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  1. Article ; Online: A Discrete-Time Homing Problem with Two Optimizers

    Mario Lefebvre

    Games, Vol 14, Iss 6, p

    2023  Volume 68

    Abstract: A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk ... { X n , n = 0 , 1 , … } ... in the continuation region ... C : = { 1 , 2 , … } ...

    Abstract A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk <semantics> { X n , n = 0 , 1 , … } </semantics> in the continuation region <semantics> C : = { 1 , 2 , … } </semantics> , and the second player seeks to maximize the survival time in C . The process starts at <semantics> X 0 = x > 0 </semantics> and the game ends the first time <semantics> X n ≤ 0 </semantics> . An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly.
    Keywords random walk ; first-passage time ; homing problem ; difference game ; dynamic programming ; difference equation ; Technology ; T ; Social Sciences ; H
    Subject code 511
    Language English
    Publishing date 2023-10-01T00:00:00Z
    Publisher MDPI AG
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Article ; Online: On a modified M/M/$m$/$n$ queueing model

    Mario Lefebvre

    Computer Science Journal of Moldova, Vol 29, Iss 1(85), Pp 29-

    2021  Volume 40

    Abstract: The classic M/M/$m$/$n$ queueing model is modified by allowing a given task to require up to $m$ servers to be performed. Moreover, the maximum time that a task can wait in the queue before being executed is a random variable having an exponential ... ...

    Abstract The classic M/M/$m$/$n$ queueing model is modified by allowing a given task to require up to $m$ servers to be performed. Moreover, the maximum time that a task can wait in the queue before being executed is a random variable having an exponential distribution. Both FIFO (First In, First Out) and priority disciplines are considered. The case when $m=2$ is treated: the state space needed to fully describe the system is given, its size is calculated and the balance equations are presented when $n=1,2$ and 3. The queueing process can be used to model cluster-type multiprocessor computing systems.
    Keywords state space ; balance equations ; queue discipline ; priority ; cluster-type multiprocessor computing systems ; Electronic computers. Computer science ; QA75.5-76.95
    Language English
    Publishing date 2021-04-01T00:00:00Z
    Publisher Vladimir Andrunachievici Institute of Mathematics and Computer Science
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Article ; Online: Computer virus propagation modelled as a stochastic differential game

    Mario Lefebvre

    Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Vol 98, Iss 1, p A

    2020  Volume 3

    Abstract: The propagation of a computer virus is expressed as a stochastic differential game based on the two-dimensional Kermack-McKendrick model for the spread of epidemics. One optimizer tries to maximize the expected value of a cost function with quadratic ... ...

    Abstract The propagation of a computer virus is expressed as a stochastic differential game based on the two-dimensional Kermack-McKendrick model for the spread of epidemics. One optimizer tries to maximize the expected value of a cost function with quadratic control costs, while the other one wants to minimize this expected value. A particular problem is solved explicitly by making use of the method of similarity solutions to obtain the solution to the partial differential equation satisfied by the value function, subject to the appropriate conditions.
    Keywords Science (General) ; Q1-390
    Language English
    Publishing date 2020-05-01T00:00:00Z
    Publisher Accademia Peloritana dei Pericolanti
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Article ; Online: Modelling and forecasting temperature and precipitation in Italy

    Mario Lefebvre

    Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Vol 97, Iss 2, p A

    2019  Volume 2

    Abstract: We study the monthly average temperature in Italy for the period 1991-2015. The increase or decrease of the average temperature with respect to the previous year is modelled as a discrete-time Markov chain having four possible states. Similarly, a Markov ...

    Abstract We study the monthly average temperature in Italy for the period 1991-2015. The increase or decrease of the average temperature with respect to the previous year is modelled as a discrete-time Markov chain having four possible states. Similarly, a Markov chain is proposed as a model for the variations of the monthly amount of precipitation. Based on these models, it is possible to forecast whether the temperature and the amount of precipitation are likely to vary significantly in the long term.
    Keywords Science (General) ; Q1-390
    Language English
    Publishing date 2019-07-01T00:00:00Z
    Publisher Accademia Peloritana dei Pericolanti
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Article ; Online: An application of queueing theory in hydrology

    Mario Lefebvre

    Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Vol 97, Iss S2, p A

    2019  Volume 18

    Abstract: A model is considered for the flow of a river when it is high. The model is based on queueing theory. An application to the Delaware River, located in the United States, is presented. It is shown that an M/M/1/c queueing model is realistic when the flow ... ...

    Abstract A model is considered for the flow of a river when it is high. The model is based on queueing theory. An application to the Delaware River, located in the United States, is presented. It is shown that an M/M/1/c queueing model is realistic when the flow exceeds a certain threshold. Using this model, one can forecast what would happen if the rate at which events occur increases. The results can be extended by considering more general birth-and-death stochastic processes.
    Keywords Science (General) ; Q1-390
    Language English
    Publishing date 2019-12-01T00:00:00Z
    Publisher Accademia Peloritana dei Pericolanti
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Article ; Online: Teaching differential equations online

    Donatien N’Dri / Mario Lefebvre

    Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Vol 99, Iss S1, p A

    2021  Volume 12

    Abstract: An online version of the course on differential equations at Polytechnique Montrèal exists since 2013. The description of this online version as well as the results obtained by the online students are presented. These results are compared to the ones ... ...

    Abstract An online version of the course on differential equations at Polytechnique Montrèal exists since 2013. The description of this online version as well as the results obtained by the online students are presented. These results are compared to the ones obtained by classroom students. It is found that during the nine terms since the online version of the course has been offered, the online students had better results than their classroom colleagues. The conclusions that can be drawn from our experience with online teaching are discussed.
    Keywords Science (General) ; Q1-390
    Language English
    Publishing date 2021-09-01T00:00:00Z
    Publisher Accademia Peloritana dei Pericolanti
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Article ; Online: An optimal control problem for a Wiener process with random infinitesimal mean

    Mario Lefebvre / Abderrazak Moutassim

    Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Vol 97, Iss S2, p A

    2019  Volume 1

    Abstract: We consider a stochastic optimal control problem for one-dimensional diffusion processes with random infinitesimal mean and variance that depend on a continuoustime Markov chain. The process is controlled until it reaches either end of an interval. The ... ...

    Abstract We consider a stochastic optimal control problem for one-dimensional diffusion processes with random infinitesimal mean and variance that depend on a continuoustime Markov chain. The process is controlled until it reaches either end of an interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost. A particular case with a Wiener process will be treated in detail. Approximate and numerical solutions will be presented.
    Keywords Science (General) ; Q1-390
    Language English
    Publishing date 2019-12-01T00:00:00Z
    Publisher Accademia Peloritana dei Pericolanti
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Article ; Online: Similarity Solutions of Partial Differential Equations in Probability

    Mario Lefebvre

    Journal of Probability and Statistics, Vol

    2011  Volume 2011

    Keywords Probabilities. Mathematical statistics ; QA273-280 ; Mathematics ; QA1-939 ; Science ; Q ; DOAJ:Statistics ; DOAJ:Mathematics and Statistics
    Language English
    Publishing date 2011-01-01T00:00:00Z
    Publisher Hindawi Publishing Corporation
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Article ; Online: Maximizing the Mean Exit Time of a Brownian Motion from an Interval

    Mario Lefebvre

    International Journal of Stochastic Analysis , Vol

    2011  Volume 2011

    Keywords Mathematics ; QA1-939 ; Science ; Q ; DOAJ:Mathematics ; DOAJ:Mathematics and Statistics
    Language English
    Publishing date 2011-01-01T00:00:00Z
    Publisher Hindawi Publishing Corporation
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Article ; Online: LQG Homing in a Finite Time Interval

    Mario Lefebvre

    Journal of Control Science and Engineering, Vol

    2011  Volume 2011

    Abstract: Let X(t) be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controlling X(t) until time T(x)=min{T1(x),t1}, where T1(x) is the first-passage time of the process to a given ... ...

    Abstract Let X(t) be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controlling X(t) until time T(x)=min{T1(x),t1}, where T1(x) is the first-passage time of the process to a given boundary and t1 is a fixed constant. The optimal control is obtained explicitly in the particular case when X(t) is a controlled Wiener process.
    Keywords Engineering (General). Civil engineering (General) ; TA1-2040 ; Electronic computers. Computer science ; QA75.5-76.95
    Language English
    Publishing date 2011-01-01T00:00:00Z
    Publisher Hindawi Limited
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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