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
In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of ...In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.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.
文摘In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.
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.
