From rectangle to parallelogram:an area-weighted method to make time-space diagrams incorporate traffic waves

A time-space(TS)traffic diagram is one of the most important tools for traffic visualization and analysis.Recently,it has been empirically shown that using parallelogram cells to construct a TS diagram outperforms using rectangular cells due to its incorporation of traffic wave speed.However,it is not realistic to immediately change the fundamental method of TS diagram construction that has been well embedded in various systems.To quickly make the existing TS diagram incorporate traffic wave speed and exhibit more realistic traffic patterns,the paper proposes an area-weighted transformation method that directly transforms rectangular-cell-based TS(rTS)diagrams into parallelogram-cell-based TS(pTS)diagrams,avoiding tracing back the raw data of speed to make the transformation.Two five-hour trajectory datasets from Japanese highway segments are used to demonstrate the effectiveness of the proposed methods.The travel time-based comparison involves assessing the disparities between actual travel times and those computed using rTS diagrams,as well as travel times derived directly from pTS diagrams based on rTS diagrams.The results show that travel times calculated from pTS diagrams converted from rTS diagrams are closer to the actual values,especially in congested conditions,demonstrating superior performance in parallelogram representation.The proposed transformation method has promising prospects for practical applications,making the widely-existing TS diagrams show more realistic traffic patterns.

DESCRIPTION AND WENO NUMERICAL APPROXIMATION TO NONLINEAR WAVES OF A MULTI-CLASS TRAFFIC FLOW LWR MODEL

A strict proof of the hyperbolicity of the multi-class LWR ( Lighthill-Whitham-Richards) traffic flow model, as well as the descriptions on those nonlinear waves characterized in the traffic flow problems were given. They were mainly about the monotonicity of densities across shocks and in rarefactions. As the system had no characteristic decomposition explicitly, a high resolution and higher order accuracy WENO( weighted essentially non-oscillatory) scheme was introduced to the numerical simulation, which coincides with the analytical description.

Travel time function for basic link considering signal control in network traffic model

In order to describe the travel time of signalcontrolled roads, a travel time model for urban basic roads based on the cumulative curve is proposed. First, the traffic wave method is used to analyze the formation and dispersion of the vehicle queue. Cumulative curves for road entrances and exits are established. Based on the cumulative curves, the travel time of the one-lane road under stable flow input is derived. And then, the multi-lane road is decomposed into a series of single-lane links based on its topological characteristics. Hence, the travel time function for the basic road is obtained. The travel time is a function of road length, flow and control parameters. Numerical analyses show that the travel time depends on the supply-demand condition, and it has high sensitivity during peak hours.

On the critical conditions of traffic jams

Traffic wave theory is used to study the critical conditions for traffic jams according to their features. First, the characteristics of traffic wave propagation is analyzed for the simple signal-controlled lane and the critical conditions for oversaturation is established. Then, the basic road is decomposed into a series of one-way links according to its topological characteristics. Based on the decomposition, traffic wave propagation under complex conditions is studied. Three complicated factors are considered to establish the corresponding critical conditions of jam formation, namely, dynamic and insufficient split, channelized section spillover and endogenous traffic flow. The results show that road geometric features, traffic demand structures and signal settings influence the formation and propagation of traffic congestion. These findings can serve as a theoretical basis for future network jam control.