Phase Diagram of Traffic States in the Presence of Inhomogeneities

Abstract

We present a phase diagram of the different kinds of congested traffic that are triggered by disturbances when passing ramps or other spatial inhomogeneities of a freeway. The simulation results obtained by the nonlocal, gaskinetic-based traffic model are in good agreement with empirical findings.They allow to understand the observed transitions between free and various kinds of congested traffic, among them localized clusters, stop-and-go waves, and different types of "synchronized" traffic. We also give analytical conditions for the existence of these states which suggest that the phase diagram is universal for a class of different microscopic and macroscopic traffic models. 05.70.Fh,51.30.+i,89.40.+k Typeset using REVT E X For some years now, the various observed nonlinear states of freeway traffic flow, including traffic jams and stop-and-go waves, have attracted the interest of a rapidly growing community of physicists [1,2]. The same applies to simulation approaches that allow to reproduce the transitions between the different collective states of motion [2][3][4][5]. A particular attention received the recent discovery of a first-order phase transition to "synchronized" congested traffic [6,7], which stimulated an intense investigation of the complex phenomena associated with ramps, yielding an explanation of the hysteretic phase transition [8,5]. It is also known from other effectively one-dimensional many-body systems with short-range interactions that localized inhomogeneities can cause a variety of phenomena, including phase transitions [9] and spontaneous symmetry breaking [10].To characterize the parameter-dependence of the possible states of a system resulting in the long run, phase diagrams are a very powerful method. They are of great importance in thermodynamics with various applications in metallurgy, chemistry, etc. Moreover, they allow to compare very different kinds of systems like equilibrium and nonequilibrium ones, or microscopic and macroscopic ones, whose equivalence cannot simply be shown by transformation to normal forms [11,12]. Defining universality classes by mathematically equivalent phase diagrams, one can even classify so different systems as physical, chemical, biological and social ones, as done in systems theory.In the following, we will present and explain the phase diagram that we obtained for the nonlocal, gas-kinetic-based traffic model [5], when we studied a freeway with a ramp in the presence of a single perturbation [ Fig. 1]. By systematical variation of the inflow at the upstream freeway boundary and the ramp, we were able to reproduce the observed transitions between different traffic states, some of which have not been explained before.We will also present analytical conditions for the existence of the various traffic states. Since we are interested in the generic properties of the model, we will formulate it in dimensionless V denotes the average vehicle velocity, L rmp is the length of the ramp, Q rmp is the flow of vehicles entering the freeway (Q r...

Delays, inaccuracies and anticipation in microscopic traffic models

“…Besides using a different model, the control parameters making up the phase space were extrinsic in the previous work, while the phase space is spanned by intrinsic model parameters in the present work. A closer look at the analytic expressions for the phase boundaries [41] containing both extrinsic flow parameters and intrinsic stability limits indicates that variations of both kinds of control parameters can lead to phase transitions.…”

“…Thus, different traffic states can be produced not only by varying the bottleneck strength as in the phase diagram proposed in Ref. [41], but also by varying model parameters that influence stability. We have compared the spatiotemporal dynamics with traffic data from the German freeway A9 South near Munich.…”

“…All of the above dynamic phases can be either reduced by varying the inflow and the bottleneck capacity [41,42,26], or by varying the model parameters, which we do in the following. The left lower corner of Fig.…”

Theory of Collective Intelligence

“…(Viewing the overall system as an instance of the Prisoner's dilemma, this paradox in essence arises through the creation of a novel defect-defect' option for the overall system.) Greedy behavior on the part of individuals also results in very rich global dynamic patterns, such as stop and go waves and clusters 119,120].…”

An Adaptive Smoothing Method for Traffic State Identification from Incomplete Information

“…Both, theoretical [5,6,7] and empirical [8,9,10,11,12,13,14,15,16,17] studies indicate that the phenomenology of congested traffic is more complex than originally expected. There seems to be a rich spectrum of traffic states [5,6,12,13], hysteretic or continuous temporal or spatial transitions among them [7,11,12,13,18,19], and fluctuations or a erratically appearing dynamics play a significant role [13,16,20,21,22]. In order to make sense out of this, it is increasingly important to have suitable ways of data processing, in order to extract the information relevant for scientific investigations or specific applications.…”