论文标题
马尔可夫到达下的开关中的交通流量排队长度行为
Heavy Traffic Queue Length Behaviour in a Switch under Markovian Arrivals
论文作者
论文摘要
本文研究了到达时，根据马尔可夫流程时，在最大量化算法下运行的输入排队开关。我们精确地表征了繁重的交通拥堵限制的较重流量缩放的平均总和长度，并表明它的限制不到$ 2 $的$ 2 $。此外，我们获得了适用于所有交通状态的下层和上限，并且在繁重的人流中变得紧绷。 该论文通过概括为I.I.D的情况下开发的漂移方法获得了这些结果。到达，是马尔可夫到达的情况。本文通过首先获得马尔可夫到达下的单个服务器队列中的重量流量平均队列长度及其在单个服务器队列中的分布，然后将其应用于输入排队开关的情况下，以说明了这种概括。关键思想是利用有限状态马尔可夫链的几何混合，并与选择的时间范围一起工作，以便由于混合而导致的误差取决于重型交通参数。
This paper studies the input queued switch operating under the MaxWeight algorithm when the arrivals are according to a Markovian process. We exactly characterize the heavy-traffic scaled mean sum queue length in the heavy-traffic limit, and shows that it is within a factor of less than $2$ from a universal lower bound. Moreover, we obtain lower and upper bounds, that are applicable in all traffic regimes, and they become tight in the heavy-traffic regime. The paper obtains these results by generalizing the drift method recently developed for the case of i.i.d. arrivals, to the case of Markovian arrivals. The paper illustrates this generalization by first obtaining the heavy-traffic mean queue length and its distribution in a single server queue under Markovian arrivals and then applying it to the case of input queued switch. The key idea is to exploit the geometric mixing of finite-state Markov chains, and to work with a time horizon that is picked so that the error due to mixing depends on the heavy-traffic parameter.
