We study the system optimum dynamic traffic assignment (SODTA) in a network consisting of a freeway and neighboring city streets. There is only one bottleneck in the freeway and every destination is somewhere downstream of the bottleneck. Vehicles can be diverted through off-ramps leading to alternative local street routes. We formulate the problem and determine a graphical solution procedure based on Newell's cumulative plots, which yields the optimal diverted flow over time. On-ramps can be conveniently incorporated in this procedure yielding SO metering rates. The following variants are...
This paper proposes a macroscopic behavioral theory of traffic dynamics for homogeneous, multi-lane freeways. The theory makes predictions for separate groups of lanes while recognizing that the traffic stream is usually composed of aggressive and timid drivers. Its principles are so simple that non-scientist drivers can understand them. The simplest version of the theory, which is described in its full complexity without calculus, is shown to be qualitatively consistent with experimental observations, including the most puzzling. Its predictions agree with the following phenomena: (i) the...
Most special-use freeway lanes in the US, whether reserved for carpools, toll-paying commuters or both, are physically separated from the adjacent regular-use lanes by some form of barrier. Vehicle movements in and out of a special lane of this type are permitted only at select access points along the route. The barrier at each select point might open for a distance of 400 m or so. Limiting access in this way is said to reduce the “turbulence” that might otherwise occur were the special lane not to have a buffer, such that vehicles could instead enter or exit that lane anywhere along its...
This paper proves that the vehicle trajectories predicted by (i) a simple linear carfollowing model, CF(L), (ii) the kinematic wave model with a triangular fundamental diagram, KW(T), and (iii) two cellular automata models CA(L) and CA(M) match everywhere to within a tolerance comparable with a single "jam spacing". Thus, CF(L) = KW(T) = CA(L,M).
It is shown that all the phase transitions in and out of freely flowing traffic reported earlier for a German site could be caused by bottlenecks, as are all the transitions observed at two other sites examined here. Furthermore, all the evidence indicates that bottlenecks cause these transitions in a predictable way, and no evidence is found that stoppages (jams) appear spontaneously in free flow traffic for no apparent reason. The most salient phenomena observed at all locations are explained in terms of a simple theory specific to traffic.
This paper examines the behavior of multi-lane freeway traffic past on-ramps, building on the continuum model of part I and focusing on the onset of congestion. The main complication with merges is that rabbits (fast vehicles) entering from an on-ramp usually stay on the shoulder lane(s) of the freeway for some distance before merging into the fast lane(s). An idealization is proposed where this distance is taken to be the same for all vehicles. As a result, the system behaves as if there was a fixed buffer zone where entering rabbits cannot change lanes. The model of part I is extended to...
Offered here is a critique of a simple scheme recently proposed for metering freeway on-ramps. An earlier report of this scheme's potential for reducing commuter delay is shown to be exaggerated. The discussion makes clear that to reduce delay, metering should increase the rates at which commuters exit the freeway. The scheme critiqued here, as well as other well-known metering algorithms, are shown to have deficiencies in this, particularly when the freeway is plagued by a diverge bottleneck with a congested off-ramp. Other more effective schemes for reducing the delay caused by these...
This paper presents a departure-time user equilibrium model that explicitly considers the most important determinants of congestion behavior in cities during the morning commute: different commuter origins, merge interactions and queue spillovers. The proposed model combines three previous works: the departure-time equilibrium theory in Vickrey (1969), the traffic flow model of Newell (1993) and the merge theory in Daganzo (1996). The paper examines the simplest possible network exhibiting the three important features and discusses the ensuing policy implications. The solution algorithm...
This paper presents a numerical method to model kinematic wave (KW) traffic streams containing slow vehicles. The slow vehicles are modeled discretely as moving boundaries that can affect the traffic stream. The proposed scheme converges in flows, densities and speeds without oscillations, and therefore can be readily used in situations where one wishes to model the effect of the traffic stream on the bottlenecks too. The approach is more accurate than Godunov's method in situations where the latter can be applied.
This paper is about the modular compilation and distribution of a sub-class of Simulink programs [10] across networks using bounded FIFO queues. The problem is first addressed mathematically. Then, based on these formal results, a software library for the modular compilation and distribution of Simulink program is given. The performance the library is given. The value of synchronous programming for the next generation of traffic control value is discussed. The adoption of these tools seems to be the natural candidate to address the needs of the traffic engineers. As a case study we present...
