非对称情形下最短队列优先服务策略的平稳性分析
Stationary analysis of the "Shortest Queue First" service policy: the asymmetric case
摘要：
作为后续行动，最近的论文考虑两个对称队列，\textit{Shortest Queue First}服务纪律，目前分析了两个一般的非对称队列。使用先前建立的结果，并假设指数分布的服务时间，在每个队列中的工作负载的双变量拉普拉斯变换被示出为依赖于二维函数方程$$ \mathbf{M} = Q_1 \cdot \mathbf{M}\circ h_1 + Q_2 \cdot \mathbf{M}\circ h_2 + \mathbf{L} $$的解$\mathbf{M}$，该二维函数方程具有给定的矩阵$Q_1$、$Q_2$和向量$\mathbf{L}$，并且其中函数$h_1$和$h_2$各自被定义在一些有理曲线上;解$\mathbf{M}$然后可以由涉及由这两个函数生成的半群$< h_1, h_2 >$的级数展开来表示。空队列的概率以及在每个队列的工作量分布的尾部行为的特点。
英文摘要：
As a follow-up to a recent paper considering two symmetric queues, the \textit{Shortest Queue First} service discipline is presently analysed for two general asymmetric queues. Using the results previously established and assuming exponentially distributed service times, the bivariate Laplace transform of workloads in each queue is shown to depend on the solution $\mathbf{M}$ to a two-dimensional functional equation $$ \mathbf{M} = Q_1 \cdot \mathbf{M}\circ h_1 + Q_2 \cdot \mathbf{M}\circ h_2 + \mathbf{L} $$ with given matrices $Q_1$, $Q_2$ and vector $\mathbf{L}$ and where functions $h_1$ and $h_2$ are defined each on some rational curve; solution $\mathbf{M}$ can then represented by a series expansion involving the semi-group $< h_1, h_2 >$ generated by these two functions. The empty queue probabilities along with the tail behaviour of the workload distribution at each queue are characterised.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
