Ellipsoidal Toolbox is the first free MATLAB package that implements the operations of ellipsoidal calculus: geometric (Minkowski) sums and differences of ellipsoids, intersections of ellipsoids, and ellipsoids with hyperlanes and polyhedra. The toolbox uses ellipsoidal methods to compute forward and backward reach sets of continuous-and discretetime piecewise affine systems. Forward and backward reach sets can be also computed for continuous-time piece-wise linear systems with disturbances.

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Active traffic management (ATM) is the ability to dynamically manage recurrent and non-recurrent congestion based on prevailing traffic conditions in order to maximize the effectiveness and efficiency of road networks. It is a continuous process of (i) obtaining and analysing traffic measurement data, (ii) operations planning, i.e. simulating various scenarios and control strategies, (iii) implementing the most promising control strategies in the field, and (iv) maintaining a real-time decision support system that filters current traffic measurements to predict the traffic state in the near future, and to suggest the best available control strategy for the predicted situation. ATM relies on a fast and trusted traffic simulator for the rapid quantitative assessment of a large number of control strategies for the road network under various scenarios, in a matter of minutes. The opensource macrosimulation tool AURORA ROAD NETWORK MODELER is a good candidate for this purpose. The paper describes the underlying dynamical traffic model and what it takes to prepare the model for simulation; covers the traffic performance measures and evaluation of scenarios as part of operations planning; introduces the framework within which the control strategies are modelled and evaluated; and presents the algorithm for real-time traffic state estimation and short-term prediction.

The paper evaluates the influence of the maximum vehicle acceleration and variable proportions of ACC/CACC vehicles on the throughput of an intersection. Two cases are studied: (1) free road downstream of the intersection; and (2) red light at some distance downstream of the intersection. Simulation of a 4-mile stretch of an arterial with 13 signalized intersections is used to evaluate the impact of (C)ACC vehicles on the mean and standard deviation of travel time as the proportion of (C)ACC vehicles is increased. The results suggest a very high urban mobility benefit of (C)ACC vehicles at little or no cost in infrastructure.

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Macroscopic traffic models are necessary for simulation and study of traffic's complex macro-scale dynamics, and are often used by practitioners for road network planning, integrated corridor management, and other applications. These models have two parts: a link model, which describes traffic flow behavior on individual roads, and a node model, which describes behavior at road junctions. As the road networks under study become larger and more complex --- nowadays often including arterial networks --- the node model becomes more important. This paper focuses on the first order node model and has two main contributions. First, we formalize the multi-commodity flow distribution at a junction as an optimization problem with all the necessary constraints. Most interesting here is the formalization of input flow priorities. Then, we discuss a very common "conservation of turning fractions" or "first-in-first-out" (FIFO) constraint, and how it often produces unrealistic spillback. This spillback occurs when, at a diverge, a queue develops for a movement that only a few lanes service, but FIFO requires that all lanes experience spillback from this queue. As we show, avoiding this unrealistic spillback while retaining FIFO in the node model requires complicated network topologies. Our second contribution is a "partial FIFO" mechanism that avoids this unrealistic spillback, and a node model and solution algorithm that incorporates this mechanism. The partial FIFO mechanism is parameterized through intervals that describe how individual movements influence each other, can be intuitively described from physical lane geometry and turning movement rules, and allows tuning to describe a link as having anything between full FIFO and no FIFO. Excepting the FIFO constraint, the present node model also fits within the well-established "general class of first-order node models" for multi-commodity flows.Comment: The abstract on this info page is slightly abbreviated, please see the paper for the full abstrac