In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we direct...In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at any time t , as well as the recursion formula of the equilibrium distribution for calculating conveniently.Furthermore we obtain the stochastic decompositions of the queue length and waiting time in equilibrium.展开更多
A computational thermodynamics model for the oxygen bottom-blown copper smelting process(Shuikoushan,SKS process)was established,based on the SKS smelting characteristics and theory of Gibbs free energy minimization.T...A computational thermodynamics model for the oxygen bottom-blown copper smelting process(Shuikoushan,SKS process)was established,based on the SKS smelting characteristics and theory of Gibbs free energy minimization.The calculated results of the model show that,under the given stable production condition,the contents of Cu,Fe and S in matte are71.08%,7.15%and17.51%,and the contents of Fe,SiO2and Cu in slag are42.17%,25.05%and3.16%.The calculated fractional distributions of minor elements among gas,slag and matte phases are As82.69%,11.22%,6.09%,Sb16.57%,70.63%,12.80%,Bi68.93%,11.30%,19.77%,Pb19.70%,24.75%,55.55%and Zn17.94%,64.28%,17.79%,respectively.The calculated results of the multiphase equilibrium model agree well with the actual industrial production data,indicating that the credibility of the model is validated.Therefore,the model could be used to monitor and optimize the industrial operations of SKS process.展开更多
In this paper we study the transient property of the queue length for the M/G/1 queueing system with delay server vacations.Using the server busy period and the Laplace transformation we directly obtain the recursion ...In this paper we study the transient property of the queue length for the M/G/1 queueing system with delay server vacations.Using the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at time t , and also the recursion formula of the equilibrium distribution for calculating conveniently.As will be seen, this paper provides an intuitive and elegant method for studying transient properties of M/G/1 type queueing systems.展开更多
基金This work was supported by the National Outstanding Youth Science Foundation ( 7972 50 0 2 ) andthe Nature Education Minister
文摘In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at any time t , as well as the recursion formula of the equilibrium distribution for calculating conveniently.Furthermore we obtain the stochastic decompositions of the queue length and waiting time in equilibrium.
基金Project(51620105013)supported by the National Natural Science Foundation of China
文摘A computational thermodynamics model for the oxygen bottom-blown copper smelting process(Shuikoushan,SKS process)was established,based on the SKS smelting characteristics and theory of Gibbs free energy minimization.The calculated results of the model show that,under the given stable production condition,the contents of Cu,Fe and S in matte are71.08%,7.15%and17.51%,and the contents of Fe,SiO2and Cu in slag are42.17%,25.05%and3.16%.The calculated fractional distributions of minor elements among gas,slag and matte phases are As82.69%,11.22%,6.09%,Sb16.57%,70.63%,12.80%,Bi68.93%,11.30%,19.77%,Pb19.70%,24.75%,55.55%and Zn17.94%,64.28%,17.79%,respectively.The calculated results of the multiphase equilibrium model agree well with the actual industrial production data,indicating that the credibility of the model is validated.Therefore,the model could be used to monitor and optimize the industrial operations of SKS process.
文摘In this paper we study the transient property of the queue length for the M/G/1 queueing system with delay server vacations.Using the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at time t , and also the recursion formula of the equilibrium distribution for calculating conveniently.As will be seen, this paper provides an intuitive and elegant method for studying transient properties of M/G/1 type queueing systems.
