Modelling user behaviour at a stochastic road traffic bottleneck

Congestion in road traffic has received substantial attention in the research literature. One popular approach to modelling congesting and user response is the seminal bottleneck model introduced by Vickrey [25]. Here traffic is modelled as a fluid, and all travellers are subject to cost for waiting, early departure, and late departure. The travellers' response to the congestion is captured by assuming that they arrive at the bottleneck according to a Wardrop equilibrium, meaning that no traveller can decrease its costs by shifting its arrival time. This model and its extensions have been extensively studied in the research literature, but ignore the fact that road traffic consists of individual travellers with uncertain arrival time and speed. While the fluid approach used in the Vickrey model may be correct when the number of travellers is large, it fails to yield accurate predictions for a small number of travellers.In the present paper we propose a stochastic version of the bottleneck model, that can also handle smaller number of travellers. We discuss the error made by the fluid approximation, and show that the Wardrop equilibrium results in highly varying costs when applied in the more realistic setting with stochasticity. We then discuss an algorithm for numerically computing the equilibrium arrival rate for the stochastic bottleneck model, and propose a closed-form estimation for this equilibrium. This can be used for future studies into the effect of stochasticity in these bottleneck models.</p

Cellular automata approach to three-phase traffic theory

The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to the one of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel-Schreckenberg type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory [B. S. Kerner and S. L. Klenov. 2002. J. Phys. A: Math. Gen. 35, L31]. These features are qualitatively different than in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e., of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated.Comment: 55 pages, 24 figure

Dynamic and Static congestion models: A review

We begin by providing an overview of the conventional static equilibrium approach. In such model both the flow of trips and congestion delay are assumed to be constant. A drawback of the static model is that the time interval during which travel occurs is not specified so that the model cannot describe changes in the duration of congestion that result from changes in demand or capacity. This limitation is overcome in the Vickrey/Arnott, de Palma Lindsey bottleneck model, which combines congestion in the form of queuing behind a bottleneck with users' trip-timing preferences and departure time decisions. We derive the user equilibrium and social optimum for the basic bottleneck model, and explain how the optimum can be decentralized using a time-varying toll. They then review some extensions of the basic model that encompass elastic demand, user heterogeneity, stochastic demand and capacity and small networks. We conclude by identifying some unresolved modelling issues that apply not only to the bottleneck model but to trip-timing preferences and congestion dynamics in general

Dynamic User Equilibrium (DUE)

The quantitative analysis of road network traffic performed through static assignment models yields the transport demand-supply equilibrium under the assumption of within-day stationarity. This implies that the relevant variables of the system (i.e. user flows, travel times, costs) are assumed to be constant over time within the reference period. Although static assignment models satisfactorily reproduce congestion effects on traffic flow and cost patterns, they do not allow to represent the variation over time of the demand flows (i.e. around the rush hour) and of the network performances (i.e. in presence of time varying tolls, lane usage, signal plans, link usage permission); most importantly, they cannot reproduce some important dynamic phenomena, such as the formation and dispersion of vehicle queues due to the temporary over-saturation of road sections, and the spillback, that is queues propagation towards upstream roads

The New Italian Road Code and the virtues of the ‘shame lane’

In July 2003 a new Road Code was approved by the Italian parliament. Among many reforms whose validity is not questioned here, the new law states that on three-lane motorways the right lane should not be reserved anymore to slow vehicles alone. As in two-lane roads, all vehicles must now drive on the right lane, as long as it is not occupied by other vehicles. The model developed in this paper casts doubts on the validity of such a change, suggesting that the old rule generally performs better, in terms of number of accidents, average speed and motorway capacity, than the new one. This conclusion is shown to be extremely robust to refinements of the main assumptions concerning driving attitudes and the stochastic arrival of accidents.Traffic, Simulation, Italian Road Code

The New Italian Road Code and the Virtues of the ‘Shame Lane’

In July 2003 a new Road Code was approved by the Italian parliament. Among many reforms whose validity is not questioned here, the new law states that on three-lane motorways the right lane should not be reserved anymore to slow vehicles alone. As in two-lane roads, all vehicles must now drive on the right lane, as long as it is not occupied by other vehicles. The model developed in this paper casts doubts on the validity of such a change, suggesting that the old rule generally performs better, in terms of number of accidents, average speed and motorway capacity, than the new one. This conclusion is shown to be extremely robust to refinements of the main assumptions concerning driving attitudes and the stochastic arrival of accidents.Traffic, Simulation, Italian Road Code.

A demand model with departure time choice for within-day dynamic traffic assignment

A within-clay dynamic demand model is formulated, embodying, in addition to the classic generation, distribution and modal split stages, an actual demand model taking into account departure time choice. The work focuses on this last stage, represented through an extension of the discrete choice framework to a continuous choice set. The dynamic multimodal supply and equilibrium model based on implicit path enumeration, which have been developed in previous work are outlined here, to define within-day dynamic elastic demand stochastic multimodal equilibrium as a fixed point problem on users flows and transit line frequencies. A MSA algorithm capable, in the case of Logit route choice models, of supplying equilibrium flows and frequencies on real dimension networks, is presented, as well as the specific procedures implementing the departure time choice and actual demand models. Finally, the results obtained on a test network are presented and conclusions are drawn. (c) 2005 Elsevier B.V. All rights reserved