Toward a general framework for dynamic road pricing

This paper develops a general framework for analysing and calculating dynamic road toll. The optimal network flow is first determined by solving an optimal control problem with statedependent responses such that the overall benefit of the network system is maximized. An optimal toll is then sought to decentralise this optimal flow. This control theoretic formulation can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models. The analysis in this paper is more general and is applied to calculate the optimal flow and toll for Friesz’s whole link traffic model. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

Traffic models for dynamic system optimal assignment

Most analyses on dynamic system optimal (DSO) assignment are done by using a control theory with an outflow traffic model. On the one hand, this control theoretical formulation provides some attractive mathematical properties for analysis. On the other hand, however, this kind of formulation often ignores the importance of ensuring proper flow propagation. Moreover, the outflow models have also been extensively criticized for their implausible traffic behaviour. This paper aims to provide another framework for analysing a DSO assignment problem based upon sound traffic models. The assignment problem we considered aims to minimize the total system cost in a network by seeking an optimal inflow profile within a fixed planning horizon. This paper first summarizes the requirements on a plausible traffic model and reviews three common traffic models. The necessary conditions for the optimization problem are then derived using a calculus of variations technique. Finally, a simple working example and concluding remarks are given

Model-Independent Predictions for Low Energy Isoscalar Heavy Baryon Observables in the Combined Heavy Quark and Large NcN_c Expansion

Model-independent predictions for excitation energies, semileptonic form factors and electromagnetic decay rates of isoscalar heavy baryons and their low energy excited states are discussed in terms of the combined heavy quark and large $N_c$ expansion. At leading order, the observables are completely determined in terms of the known excitation energy of the first excited state of $\Lambda_c$. At next-to-leading order in the combined expansion all heavy baryon observables can be expressed in a model-independent way in terms of two experimentally measurable quantities. We list predictions at leading and next-to-leading order.Comment: 7 pages, LaTe

Excited Heavy Baryons and Their Symmetries III: Phenomenology

Phenomenological applications of an effective theory of low-lying excited states of charm and bottom isoscalar baryons are discussed at leading and next-to-leading order in the combined heavy quark and large $N_c$ expansion. The combined expansion is formulated in terms of the counting parameter $\lambda\sim 1/m_Q, 1/N_c$; the combined expansion is in powers of $\lambda^{1/2}$. We work up to next-to-leading order. We obtain model-independent predictions for the excitation energies, the semileptonic form factors and electromagnetic decay rates. The spin-averaged mass of the doublet of the first orbitally excited sate of $\Lambda_b$ is predicted to be approximately $5920 MeV$. It is shown that in the combined limit at leading and next-to-leading order there is only one independent form factor describing $\Lambda_b \to \Lambda_c \ell \bar{\nu}$; similarly, $\Lambda_b \to \Lambda_{c}^{*} \ell \bar{\nu}$ and $\Lambda_b \to \Lambda_{c1} \ell \bar{\nu}$ decays are described by a single independent form factor. These form factors are calculated at leading and next-to-leading order in the combined expansion. The electromagnetic decay rates of the first excited states of $\Lambda_c$ and $\Lambda_b$ are determined at leading and next-to leading order. The ratio of radiative decay rates $\Gamma(\Lambda_{c}^{*} \to \Lambda_c \gamma) / \Gamma(\Lambda_{b1} \to \Lambda_b \gamma)$ is predicted to be approximately 0.2, greatly different from the heavy quark effective theory value of unity.Comment: 21 pages, 2 figure

Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC

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