On the stability of stationary states in general road networks

Abstract

In (Jin, 2015), with a discrete map in critical demand levels, it was proved that there exist stationary states for the kinematic wave model of general road networks with constant origin demands, route choice proportions, and destination supplies. In this study we further examine the stability property of stationary states with the same map, and the results will help us to understand the long-term trend of a network traffic system. We first review a network kinematic wave model and properties of stationary states on a link, define the criticality of junctions in stationary states, and discuss information propagation in stationary states on links and junctions. We then present the map and examine information propagation in the map. We apply the map to analytically study the stability of stationary states on ring roads and divergemerge networks with circular information propagation and compare them with results obtained from the Poincaré map (Jin, 2013). We further study the stability property of general stationary states in a grid network. We find that the stability of fixed points of the map is the same as that of stationary states in a network, and the new approach is more general than the Poincaré map approach. We conclude the study with future directions and implications.

Review of driving-behaviour simulation: VISSIM and artificial intelligence approach

“…Drivers can also demonstrate varied driving behaviours, such as maintaining gaps when following a leading car, applying brakes frequently, and changing lanes continually, complicating the overall traffic dynamics. Similarly, heterogeneity is a common feature of real-world traffic flow [ 121 ]. The distinctions between homogeneous and heterogeneous traffic systems, frequently referred to as mixed traffic systems, are primarily attributable to the diverse operational and performance characteristics of vehicles.…”

Automatic Identification of Near Stationary Traffic States Using Changepoint Detection Method

“…In the stationary state, the traffic flow states of the junction are studied (21), and the fundamental diagram of a specific lane and lane flow distribution are calibrated (22,23). In recent research by Jin (24)(25)(26), both observations and theoretical studies have confirmed that the traffic states are relatively stationary during peak period on a road network, and the stability and existence of stationary states in general road networks have been proved within the framework of kinematic wave theories.…”