New Extended Discrete First-Order Model to Reproduce Propagation of Jam Waves

Abstract

In this paper we propose an extension of the discrete LWR model of the cell-transmission model type, to reproduce the capacity drop and the propagation of jam waves. Recently studies have tried to incorporate the capacity drop into discrete first-order traffic flow models for traffic optimization purpose. It is found that the inflow to a discharging cell predicted by these models might have been overestimated, which will influence the propagation of a jam wave. Empirical analysis has been carried out to confirm this assumption. Furthermore, it is found that the extent of the flow reduction depends on the state difference between the targeting cell and its upstream cell. Based on these findings, a new mathematical model formulation is given. Simulations with both a hypothetical freeway stretch and a real life freeway stretch are performed to test the behaviour of the proposed model. The previously mentioned models are also simulated for comparison. Simulation results indicate that the proposed model has a better performance in reproducing jam waves. In addition, the proposed model can be used in a linear model predictive control framework, and formulated as a linear optimization problem, which may be beneficial for a real-life, real-time application.

First order multi-lane traffic flow model – an incentive based macroscopic model to represent lane change dynamics

“…In order to maintain the simplicity of the model, extensions with linear formulations were considered for use in our model. Han et al (2016) provided an extension of first order model with a linear formulation in order to incorporate the capacity drop phenomena by modifying the supply function of the downstream cell in order to reflect the reduced flow discharge during congestion. This was an extension of a similar method employed by Roncoli, Papageorgiou, and Papamichail (2015) where the demand function is linearly modified instead of the supply function.…”

“…This was an extension of a similar method employed by Roncoli, Papageorgiou, and Papamichail (2015) where the demand function is linearly modified instead of the supply function. The approach used by Han et al (2016) is used to incorporate CD in the model. The formulation is described in brief here.…”

Resolving freeway jam waves by discrete first-order model-based predictive control of variable speed limits

“…It is found that the type of traffic jam considered by most of the above mentioned models is only the standing queue. In (Han et al, 2016), it has been tested that most of the above mentioned models can not reproduce the propagation of jam waves accurately. Thus, we have proposed a new extension of the discrete first-order model to reproduce the propagation of jam waves more accurately, which will be briefly introduced in the next section.…”

“…As has been discussed in (Han et al, 2016), the cell-transmission model and many of its variants have difficulties in reproducing the propagation of jam waves accurately. One reason is that capacity drop has not been adequately incorporated.…”

“…However, note that it is possible to make the model parameters cell-dependent. For a general presentation of the model, readers are referred to (Han et al, 2016). Without loss of generality, the index of cell number remains in the following equations.…”