This work introduces a methodology to determine an optimal vaccination strategy for the COVID-19 ... more This work introduces a methodology to determine an optimal vaccination strategy for the COVID-19 disease with limited vaccination capacity, considering the delays between vaccine doses in order to minimize the number of deaths. The evolution of the pandemic in the city of Tandil, province of Buenos Aires, Argentina, is studied through a compartmental model, where the parameters involved are calibrated according to official data. An auxiliary age-structured optimal control problem is introduced, where optimal policies are obtained taking into account the characteristics of the vaccine and the vaccination capacity. Through numerical simulations, the policy obtained is compared with other feasible strategies, considering or not strict isolation measures.
Resumen: el problema de simular los movimientos y la dinámica de un barco es estudiado principalm... more Resumen: el problema de simular los movimientos y la dinámica de un barco es estudiado principalmente para el desarrollo de simuladores de maniobra y entrenamiento. En general existen varios niveles posibles de solución, con diversos grados de complejidad y de exactitud. No obstante, todas las soluciones basadas en modelos matemáticos conducen naturalmente a dos acercamientos básicos: modelos dinámicos de desplazamiento, y modelos cinemáticos de predicción. En este trabajo se presenta el desarrolló de un nuevo modelo matemático simplificado, que permite predecir la dinámica de maniobra y la cinemática de movimiento, en base a las características del barco, y a los valores de velocidades y aceleraciones instantáneas.
This paper introduces a numerical method to solve the hydrothermal scheduling problem in oligopol... more This paper introduces a numerical method to solve the hydrothermal scheduling problem in oligopolistic markets. The electric power industry in Argentina has shifted from a scenario in which operation schedule is fully regulated to a new competitive deregulated scenario in which there is a small number of generation companies which satisfy a large amount of the total power demand of the system. To emulate this kind of market structure, an oligopolistic market model has been developed. To solve the hydrothermal coordination problem under these assumptions, both operative restrictions, and market economical aspects must be considered. In the present work we study how the price and configuration of the different units of the system are affected by the use of hydroelectric plants and also by pumped storage units through a mathematical market model represented by a variational inequality. The solution method is based on a relaxation algorithm, and the Nikaido-Isoda function is used for th...
This paper deals with optimal control problems for systems affine in the control variable. We con... more This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.
The principal purpose of this work is to test the TUC strategy in a simple case using a micro-sim... more The principal purpose of this work is to test the TUC strategy in a simple case using a micro-simulator designed ad hoc, previous to its real implementation. Using concepts of traffic engineering we describe a well known dynamic linear model of traffic flow in a urban traffic network that is controlled using the traffic-light times. This simplified model allows to obtain a Riccati feedback matrix and compute traffic-light times that will improve the congestion levels. We present some numerical experiments made with the model on an academic example and we val-idated them with a microscopic simulator that we have created based on Car Following theory and discrete event models. 2. Keywords: Optimal Control, LQ-Control, Urban traffic models. The reduction of urban traffic congestion is nowadays obtaining more and more attention. When there is a technology capable of coordinate traffic lights with green times calculated through sophisticated mathematical algorithms a moderate reduction o...
1. AbstractThe principal purpose of this work is to test the TUC strategy in a simple case using ... more 1. AbstractThe principal purpose of this work is to test the TUC strategy in a simple case using a micro-simulatordesigned ad hoc, previous to its real implementation.Using concepts of traffic engineering we describe a well known dynamic linear model of traffic flowin a urban traffic network that is controlled using the traffic-light times. This simplified model allows toobtain a Riccati feedback matrix and compute traffic-light times that will improve the congestion levels.We present some numerical experiments made with the model on an academic example and we val-idated them with a microscopic simulator that we have created based on Car Following theory anddiscrete event models.2. Keywords: Optimal Control, LQ-Control, Urban traffic models.3. IntroductionThe reduction of urban traffic congestion is nowadays obtaining more and more attention. When thereis a technology capable of coordinate traffic lights with green times calculated through sophisticatedmathematical algorithms a moderate reduction of ...
The Traffic Assignment problem consists in determining the routes used by sets of network users t... more The Traffic Assignment problem consists in determining the routes used by sets of network users taking into account the link congestions. In deterministic modelling, Wardrop Equilibriums are computed. They can be reduced to huge non-linear multiflow problems in the simplest cases. In stochastic modelling, Logit Assignments are used. They are obtained, mainly, by substituting the minplus semiring by the «Gibbs-Maslov semirings»[ ], in the deterministic assignment computations.
This work introduces a methodology to determine an optimal vaccination strategy for the COVID-19 ... more This work introduces a methodology to determine an optimal vaccination strategy for the COVID-19 disease with limited vaccination capacity, considering the delays between vaccine doses in order to minimize the number of deaths. The evolution of the pandemic in the city of Tandil, province of Buenos Aires, Argentina, is studied through a compartmental model, where the parameters involved are calibrated according to official data. An auxiliary age-structured optimal control problem is introduced, where optimal policies are obtained taking into account the characteristics of the vaccine and the vaccination capacity. Through numerical simulations, the policy obtained is compared with other feasible strategies, considering or not strict isolation measures.
Resumen: el problema de simular los movimientos y la dinámica de un barco es estudiado principalm... more Resumen: el problema de simular los movimientos y la dinámica de un barco es estudiado principalmente para el desarrollo de simuladores de maniobra y entrenamiento. En general existen varios niveles posibles de solución, con diversos grados de complejidad y de exactitud. No obstante, todas las soluciones basadas en modelos matemáticos conducen naturalmente a dos acercamientos básicos: modelos dinámicos de desplazamiento, y modelos cinemáticos de predicción. En este trabajo se presenta el desarrolló de un nuevo modelo matemático simplificado, que permite predecir la dinámica de maniobra y la cinemática de movimiento, en base a las características del barco, y a los valores de velocidades y aceleraciones instantáneas.
This paper introduces a numerical method to solve the hydrothermal scheduling problem in oligopol... more This paper introduces a numerical method to solve the hydrothermal scheduling problem in oligopolistic markets. The electric power industry in Argentina has shifted from a scenario in which operation schedule is fully regulated to a new competitive deregulated scenario in which there is a small number of generation companies which satisfy a large amount of the total power demand of the system. To emulate this kind of market structure, an oligopolistic market model has been developed. To solve the hydrothermal coordination problem under these assumptions, both operative restrictions, and market economical aspects must be considered. In the present work we study how the price and configuration of the different units of the system are affected by the use of hydroelectric plants and also by pumped storage units through a mathematical market model represented by a variational inequality. The solution method is based on a relaxation algorithm, and the Nikaido-Isoda function is used for th...
This paper deals with optimal control problems for systems affine in the control variable. We con... more This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.
The principal purpose of this work is to test the TUC strategy in a simple case using a micro-sim... more The principal purpose of this work is to test the TUC strategy in a simple case using a micro-simulator designed ad hoc, previous to its real implementation. Using concepts of traffic engineering we describe a well known dynamic linear model of traffic flow in a urban traffic network that is controlled using the traffic-light times. This simplified model allows to obtain a Riccati feedback matrix and compute traffic-light times that will improve the congestion levels. We present some numerical experiments made with the model on an academic example and we val-idated them with a microscopic simulator that we have created based on Car Following theory and discrete event models. 2. Keywords: Optimal Control, LQ-Control, Urban traffic models. The reduction of urban traffic congestion is nowadays obtaining more and more attention. When there is a technology capable of coordinate traffic lights with green times calculated through sophisticated mathematical algorithms a moderate reduction o...
1. AbstractThe principal purpose of this work is to test the TUC strategy in a simple case using ... more 1. AbstractThe principal purpose of this work is to test the TUC strategy in a simple case using a micro-simulatordesigned ad hoc, previous to its real implementation.Using concepts of traffic engineering we describe a well known dynamic linear model of traffic flowin a urban traffic network that is controlled using the traffic-light times. This simplified model allows toobtain a Riccati feedback matrix and compute traffic-light times that will improve the congestion levels.We present some numerical experiments made with the model on an academic example and we val-idated them with a microscopic simulator that we have created based on Car Following theory anddiscrete event models.2. Keywords: Optimal Control, LQ-Control, Urban traffic models.3. IntroductionThe reduction of urban traffic congestion is nowadays obtaining more and more attention. When thereis a technology capable of coordinate traffic lights with green times calculated through sophisticatedmathematical algorithms a moderate reduction of ...
The Traffic Assignment problem consists in determining the routes used by sets of network users t... more The Traffic Assignment problem consists in determining the routes used by sets of network users taking into account the link congestions. In deterministic modelling, Wardrop Equilibriums are computed. They can be reduced to huge non-linear multiflow problems in the simplest cases. In stochastic modelling, Logit Assignments are used. They are obtained, mainly, by substituting the minplus semiring by the «Gibbs-Maslov semirings»[ ], in the deterministic assignment computations.
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