Using the general link transmission model in a dynamic traffic assignment to simulate congestion on urban networks

This article presents two new models of Dynamic User Equilibrium that are particularly suited for ITS applications, where the evolution of vehicle flows and travel times must be simulated on large road networks, possibly in real-time. The key feature of the proposed models is the detail representation of the main congestion phenomena occurring at nodes of urban networks, such as vehicle queues and their spillback, as well as flow conflicts in mergins and diversions. Compared to the simple word of static assignment, where only the congestion along the arc is typically reproduced through a separable relation between vehicle flow and travel time, this type of DTA models are much more complex, as the above relation becomes non-separable, both in time and space. Traffic simulation is here attained through a macroscopic flow model, that extends the theory of kinematic waves to urban networks and non-linear fundamental diagrams: the General Link Transmission Model. The sub-models of the GLTM, namely the Node Intersection Model, the Forward Propagation Model of vehicles and the Backward Propagation Model of spaces, can be combined in two different ways to produce arc travel times starting from turn flows. The first approach is to consider short time intervals of a few seconds and process all nodes for each temporal layer in chronological order. The second approach allows to consider long time intervals of a few minutes and for each sub-model requires to process the whole temporal profile of involved variables. The two resulting DTA models are here analyzed and compared with the aim of identifying their possible use cases. A rigorous mathematical formulation is out of the scope of this paper, as well as a detailed explanation of the solution algorithm. The dynamic equilibrium is anyhow sought through a new method based on Gradient Projection, which is capable to solve both proposed models with any desired precision in a reasonable number of iterations. Its fast convergence is essential to show that the two proposed models for network congestion actually converge at equilibrium to nearly identical solutions in terms of arc flows and travel times, despite their two diametrical approaches wrt the dynamic nature of the problem, as shown in the numerical tests presented here

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported

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

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

Dynamic Congestion and Tolls with Mobile Source Emission

This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical program with equilibrium constraints (MPEC) problem and then reformulated as a mathematical program with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty-based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the Proceedings of the 20th International Symposium on Transportation and Traffic Theory, 2013, the Netherland