a direct comparison between point-based and cell-based schemas. For the latter, the resolution parameter defines cell granularity. • Workload: TDWbench includes a representative analytical workload comprising common analytical operations such as grouping, joins, and filtering, reflecting realistic trajectory analytical queries. 1https://github.com/rimmmmm/TDWbench • Performance and accuracy reporting: the benchmark provides a comprehensive evaluation of both performance and the quality or query results measured by accuracy. The performance metric includes query execution time, while the accuracy metric quantifies the accuracy loss induced by spatial aggregation and discretization, enabling an explicit trade-of analysis between eficiency and analytical precision. • Implementation: TDWbench is implemented using relational DBMS PostgreSQL v.11 and its spatial extension PostGIS. Such an implementation does not compromise its genericity, as deploying the benchmark on another relational DBMS is generally a straightforward task.
We consider three data sources for building the TDW, namely: (
In the point-based schema, a trajectory is defined as: = ⟨1, 2, . . . , ⟩, where each position is a spatial-temporal point: = ⟨, , ⟩ such that: , ∈ R represent the geographical coordinates (longitude and latitude); ∈ R represents the timestamp of the location (1 < 2 < · · · < ).
In the cell-based schema, each point is mapped to a spatial cell represented as a polygon. A trajectory is represented as: = ⟨1, 2, . . . , ⟩ where = ⟨, _, _⟩, where is a polygon describing the boundaries of the cell containing sequential positions; _ denotes the timestamp corresponding to the vessel’s entry into the cell ; and _ denotes the timestamp corresponding to the vessel’s departure from the cell .
On the one hand, points representing a trajectory result in the most accurate trajectory, whereas cells ofer an approximate trajectory. On the other hand point-based storage occupies a larger disk space as compared to cell-based, and as a consequence queries on a point-based DW schema are more expensive. Moreover, the size of a cell plays a crucial role in the trade-of between accuracy of a query result, data storage, and query execution time. Figures 1 and 2 illustrate a trip trajectory represented as a sequence of points (red curve) alongside its corresponding spatial cell polygons (blue cells). RES2 resolution illustrates a finer spatial granularity compared to RES1 resolution.
The analytical workload consists of 12 batches (see Table 1) of 7 queries each. Queries either include
ifltering on the fact tables or incorporate temporal or spatial selectivity predicates. Three spatial
selectivity values (6%, 18%, 36%) and three temporal selectivity values (8%, 16%, 33%) are considered,
resulting in a total of 84 queries. The proposed workload is designed to: (
The main metrics we use in TDWbench are: storage size, time performance, and query accuracy, for a given cell resolution. The time performance is measured as the total runtime for a given TDW volume. The query accuracy is a new metric that quantifies the deviation of approximate query results on cell-based schemata from the exact results obtained on the point-based schema.
To evaluate the query accuracy we use the Root Mean Squared Error (RMSE). For a given measure m, RMSE is computed using the value of m for the cell-based model () and the value of m for the point-based model (), for all the values of m output by a query. The formula is the following: ⎯ =1
RMSE = ⎷⎸⎸ 1 ∑︁ (︀ () − ( ))︀ 2
In this section, we report some experiments to show how TDWbench supports comparing TDW implementations according to diferent parameters: the type of a model, the scaling factor, the resolution, and queries.
The trajectory data warehouse was implemented in PostgreSQL v11. The TDW stored AIS logs from
Jan 2023, in two cell resolutions: (
The point-based schema (TripPoint) needs the highest storage volume since it stores individual vessel positions with the highest spatial and temporal resolution (i.e., 35 GB for SF=30). The cell-based schema reduces the storage size according to the resolution used. RES2 has a higher resolution than RES1, therefore the fact table for RES1 occupies less space than that of RES2 (i.e., 3 GB vs 5.5 GB for SF=30). Runtime: Figure 3 presents the aggregated runtime results per schema for the two evaluated scale factors. The cell-based schema provides substantial performance benefits. Figure 4 presents the runtime distribution across all batches. Batches that include a spatial join consistently show higher runtime. l]e103 a c s g o l [ ) n i (m102 e m i t n u R l tToa101 38 point 5,086
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Accuracy: TDWbench allows also to compare the accuracy of query results, represented by the RMSE. An example is shown in Figure 5 that details the accuracy for each query of Batch 7 and the two resolutions. As expected, the more fine-grained cell size, the lower RMSE is. The diferences in the RMSE values between RES1 and RES2 for the same query can be substantial, see SpatialFilter of 6% and 18%.
In this paper we presented TDWbench - a benchmark for evaluating TDWs. Built upon over a 2TB
trajectory dataset from the Danish Maritime Authority, TDWbench implements a scaled dataset and a
representative analytics workload to facilitate a detailed investigation of the trade-ofs between: (
1527.27 100 l] d scoaeg l[ E S RM10 1 experimental work on alternative DW schemas for storing spatial data and on in-depth analysis of their impact on query accuracy. Further works with focus on evaluating all 84 queries of TDWbench, and evaluating alternative storage systems, like MobilityDB.
The work of S. Bimonte is supported by the CHIST-ERA grant ANR-24-CHR4-0004-0 ’GIS4IoRT’. The work of R. Wrembel is supported from the National Science Centre (NCN), Poland, grant no. 2024/06/Y/ST6/00136, originally funded from the EU project Chist-Era call 2023.
The author(s) have not employed any Generative AI tools. [3] L. Leonardi, G. Marketos, E. Frentzos, N. Giatrakos, S. Orlando, N. Pelekis, A. Rafaetà, A. Roncato, C. Silvestri, Y. Theodoridis, T-warehouse: Visual OLAP analysis on trajectory data, in: Int. Conf. on Data Engineering (ICDE), IEEE, 2010. [4] C. Renso, S. Spaccapietra, E. Zimányi, Mobility Data: Modeling, Management, and Understanding,
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City-scale and longitudinal dataset of anonymized human mobility trajectories (version 2), 2023. [12] Danish Maritime Authority makes historical AIS data available, 2018. URL: https://safety4sea.com/ danish-maritime-authority-publishes-historical-ais-data/, accessed Jan, 2026. [13] Natural earth, 2025. URL: https://www.naturalearthdata.com/downloads/, accessed Jan, 2026. [14] National Geospatial Intelligence Agency. World Port Index, 2019. URL: https://msi.nga.mil/ Publications/WPI, accessed Jan, 2026.