An Ethereum blockchain based on proof of stake ( PoS) consensus mechanism is used to achieve the data sharing within the civil aviation service platform for both airport group management and passengers. Considering th...An Ethereum blockchain based on proof of stake ( PoS) consensus mechanism is used to achieve the data sharing within the civil aviation service platform for both airport group management and passengers. Considering the Gas consumption of Ethereum, the dynamic batch-service capacity constraint by the Block Gas Limit and the priority mechanism depending on the different Gas Price of transactions, M/ G/1 queuing theory with batch-service is used to construct the service model of transactions confirmation process in the proposed blockchain system, where the effects of transactions arrival rate, block capacity, service rate and number of nodes on the average confirmation time of transactions with different priority are analyzed, and eventually a performance analysis model of blockchain for civil aviation business data is proposed. The simulation results prove the usability and accuracy of the model, which can provide both theoretical basis for data sharing of civil aviation using Ethereum blockchain and the further optimization of transactions confirmation time.展开更多
马尔可夫链的遍历性研究在随机过程理论中占有重要地位,本文聚焦于马尔可夫链的次几何遍历性,提出了次几何遍历的六个等价判定条件,这些等价条件对进一步探索一般马尔可夫过程的次几何遍历性提供了理论基础,并将其应用于排队论中经典的M...马尔可夫链的遍历性研究在随机过程理论中占有重要地位,本文聚焦于马尔可夫链的次几何遍历性,提出了次几何遍历的六个等价判定条件,这些等价条件对进一步探索一般马尔可夫过程的次几何遍历性提供了理论基础,并将其应用于排队论中经典的M/G/1嵌入过程,得到了易验证的M/G/1嵌入排队过程次几何遍历的判定条件。The study of the ergodicity of Markov chains holds a significant position in the theory of stochastic processes. This paper focuses on the subgeometric ergodicity of Markov chains and proposes six equivalent criteria for subgeometric ergodicity of Markov chains. These equivalent conditions provide a theoretical foundation for further exploration of the subgeometric ergodicity of general Markov processes. In addition, this paper applies these criteria to the classical M/G/1 embedded process in queueing theory, obtaining easily verifiable conditions for determining the subgeometric ergodicity of the M/G/1 embedded queueing process.展开更多
By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its s...By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.展开更多
This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of th...This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.展开更多
In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M...In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.展开更多
基金the Open Foundation of Key Laboratory of Airports Cluster Intelligent Operation(No.KLACIO201900006124)National Natural Science Foundation of China(No.61901011)+1 种基金Foundation of Beijing Municipal Commission of Education(No.KM202010005017,KM202110005021)Beijing Natural Science Foundation(No.L192002).
文摘An Ethereum blockchain based on proof of stake ( PoS) consensus mechanism is used to achieve the data sharing within the civil aviation service platform for both airport group management and passengers. Considering the Gas consumption of Ethereum, the dynamic batch-service capacity constraint by the Block Gas Limit and the priority mechanism depending on the different Gas Price of transactions, M/ G/1 queuing theory with batch-service is used to construct the service model of transactions confirmation process in the proposed blockchain system, where the effects of transactions arrival rate, block capacity, service rate and number of nodes on the average confirmation time of transactions with different priority are analyzed, and eventually a performance analysis model of blockchain for civil aviation business data is proposed. The simulation results prove the usability and accuracy of the model, which can provide both theoretical basis for data sharing of civil aviation using Ethereum blockchain and the further optimization of transactions confirmation time.
文摘马尔可夫链的遍历性研究在随机过程理论中占有重要地位,本文聚焦于马尔可夫链的次几何遍历性,提出了次几何遍历的六个等价判定条件,这些等价条件对进一步探索一般马尔可夫过程的次几何遍历性提供了理论基础,并将其应用于排队论中经典的M/G/1嵌入过程,得到了易验证的M/G/1嵌入排队过程次几何遍历的判定条件。The study of the ergodicity of Markov chains holds a significant position in the theory of stochastic processes. This paper focuses on the subgeometric ergodicity of Markov chains and proposes six equivalent criteria for subgeometric ergodicity of Markov chains. These equivalent conditions provide a theoretical foundation for further exploration of the subgeometric ergodicity of general Markov processes. In addition, this paper applies these criteria to the classical M/G/1 embedded process in queueing theory, obtaining easily verifiable conditions for determining the subgeometric ergodicity of the M/G/1 embedded queueing process.
基金supported by the National Natural Science Foundation of China(11371303)Natural Science Foundation of Xinjiang(2012211A023)Science Foundation of Xinjiang University(XY110101)
文摘By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.
基金This work was suPPorted by the Natiotal Out-standing YOuth Sdence FOundstion (79725tX)2) the suPporting program of the Nat
文摘This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.
基金Project supported by the National Natural Science Foundation of China(Grant No.70171059)
文摘In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.
