Quantum mechanics

Algorithm

Control (management)

Recursion (computer science)

Engineering

Aerospace engineering

Microscopic traffic flow model

Materials science

Traffic flow (computer networking)

Applied mathematics

Computer security

Real-time computing

Basis (linear algebra)

Data mining

Computer science

Mathematical optimization

Matrix (chemical analysis)

Traffic generation model

Physics

Mathematics

Flow (mathematics)

Differential (mechanical device)

Mathematical analysis

Artificial intelligence

Geometry

Composite material

Partial differential equation

Term (time)

Control theory (sociology)

Applied Mathematical Modelling

Short-term traffic flow analysis is the core part of the intelligent transportation system, and also the critical basis for traffic management and control system to guide traffic flow. Real-time and accurate short-term traffic flow prediction can be effectively applied to traffic control and guidance, providing reliable and effective information for traffic managers and travelers, and improving travel efficiency. Based on the spatiotemporal characteristics of traffic flow and periodicity of traffic flow, this paper uses partial differential equation variables to reflect the spatiotemporal characteristics of traffic flow, combines the modelling mechanism of partial differential and the grey prediction model organically, and establishes a partial grey prediction model with control matrix by using the partial derivatives of the mean sequence. At the same time, the parameters estimation and modelling steps of the novel model are obtained by matrix analysis and recursion. A set of data is used from two perspectives to verify the proposed model's effectiveness. Experimental results show that the proposed model is stable and effective. Finally, the novel model is applied to the short-time traffic flow simulation and prediction of the highway. The research results show that the novel model is better than other comparison models. The novel model mainly aims at the matrix data form of traffic flow and is applied to general short-term traffic flow prediction. On the one hand, the prediction results of the novel model can provide theoretical basis and basic methods for the traffic management system, traffic data for traffic information system, and new ideas for the traffic flow prediction research. On the other hand, it can help traffic managers solve accurate real-time traffic flow information, provide real-time traffic information for travelers, and help them plan and adjust routes in advance.

Partial differential grey model based on control matrix and its application in short-term traffic flow prediction