We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic accor...We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.展开更多
In this work,we propose an alternative to the Pollaczek-Khinchine formula for the ultimate time survival(or ruin)probability calculation in exchange for a few assumptions on the random variables that generate the rene...In this work,we propose an alternative to the Pollaczek-Khinchine formula for the ultimate time survival(or ruin)probability calculation in exchange for a few assumptions on the random variables that generate the renewal risk model.More precisely,we demonstrate the expressibility of the distribution function n P(sup n≥1^(n)∑_(i=1)(X_(i)-cθ_(i))<u),u∈N_(0)using the roots of the probability-generating function,expectation E(X-cθ)X-cθ,and probability mass function of.We assume that the random X_(1),X_(2),...cθ_(1),cθ_(2),...variables of the mutually independent sequences and are cθc>0 X cθindependent copies of X and respectively,wherein,and are independent,θnonnegative,and integer.We also assume that the support of is finite.To illustrate the applicability of the proven theoretical statements we present a few numerical outputs when the mentioned random variables adopt some particular distributions.展开更多
We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. E...We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.展开更多
The present paper describes a multichannel digital random pulse generator implemented in a 65-nm FPGA device. The random time interval generation is based on inverse transformation method. The output pulse generation ...The present paper describes a multichannel digital random pulse generator implemented in a 65-nm FPGA device. The random time interval generation is based on inverse transformation method. The output pulse generation rate, pulse width and the probability distribution function (PDF) of each channel might be individually selected by the computer through a USB cable connection. Statistical properties of the output channels can be adjusted and recorded in a fully dynamic flexible manner. The Poisson and uniform PDFs were tested and implemented for up to eight different channels in experiment, however, the implementation of any arbitrary PDF is possible by programming capability of the device as well. Detailed experimental results are expressed in the manuscript. The proposed equipment makes it possible to verify the complicated multichannel detection systems without having the radioactive experimental tests. This is a low cost instrumentation due to the FPGA-based construction.展开更多
In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operati...In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.展开更多
基金supported by the National Natural Science Foundation of China (10771185,10926036)Zhejiang Provinicial Natural Science Foundation of China (Y6090172)
文摘We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.
文摘In this work,we propose an alternative to the Pollaczek-Khinchine formula for the ultimate time survival(or ruin)probability calculation in exchange for a few assumptions on the random variables that generate the renewal risk model.More precisely,we demonstrate the expressibility of the distribution function n P(sup n≥1^(n)∑_(i=1)(X_(i)-cθ_(i))<u),u∈N_(0)using the roots of the probability-generating function,expectation E(X-cθ)X-cθ,and probability mass function of.We assume that the random X_(1),X_(2),...cθ_(1),cθ_(2),...variables of the mutually independent sequences and are cθc>0 X cθindependent copies of X and respectively,wherein,and are independent,θnonnegative,and integer.We also assume that the support of is finite.To illustrate the applicability of the proven theoretical statements we present a few numerical outputs when the mentioned random variables adopt some particular distributions.
文摘We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.
文摘The present paper describes a multichannel digital random pulse generator implemented in a 65-nm FPGA device. The random time interval generation is based on inverse transformation method. The output pulse generation rate, pulse width and the probability distribution function (PDF) of each channel might be individually selected by the computer through a USB cable connection. Statistical properties of the output channels can be adjusted and recorded in a fully dynamic flexible manner. The Poisson and uniform PDFs were tested and implemented for up to eight different channels in experiment, however, the implementation of any arbitrary PDF is possible by programming capability of the device as well. Detailed experimental results are expressed in the manuscript. The proposed equipment makes it possible to verify the complicated multichannel detection systems without having the radioactive experimental tests. This is a low cost instrumentation due to the FPGA-based construction.
文摘In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.
