Local Polynomial Regression Models for Average Traffic Speed Estimation and Forecasting in Linear Constraint Databases

Constraint databases have the specific advantage of being able to represent infinite temporal relations by linear equations, linear inequalities, polynomial equations, and so on. This advantage can store a continuous time-line that naturally connects with other traffic attributes, such as traffic speed. In most cases, vehicle speed varies over time, that is, the speed is often nonlinear. However, the infinite representations allowed in current constraint database systems are only linear. Our article presents a new approach to estimate and forecast continuous average speed using linear constraint database systems. Our new approach to represent and query the nonlinear average traffic speed is based on a combination of local polynomial regression and piecewise-linear approximation algorithm. Experiments using the MLPQ constraint database system and queries show that our method has a high accuracy in predicting the average traffic speed. The actual accuracy is controllable by a parameter. We compared the local linear regression model with the local cubic model by using a field experiment. It was found that the local cubic model follows more closely the raw data than the linear model follows.