A CONTINUUM THEORY OF TRAFFIC DYNAMICS FOR FREEWAYS WITH SPECIAL LANES

This paper presents a generalized theory of kinematic waves for freewa ys with two vehicle types and a set of lanes reserved for one of the v ehicle classes. The theory is not restricted to freeways on which the special lanes are clearly identified by signs and pavement markings; e .g. for high occupancy vehicles. It may also apply if the restrictions are self-imposed, such as would occur on a freeway segment upstream o f a busy off-ramp where the existing traffic naturally avoids the 'far -side' lanes. Of particular interest are oversaturated time periods be cause the original theory of kinematic waves proposed by Lighthill and Whitham [Proceedings Royal Society, A 229, 281-345 (1955)] and Richar ds (1956) does not recognize that different traffic conditions (queues and speeds) may arise on the two sets of lanes, and that these may af fect the two vehicle classes in different ways. It should be intuitive that whether a single coalesced queue forms on both sets of lanes or separate queues form on each set should depend on the traffic composit ion by vehicle class. In an attempt to furnish a reasonable depiction of these phenomena, a pair of conservation-type partial differential e quations in the densities of the two vehicle types is used to model th e freeway. In their simplest form, the equations only require the intr oduction of one additional parameter (representing the fraction of lan es allocated to each vehicle type) over the basic kinematic wave theor y. The model is attractive because the nature of its solution can be d escribed in complete physical detail by means of simple intuitive diag rams that show how the simple kinematic wave model is improved. The pa per also introduces an exact solution method for problems with piece-w ise constant initial data that can either be applied graphically or nu merically. For general (piece-wise smooth) data, the numerical techniq ue can be used to approximate the true solution as closely as desired in a way that does not deteriorate with time. A less precise finite-di fference approach that always moves vehicles forward is also presented . (C) 1997 Elsevier Science Ltd.