In contrast to microscopic traffic flow models, macroscopic models describe traffic in terms of aggregate variables such as traffic density, flow-rate, and velocity. The implied mean traffic behavior depends on the traffic conditions in the direct environment of the vehicles in the traffic stream. Using the analogy between the vehicular flow and flow in fluids encouraged deriving these models (e.g. Lighthill and Whitham (1955), Payne (1979)), The advantages of macroscopic models are among others the insight gained into traffic now operations (e.g. shock-wave analysis), the applicability in model based control, the relatively small number of parameters simplifying model calibration, and the applicability to large traffic networks. Generally, macroscopic models consider the behavior of the aggregate traffic flow. That is, neither a distinction of user-classes, such as traveler types (commuters, freight, recreational, etc.), vehicles types (person-cars, trucks, busses, vans), paying and non-paying traffic, and various types of guided vehicles, nor a distinction of roadway lanes is made. However, we envisage that a generalization of macroscopic traffic flow models to both user-classes and lanes is advantageous. On the one hand, this generalization increases the applicability of macroscopic models to the synthesis and analysis of multilane multiclass (MLMC) traffic flow. As a result, more insight is gained into the response-behavior of the heterogeneous multilane flow, such as effective capacity, velocity distribution, and the distribution of vehicles over the roadway lanes. On the other hand, from the traffic control perspective, contemporary policies pursue a more efficient use of the available infrastructure (e.g dynamic allocation of roadway lanes to classes, class-selective ramp-metering). The heterogeneous multilane network-wide traffic control problem is characterized by multiple objectives (efficiency, safety, etc.), multiple target groups (the user-classes), and a high complexity. The latter is caused by the interaction between the user-classes, the interplay between the available control instruments, and the interaction between the different parts of the network. This complexity requires a model-based approach, demanding the availability of operational models providing deterministic conditional predictions of the multilane heterogeneous traffic now, given some specific control configuration. Only very recently, attempts to generalize the classical macroscopic models emerged. Hoogendoorn (1997), and Hoogendoorn and Bovy (1998a) present a multiclass generalization of the model of Helbing (1996) based on gas-kinetic principles. Research on the multilane generalization of macroscopic flow models is reported by Daganzo (1997), Helbing (1997), and Klar ct al. (1998). Welbing (1997) briefly discusses the multiclass generalization of the gas kinetic multilane equations. In this paper, we present a macroscopic model describing the dynamics of heterogeneous multilane traffic Row, based on gas-kinetic multiclass multilane traffic dynamics. In contrast to the aforementioned models, the MLMC model describes the traffic now by considering the conservative variables density, momentum, and energy, rather than the primitive variables density, velocity, and velocity variance. Using these so-called conservatives simplifies the derivation approach and enables improved mathematical and numerical analysis (cf. Hoogendoorn and Bovy (1998d,1999)). Since the acceleration and lane-changing behavior differs significantly between free-flowing and constrained drivers, the macroscopic flow model considers both driver's states. Other novelties are the derived expressions of the MLMC equilibrium momentum and energy, quantifying the asymmetric user-class and lane interaction. From these expressions, the MLMC equilibrium velocity and velocity variance can be determined. The equilibrium relations result from competitive acceleration and deceleration processes: on the one hand, vehicles accelerate towards their desired velocity, while on the other hand, vehicles that interact with slower vehicles from different user-classes - without being able to immediately overtake to an adjacent lane - decelerate. Also, the equilibrium lane-distribution of the classes as a result of overtaking can be determined. On the input-side, the model allows the specification of the class specific desired velocity, acceleration time, and overtaking probabilities. The paper is organized as follows. First we present the MLMC generalization of the gas-kinetic flow equations of Paveri-Fontana (1975) for constrained and free-Rowing vehicles. Secondly, we present the macroscopic flow model using conservative variables, while subsequently discussing the equilibrium speed-density relations and the density lane distribution. After discussing the numerical solution approach, we present results from application of the macroscopic model to two test cases. Finally, in the closing section we summarize our research findings.
