رویکرد فازی نوری تطبیقی برای مدل سازی تعادل رابطه سرعت با چگالی Adaptive neuro-fuzzy approach for modeling equilibrium speed–density relationship

1. Introduction The fundamental diagram (FD), that is bivariate equilibrium relationships of traffic flow (q), speed (v), and density (ρ), is of great importance in analysis of traffic flow and modeling of traffic behavior. For example, the concept of level of service for a highway relies on input from the speed–flow relationship (TRB 2010). The flow–density relationship is central in many investigations associated with traffic flow dynamics (Daganzo 1995). In high-order traffic flow models (Messmer and Papageorgiou 1990; Kotsialos et al. 2002), the speed–density relationship plays an important role. However, among the three ‘pairwise’ relationships (e.g. speed–density, flow–density, and speed–flow), the speed–density relationship appears to be challenging as it encapsulates a direct connection to everyday driving behavior. Traffic flow in the real world is characterized by heterogeneous driving experience, i.e. perturbation in speed choice influenced by the surrounding vehicles. Therefore, a speed–density model that better captures these effects is demanded for traffic flow analysis and efficient traffic control. Modeling of the speed–density relationship began with the Greenshields’ linear model in the seminal paper: A Study in Highway Capacity (Greenshields 1935). This seminal work has inspired a slew of new models (Greenberg 1959; Underwood 1961; Pipes 1967; Drew 1968) which propose a variety of mathematical models containing several parameters. The values of these parameters are estimated by fitting these models to empirical traffic data. A comprehensive explanation of the parameters in terms of traffic flow dynamics is then developed to endow the mathematical model with a phenomenological interpretation. However, these models are limited in the sense that they try to fit the traffic dynamics to a definite shape (i.e. logarithmic, exponential, and exponential to the quadratic and various forms of polynomials). Nevertheless, a live transportation system is dictated by traffic streams with dynamical randomness effects, which result from heterogeneity in both vehicle attributes and driver preferences. For example, in a multimodal system, passenger cars, trucks, and public transportation travel in the same right-of-way. The difference in vehicle dynamics necessarily endows them with heterogeneous gap maintaining behavior, lateral movement and longitudinal motion, and lanes to travel on. As another example, drivers demonstrate heterogeneous driving behavior, e.g. minimum headway distances to keep when following leading vehicles, frequency in applying brakes, fluctuation in arrival pattern, etc. These lead to a complex traffic dynamics, which cannot be replicated by conventional speed–density models. To address this phenomenon, the proposed model must have sufficient shape flexibility to be fitted accurately to the measured field data (MacNicholas 2008). A number of studies suggest that changes in behavior of the leading vehicle cause fluctuations in the reaction of drivers; this phenomenon causes traffic flow instability (Chandler, Herman, and Montroll 1958; Kometani and Sasaki 1961). At low densities, vehicle interactions are occasional and the drivers travel at their most comfortable speed. This leads to a stable traffic flow and, therefore, there are no substantial speed drops. This type of traffic flow pattern corresponds to a density range from 0 to 32 vehicle/mile/lane (del Castillo 2001). Near critical density, the interaction between drivers becomes pivotal to maintain stability of traffic flow. In particular, it has been observed that drivers vary their choice in speed and spacing selection somewhat randomly between two branches in the flow–density FD. It is assumed that drivers continuously vary their spacing and seek for lane-changing opportunities (Kerner 2004).