In this paper, we analyze the effects of erroneous load comparisons on the performance of the Po2 scheme. Specifically, we consider load-dependent and load-independent errors. In the load-dependent error model, an incoming job is sent to the server with the larger queue length among the two sampled servers with probability $\epsilon$ if the difference in the queue lengths of the two sampled servers is less than or equal to a constant $g$; no error is made if the queue-length difference is higher than $g$. For this type of errors, we show that the benefits of the Po2 scheme is retained as long as the system size is sufficiently large and $\lambda$ is sufficiently close to $1$. Furthermore, we show that, unlike the standard Po2 scheme, the performance of the Po2 scheme under this type of errors can be worse than the random scheme if $\epsilon > 1/2$ and $\lambda$ is sufficiently small. In the load-independent error model, the incoming job is sent to the sampled server with the {\em maximum load} with an error probability of $\epsilon$ independent of the loads of the sampled servers. For this model, we show that the performance benefits of the Po2 scheme are retained only if $\epsilon \leq 1/2$; for $\epsilon > 1/2$ we show that the stability region of the system reduces and the system performs poorly in comparison to the {\em random scheme}.
翻译:在本文中, 我们分析错误的负载比较对 Po2 方案性能的影响。 具体地说, 我们考虑以负负负为主和以负负负为主的错误。 在依赖负负负的错误模型中, 输入的任务被发送到两个抽样服务器中队列长度较长的服务器上, 概率为$\ epsilon$, 如果两个抽样服务器队列长度的差异小于或等于恒定的$g$; 如果队列长度差高于$g$, 则没有错误。 对于这种类型的错误模型, 我们显示只要系统规模足够大且$\ lambda$足够接近$, 就会保留 Po2 计划的好处。 此外, 我们显示, 与标准的 Po2 计划不同的是, 如果 $\ eplon > 和 lambda$ 的队列长度差异足够小, 那么波2 计划的效果就会比随机方案差。 在重的错误模型中, 即将发送给抽样服务器 $xxxxxxxx 。 我们的系统运行 1 的系统性能 。</s>