In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using...In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.展开更多
This paper presents a generic mathematical model for depicting the diffusion of an innovative product on a given market. Our approach relies on a probabilistic modeling of each customer behavior with respect to the co...This paper presents a generic mathematical model for depicting the diffusion of an innovative product on a given market. Our approach relies on a probabilistic modeling of each customer behavior with respect to the commercial process which is used to promote such a product. We introduce in particular the concept of coherent market that corresponds to a market which can be analyzed in a uniform way within our model. This last notion allows us to recover the classical empirical results that were discovered and widely studied by E.M. Rogers and his school. We explain finally how to use our approach as a support for analytic predictive marketing.展开更多
This paper studies price-based residential demand response management(PB-RDRM)in smart grids,in which non-dispatchable and dispatchable loads(including general loads and plug-in electric vehicles(PEVs))are both involv...This paper studies price-based residential demand response management(PB-RDRM)in smart grids,in which non-dispatchable and dispatchable loads(including general loads and plug-in electric vehicles(PEVs))are both involved.The PB-RDRM is composed of a bi-level optimization problem,in which the upper-level dynamic retail pricing problem aims to maximize the profit of a utility company(UC)by selecting optimal retail prices(RPs),while the lower-level demand response(DR)problem expects to minimize the comprehensive cost of loads by coordinating their energy consumption behavior.The challenges here are mainly two-fold:1)the uncertainty of energy consumption and RPs;2)the flexible PEVs’temporally coupled constraints,which make it impossible to directly develop a model-based optimization algorithm to solve the PB-RDRM.To address these challenges,we first model the dynamic retail pricing problem as a Markovian decision process(MDP),and then employ a model-free reinforcement learning(RL)algorithm to learn the optimal dynamic RPs of UC according to the loads’responses.Our proposed RL-based DR algorithm is benchmarked against two model-based optimization approaches(i.e.,distributed dual decomposition-based(DDB)method and distributed primal-dual interior(PDI)-based method),which require exact load and electricity price models.The comparison results show that,compared with the benchmark solutions,our proposed algorithm can not only adaptively decide the RPs through on-line learning processes,but also achieve larger social welfare within an unknown electricity market environment.展开更多
In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved.As an application of this result,the well-kn...In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved.As an application of this result,the well-known Strassen’s theorem is generalized.Moreover,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.展开更多
Technical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmo...Technical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmogorov equations, describing homogenous Markovian processes with discrete states and continuous time, are listed in symmetric matrix form. Properties of symmetry of matrix of subsystem failure and recovery flow intensity are analyzed. Dependences of characteristic equation coefficients on intensity of failure and recovery flows are obtained. It is demonstrated that the coefficients of characteristic equation meet the demands of functional dependence matching proposed visible analytical solution of complete algebraic equation of fourth order. Depending upon intensity of failure and recovery flows, four roots of characteristic equation are analytically found out. Analytical formulae for state probability of interactive technical system depending upon the roots of characteristic equation are determined using structurally ordered symmetric determinants, involving proper column of set initial data as well as subsystem failure and recovery flow intensity are proposed.展开更多
文摘In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.
基金This paper was supported by the Ecole Polytechnique and Thales chair "Engineering of Complex Systems".
文摘This paper presents a generic mathematical model for depicting the diffusion of an innovative product on a given market. Our approach relies on a probabilistic modeling of each customer behavior with respect to the commercial process which is used to promote such a product. We introduce in particular the concept of coherent market that corresponds to a market which can be analyzed in a uniform way within our model. This last notion allows us to recover the classical empirical results that were discovered and widely studied by E.M. Rogers and his school. We explain finally how to use our approach as a support for analytic predictive marketing.
基金This work was supported in part by the National Natural Science Foundation of China(61922076,61725304,61873252,61991403,61991400)in part by the Australian Research Council Discovery Program(DP200101199).
文摘This paper studies price-based residential demand response management(PB-RDRM)in smart grids,in which non-dispatchable and dispatchable loads(including general loads and plug-in electric vehicles(PEVs))are both involved.The PB-RDRM is composed of a bi-level optimization problem,in which the upper-level dynamic retail pricing problem aims to maximize the profit of a utility company(UC)by selecting optimal retail prices(RPs),while the lower-level demand response(DR)problem expects to minimize the comprehensive cost of loads by coordinating their energy consumption behavior.The challenges here are mainly two-fold:1)the uncertainty of energy consumption and RPs;2)the flexible PEVs’temporally coupled constraints,which make it impossible to directly develop a model-based optimization algorithm to solve the PB-RDRM.To address these challenges,we first model the dynamic retail pricing problem as a Markovian decision process(MDP),and then employ a model-free reinforcement learning(RL)algorithm to learn the optimal dynamic RPs of UC according to the loads’responses.Our proposed RL-based DR algorithm is benchmarked against two model-based optimization approaches(i.e.,distributed dual decomposition-based(DDB)method and distributed primal-dual interior(PDI)-based method),which require exact load and electricity price models.The comparison results show that,compared with the benchmark solutions,our proposed algorithm can not only adaptively decide the RPs through on-line learning processes,but also achieve larger social welfare within an unknown electricity market environment.
基金Research supported in part by DPFIHE(Grant No.96002704)NNSFC(Grant No.19771008)
文摘In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved.As an application of this result,the well-known Strassen’s theorem is generalized.Moreover,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.
文摘Technical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmogorov equations, describing homogenous Markovian processes with discrete states and continuous time, are listed in symmetric matrix form. Properties of symmetry of matrix of subsystem failure and recovery flow intensity are analyzed. Dependences of characteristic equation coefficients on intensity of failure and recovery flows are obtained. It is demonstrated that the coefficients of characteristic equation meet the demands of functional dependence matching proposed visible analytical solution of complete algebraic equation of fourth order. Depending upon intensity of failure and recovery flows, four roots of characteristic equation are analytically found out. Analytical formulae for state probability of interactive technical system depending upon the roots of characteristic equation are determined using structurally ordered symmetric determinants, involving proper column of set initial data as well as subsystem failure and recovery flow intensity are proposed.
