We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the system...We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the systems. Such queueing networks appear typically in high-speed integrated services packet networks about telecommunication system. In the network, there is a number of packet traffic types. Each type needs a number of job classes (stages) of processing and each type of jobs is assigned the same priority rank at every station where it possibly receives service. Moreover, there is no inter-routing among different traffic types throughout the entire network.展开更多
In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general g...In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general gases including ideal poly tropic gas.Moreover,the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity,temperature,and radiation field.展开更多
This paper studies a multitype re-entrant line under smaller-buffer-first-served policy, which is an extension of first-buffer-first-served re-entrant line. We prove a heavy traffic limit theorem. The key to the proof...This paper studies a multitype re-entrant line under smaller-buffer-first-served policy, which is an extension of first-buffer-first-served re-entrant line. We prove a heavy traffic limit theorem. The key to the proof is to prove the uniform convergence of the corresponding critical fluid model.展开更多
A birth-death process is considered as an epidemic model with recovery and transmittance from outside.The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differe...A birth-death process is considered as an epidemic model with recovery and transmittance from outside.The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differential equation taking values in[0,1].For intermediate size or semilarge populations,the fraction of infected individuals is approximated by a diffusion formulated as a stochastic differential equation.That diffusion approximation however needs to be killed at the boundary{0}U{1}.An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.展开更多
Numerical algorithms for stiff stochastic differential equations are developed using lin-ear approximations of the fast diffusion processes,under the assumption of decoupling between fast and slow processes.Three nume...Numerical algorithms for stiff stochastic differential equations are developed using lin-ear approximations of the fast diffusion processes,under the assumption of decoupling between fast and slow processes.Three numerical schemes are proposed,all of which are based on the linearized formulation albeit with different degrees of approximation.The schemes are of comparable complexity to the classical explicit Euler-Maruyama scheme but can achieve better accuracy at larger time steps in stiff systems.Convergence analysis is conducted for one of the schemes,that shows it to have a strong convergence order of 1/2 and a weak convergence order of 1.Approximations arriving at the other two schemes are discussed.Numerical experiments are carried out to examine the convergence of the schemes proposed on model problems.展开更多
In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are o...In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.展开更多
In this paper,we derive the strong approximations for a four-class two station multi-class queuing network(Kumar-Seidman network) under a priority service discipline.Within a group,jobs are served in the order of ar...In this paper,we derive the strong approximations for a four-class two station multi-class queuing network(Kumar-Seidman network) under a priority service discipline.Within a group,jobs are served in the order of arrival,that is,a first-in-first-out disciple,and among groups,jobs are served under a pre-emptiveresume priority disciple.We show that if the input data(i.e.,the arrival and service processe) satisfy an approximation(such as the functional law-of-iterated logarithm approximation or the strong approximation),the output data(the departure processes) and the performance measures(such as the queue length,the work load and the sojourn time process) satisfy a similar approximation.展开更多
In this paper,we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function,solution of a kinetic equation.This closure is of non local typ...In this paper,we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function,solution of a kinetic equation.This closure is of non local type in the sense that it involves convolution or pseudo-differential operators.We show it is consistent with the diffusion limit and we propose numerical approximations to treat the non local terms.We illustrate how this approach can be incorporated in complex models involving a coupling with hydrodynamic equations,by treating examples arising in radiative transfer.We pay a specific attention to the conservation of the total energy by the numerical scheme.展开更多
In this paper,a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional(3 D)four-directional braided composites.Using this approach,the prediction process...In this paper,a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional(3 D)four-directional braided composites.Using this approach,the prediction process becomes feasible with only a limited number of training points.The surrogate models constructed using Finite Element(FE)method and Diffuse Approximation,reduce the computational time and cost for preparing experimental samples.In the FE model,multiscale method is applied to couple the computations of elastic properties at microscale and mesoscale.Subsequently,a parametric study is performed to analyze the effects of the three design parameters on the elastic properties.Satisfactory results are obtained via the surrogatebased modeling predictions,which are compared with the experimental measurements.Moreover,the predictions obtained from surrogate models concur well with the FE predictions.This study orients a new direction for predicting the mechanical properties based on surrogate models which can effectively reduce the sample preparation cost and computational efforts.展开更多
Spatio-temporal imaging of light propagation is very important in photonics because it provides the most direct tool available to study the interaction between light and its host environment.Sub-ps time resolution is ...Spatio-temporal imaging of light propagation is very important in photonics because it provides the most direct tool available to study the interaction between light and its host environment.Sub-ps time resolution is needed to investigate the fine and complex structural features that characterize disordered and heterogeneous structures,which are responsible for a rich array of transport physics that have not yet been fully explored.A newly developed wide-field imaging system enables us to present a spatiotemporal study on light transport in various disordered media,revealing properties that could not be properly assessed using standard techniques.By extending our investigation to an almost transparent membrane,a configuration that has been difficult to characterize until now,we unveil the peculiar physics exhibited by such thin scattering systems with transport features that go beyond mainstream diffusion modeling,despite the occurrence of multiple scattering.展开更多
基金the National Natural Science Foundation of China(No.10371053)
文摘We prove a heavy traffic limit theorem to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the systems. Such queueing networks appear typically in high-speed integrated services packet networks about telecommunication system. In the network, there is a number of packet traffic types. Each type needs a number of job classes (stages) of processing and each type of jobs is assigned the same priority rank at every station where it possibly receives service. Moreover, there is no inter-routing among different traffic types throughout the entire network.
基金Supported by Institute of Mathematics,State Academy of Sciences,Pyongyang,Democratic Peoples Republic of Korea。
文摘In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general gases including ideal poly tropic gas.Moreover,the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity,temperature,and radiation field.
基金Supported by the Fundamental Research Funds for the Central Universities (BUPT 2009RC0707) and National Natural Science Foundation of China (Grant No. 10901023)
文摘This paper studies a multitype re-entrant line under smaller-buffer-first-served policy, which is an extension of first-buffer-first-served re-entrant line. We prove a heavy traffic limit theorem. The key to the proof is to prove the uniform convergence of the corresponding critical fluid model.
文摘A birth-death process is considered as an epidemic model with recovery and transmittance from outside.The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differential equation taking values in[0,1].For intermediate size or semilarge populations,the fraction of infected individuals is approximated by a diffusion formulated as a stochastic differential equation.That diffusion approximation however needs to be killed at the boundary{0}U{1}.An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.
文摘Numerical algorithms for stiff stochastic differential equations are developed using lin-ear approximations of the fast diffusion processes,under the assumption of decoupling between fast and slow processes.Three numerical schemes are proposed,all of which are based on the linearized formulation albeit with different degrees of approximation.The schemes are of comparable complexity to the classical explicit Euler-Maruyama scheme but can achieve better accuracy at larger time steps in stiff systems.Convergence analysis is conducted for one of the schemes,that shows it to have a strong convergence order of 1/2 and a weak convergence order of 1.Approximations arriving at the other two schemes are discussed.Numerical experiments are carried out to examine the convergence of the schemes proposed on model problems.
基金the National Natural Science Foundation of China(No.10571092)
文摘In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.
文摘In this paper,we derive the strong approximations for a four-class two station multi-class queuing network(Kumar-Seidman network) under a priority service discipline.Within a group,jobs are served in the order of arrival,that is,a first-in-first-out disciple,and among groups,jobs are served under a pre-emptiveresume priority disciple.We show that if the input data(i.e.,the arrival and service processe) satisfy an approximation(such as the functional law-of-iterated logarithm approximation or the strong approximation),the output data(the departure processes) and the performance measures(such as the queue length,the work load and the sojourn time process) satisfy a similar approximation.
文摘In this paper,we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function,solution of a kinetic equation.This closure is of non local type in the sense that it involves convolution or pseudo-differential operators.We show it is consistent with the diffusion limit and we propose numerical approximations to treat the non local terms.We illustrate how this approach can be incorporated in complex models involving a coupling with hydrodynamic equations,by treating examples arising in radiative transfer.We pay a specific attention to the conservation of the total energy by the numerical scheme.
基金financial support from National Natural Science Foundation of China(No.U1833116)the China Postdoctoral Science Foundation Funded Project(No.2018M642775)supported by Key Scientific Research Project of Colleges and Universities in Henan Province(No.20A460003)。
文摘In this paper,a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional(3 D)four-directional braided composites.Using this approach,the prediction process becomes feasible with only a limited number of training points.The surrogate models constructed using Finite Element(FE)method and Diffuse Approximation,reduce the computational time and cost for preparing experimental samples.In the FE model,multiscale method is applied to couple the computations of elastic properties at microscale and mesoscale.Subsequently,a parametric study is performed to analyze the effects of the three design parameters on the elastic properties.Satisfactory results are obtained via the surrogatebased modeling predictions,which are compared with the experimental measurements.Moreover,the predictions obtained from surrogate models concur well with the FE predictions.This study orients a new direction for predicting the mechanical properties based on surrogate models which can effectively reduce the sample preparation cost and computational efforts.
基金supported by the European Network of Excellence Nanophotonics for Energy Efficiency and the ERC through the Advanced Grant PhotBots(Proj.Ref.291349).
文摘Spatio-temporal imaging of light propagation is very important in photonics because it provides the most direct tool available to study the interaction between light and its host environment.Sub-ps time resolution is needed to investigate the fine and complex structural features that characterize disordered and heterogeneous structures,which are responsible for a rich array of transport physics that have not yet been fully explored.A newly developed wide-field imaging system enables us to present a spatiotemporal study on light transport in various disordered media,revealing properties that could not be properly assessed using standard techniques.By extending our investigation to an almost transparent membrane,a configuration that has been difficult to characterize until now,we unveil the peculiar physics exhibited by such thin scattering systems with transport features that go beyond mainstream diffusion modeling,despite the occurrence of multiple scattering.