论文标题
在二项式避免政策下的投票系统时刻的存在和近似
Existence and Approximations of Moments for Polling Systems under the Binomial-Exhaustive Policy
论文作者
论文摘要
我们为在二项式避免政策（BEP）下运行的轮询系统中的稳态队列的矩存在建立了足够的条件。我们假设服务器根据预先指定的表在不同的缓冲区之间进行切换，并且每当服务器从一个缓冲区移动到另一个缓冲区时，切换时间就会发生。我们进一步假设客户根据独立的泊松过程到达，并且服务和切换时间是具有一般分布的独立随机变量。然后，我们提出了一个简单的方案来近似矩，这在切换时间没有界限时被证明是渐近的，并且其计算复杂性并不能随着矩的顺序增长。最后，我们证明了矩的提议的渐近近似与大转换时间缩放下的流体极限有关。因此，通过简单地识别这些控件下的流体限制，可以轻松地为其他服务器转换策略得出类似的近似值即可。数值示例证明了我们对BEP和其他策略下矩的近似值的有效性，并且随着切换时间的增加，它们的准确性提高。
We establish sufficient conditions for the existence of moments of the steady-state queue in polling systems operating under the binomial-exhaustive policy (BEP). We assume that the server switches between the different buffers according to a pre-specified table, and that switchover times are incurred whenever the server moves from one buffer to the next. We further assume that customers arrive according to independent Poisson processes, and that the service and switchover times are independent random variables with general distributions. We then propose a simple scheme to approximate the moments, which is shown to be asymptotically exact as the switchover times grow without bound, and whose computation complexity does not grow with the order of the moment. Finally, we demonstrate that the proposed asymptotic approximation for the moments is related to the fluid limit under a large-switchover-time scaling; thus, similar approximations can be easily derived for other server-switching policies, by simply identifying the fluid limits under those controls. Numerical examples demonstrate the effectiveness of our approximations for the moments under BEP and under other policies, and their increased accuracy as the switchover times increase.
