The Poisson process is a stochastic process that models many real-world phenomena. We present the definition of the Poisson process and discuss some facts as well as some related probability distributions. Finally, we...The Poisson process is a stochastic process that models many real-world phenomena. We present the definition of the Poisson process and discuss some facts as well as some related probability distributions. Finally, we give some new applications of the process.展开更多
Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rate...Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.展开更多
For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions...For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.展开更多
Markovian arrival processes were introduced by Neuts in 1979 （Neuts 1979） and have been used extensively in the stochastic modeling of queueing, inventory, reliability, risk, and telecommunications systems. In this ...Markovian arrival processes were introduced by Neuts in 1979 （Neuts 1979） and have been used extensively in the stochastic modeling of queueing, inventory, reliability, risk, and telecommunications systems. In this paper, we introduce a constructive approach to define continuous time Markovian arrival processes. The construction is based on Poisson processes, and is simple and intuitive. Such a construction makes it easy to interpret the parameters of Markovian arrival processes. The construction also makes it possible to establish rigorously basic equations, such as Kolmogorov differential equations, for Markovian arrival processes, using only elementary properties of exponential distributions and Poisson processes. In addition, the approach can be used to construct continuous time Markov chains with a finite number of states展开更多
泊松自回归模型假设到达过程为期望与方差相等的泊松分布,但事实上真正的数据生成过程中的到达过程的方差既可以高于期望也可以低于期望.本文提出了基于Katz到达过程(Katz arrivals)的计数数据自回归模型(INAR-Katz:integer valued auto...泊松自回归模型假设到达过程为期望与方差相等的泊松分布,但事实上真正的数据生成过程中的到达过程的方差既可以高于期望也可以低于期望.本文提出了基于Katz到达过程(Katz arrivals)的计数数据自回归模型(INAR-Katz:integer valued autoregressive process with Katz arrivals).并采用蒙特卡罗模拟方法(Monte Carlo simulations)比较了INAR-Katz模型在矩估计以及极大似然估计下的估计准确程度.最后采用INAR-Katz模型对患呼吸系统疾病的急诊就诊人数进行建模,结果显示INAR-Katz模型优于普通泊松模型、PAR模型,具有很好的应用前景.展开更多
This paper introduces two source models: MAP(Markovian arrival process) model for the traffic with correlation and burst, e.g., voice, video, etc. and PAP(Poisson arrival process) model for the traffic with non-correl...This paper introduces two source models: MAP(Markovian arrival process) model for the traffic with correlation and burst, e.g., voice, video, etc. and PAP(Poisson arrival process) model for the traffic with non-correlation, such as data, etc. Then a movable boundary bandwidth access policy is chosen.Basing on above model, the performance measures, e.g., mean waiting time and loss probability,especially the queue length time distribution are obtained. Finally, a number of numerical results are provided and shown through simulation.展开更多
文摘The Poisson process is a stochastic process that models many real-world phenomena. We present the definition of the Poisson process and discuss some facts as well as some related probability distributions. Finally, we give some new applications of the process.
文摘Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11571052,11731012)the Natural Science Foundation of Hunan Province(Grant Nos.2018JJ2417,2019JJ50405)+3 种基金the Outstanding Youth Foundation of Hunan Province Department of Education(Grant No.18B401)the China Scholarship Council(Grant No.201808430239)Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(Grant No.2018MMAEZD02)the Doctoral Scientific Research Project of Hunan University of Arts and Science.
文摘For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.
文摘Markovian arrival processes were introduced by Neuts in 1979 （Neuts 1979） and have been used extensively in the stochastic modeling of queueing, inventory, reliability, risk, and telecommunications systems. In this paper, we introduce a constructive approach to define continuous time Markovian arrival processes. The construction is based on Poisson processes, and is simple and intuitive. Such a construction makes it easy to interpret the parameters of Markovian arrival processes. The construction also makes it possible to establish rigorously basic equations, such as Kolmogorov differential equations, for Markovian arrival processes, using only elementary properties of exponential distributions and Poisson processes. In addition, the approach can be used to construct continuous time Markov chains with a finite number of states
文摘泊松自回归模型假设到达过程为期望与方差相等的泊松分布,但事实上真正的数据生成过程中的到达过程的方差既可以高于期望也可以低于期望.本文提出了基于Katz到达过程(Katz arrivals)的计数数据自回归模型(INAR-Katz:integer valued autoregressive process with Katz arrivals).并采用蒙特卡罗模拟方法(Monte Carlo simulations)比较了INAR-Katz模型在矩估计以及极大似然估计下的估计准确程度.最后采用INAR-Katz模型对患呼吸系统疾病的急诊就诊人数进行建模,结果显示INAR-Katz模型优于普通泊松模型、PAR模型,具有很好的应用前景.
基金Supported by the National Natural Science Foundation of China
文摘This paper introduces two source models: MAP(Markovian arrival process) model for the traffic with correlation and burst, e.g., voice, video, etc. and PAP(Poisson arrival process) model for the traffic with non-correlation, such as data, etc. Then a movable boundary bandwidth access policy is chosen.Basing on above model, the performance measures, e.g., mean waiting time and loss probability,especially the queue length time distribution are obtained. Finally, a number of numerical results are provided and shown through simulation.
