Cf. Daganzo, A CONTINUUM THEORY OF TRAFFIC DYNAMICS FOR FREEWAYS WITH SPECIAL LANES, Transportation research. Part B: methodological, 31(2), 1997, pp. 83-102
Citations number
16
Categorie Soggetti
Transportation,"Operatione Research & Management Science","Engineering, Civil
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.