论文标题
在灾难的分数排队模型上
On a fractional queueing model with catastrophes
论文作者
论文摘要
$ m/m/1 $的队列带有灾难性的是修改后的$ m/m/1 $队列型号，根据泊松过程的时代，灾难发生了，使系统空了。在这项工作中，我们研究了与灾难的分数$ m/m/1 $队列，该灾难是通过考虑原始Markov过程的Kolmogorov的前方方程中的分数衍生物来提出的。对于由此产生的分数过程，我们可以随时获得客户数量的状态概率，平均值和差异。此外，我们讨论了参数的估计。
A $M/M/1$ queue with catastrophes is a modified $M/M/1$ queue model for which, according to the times of a Poisson process, catastrophes occur leaving the system empty. In this work, we study a fractional $M/M/1$ queue with catastrophes, which is formulated by considering fractional derivatives in the Kolmogorov's Forward Equations of the original Markov process. For the resulting fractional process, we obtain the state probabilities, the mean and the variance for the number of customers at any time. In addition, we discuss the estimation of parameters.
