# Towards Moving Objects Behavior Analysis: Region Speed Limit Rate Measure
## 1 Introduction
Different trajectory systems are classified according to several criteria, such as evaluation type, i.e., integration, design, and analytics, geometric representation, i.e., vector or graph, platform and storage technology used, support of semantic information (which includes annotations associated with a trajectory as a whole, e.g., duration, size, and objective, among others), design type, i.e., cell or segment, model type, and implementation. A more recent, extensive, and thorough survey concerning several research aspects about trajectory data management systems and applications focused mainly on urban trajectories is included in [16]. Different research approaches are grouped and classified in terms of trajectory representation, storage, processing, similarity computation, operations, querying, indexing, and clustering (based on some similarity measure, such as pointwise measures, which are divided into five categories: curve-based, real-distance, edit-distance, temporal aware, and segment-based). Related to our work, road traffic applications are also categorized. They can be classified as follows [17]:  
* Sketch-planning tools: these tools produce general estimates of travel demand and traffic operations in response to transportation improvements. * Travel demand models: these are mathematical models that forecast long-term future travel demand based on current conditions and major highway improvements in metropolitan areas. * Analytical/deterministic tools: these tools predict capacity, density, speed, delay, and queuing at a variety of transportation facilities. * Traffic signal optimization tools: these tools are designed to develop optimal signal phasing and timing plans for isolated signal intersections, arterial streets, or signal networks. * Macroscopic simulation models: these models are based on the relationships between the flow, speed, and density of the traffic. The simulation takes place on a section-by-section basis rather than by tracking individual vehicles. * Microscopic simulation models: these models simulate the movement of individual vehicles. These models evaluate heavily congested conditions, complex geometric configurations, and system-level impacts of future transportation improvements. However, these models are time consuming, costly, and can be difficult to calibrate. Thus, in a microscope simulation model, individuals that comprise traffic flows (vehicles, bicycles, pedestrians, etc.) are the minimum element of analysis, unlike a macroscopic simulation model, which simulates the flows of vehicles within the minimum work units that are the network sections [18]. Our proposal is a microscope model because it processes individual trajectories. Each trajectory is processed (traversed) only once, and we use basic spatial operations (Euclidean distance and speed between two points, spatial inclusion of a point in a square) to generate our measure. However, our results are applied at a macroscopic level, where the element of analysis is the region (cell) where the trajectories take place. Although we are not working in a TDW environment, our measure could be included as a measure in a TDW, enabling additional TDW analysis. For this purpose, the semantics of the corresponding aggregation operators and the aggregation hierarchy of the spatial dimension (where the cell would possibly be the most detailed level of aggregation) must be defined. We believe that our speed limit rate measure might serve also as a rough estimate for calculating the congestion of a cell. However, note that our focus is not vehicular congestion, and our measure is not intended to compete with such proposals [19]. Furthermore, our work is not about congestion or traffic prediction [20], although its results could be roughly applied in these fields. The paper is organized as follows: In Section 2, we present our definitions and methods. In Section 3, we present results and discuss our experiments. In Section 4, we conclude our paper and give ideas for future work.