具有负载比较误差的两种选择的幂
The Power of Two Choices with Load Comparison Errors
摘要：
在本文中，我们分析了错误的负载比较的性能的Po 2计划的影响。具体来说，我们考虑负载相关和负载无关的错误。在负载相关错误模型中，如果两个采样服务器的队列长度差小于或等于常数$g$，则以概率$ε$将传入作业发送到两个采样服务器中具有较大队列长度的服务器;如果队列长度差大于$g$，则不出错。对于这种类型的错误，我们表明，只要系统大小足够大，$λ$足够接近$1$，Po 2方案的好处被保留。此外，我们表明，不像标准的Po 2计划，这种类型的错误下的Po 2计划的性能可以比随机计划，如果$ε> 1/2$和$λ$是足够小。在与负载无关的错误模型中，传入作业被发送到具有{ \em最大负载}的采样服务器，错误概率为$ε$，与采样服务器的负载无关。对于这个模型，我们表明，只有当$ε\leq 1/2$的Po 2方案的性能优势被保留;对于$ε> 1/2$，我们表明，系统的稳定区域减少，系统表现不佳的比较{ \em随机方案}。
英文摘要：
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 $ε$ 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 $λ$ 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 $ε> 1/2$ and $λ$ 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 $ε$ 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 $ε\leq 1/2$; for $ε> 1/2$ we show that the stability region of the system reduces and the system performs poorly in comparison to the {\em random scheme}.
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