Temporal Dynamics of Vehicle Flow in Interconnected Network Arteries Using Continuous Markov Chains

Abstract

This study examines the temporal dynamics of vehicle circulation within an interconnected network of arterial roads using continuous Markov chains. Traditional approaches to vehicle flow modeling rely on discrete Markov chains, where each transition represents the passage of vehicles between intersections at fixed time steps. In this paper, we introduce a modification by modeling the process as a continuous system, enhancing the temporal resolution and accuracy of traffic predictions. By representing the network as a digraph and associating it with an ad hoc steady-state matrix, we develop a continuous evolution matrix that allows for the seamless tracking of vehicle populations over time. The model begins with an initial population of vehicles within the network, represented as a vector, and applies the continuous evolution matrix iteratively to predict traffic flow dynamics. This approach improves upon traditional discrete models by enabling finer temporal predictions and providing insights into the steady-state conditions of the system. The results demonstrate the potential of continuous Markov chains to offer more accurate and efficient traffic flow predictions, supporting better traffic management strategies and optimizations for large-scale network arteries.