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：本文分析了负载比较误差对Po2方案性能的影响。具体考虑两类误差：负载相关误差与负载无关误差。在负载相关误差模型中，当两个采样服务器的队列长度差不超过常数$g$时，新作业以概率$\epsilon$被分配到队列长度较长的服务器；若队列长度差大于$g$，则不会出现分配误差。针对此类误差，我们证明当系统规模足够大且参数$\lambda$充分接近1时，Po2方案的性能优势仍能保持。进一步分析表明，与标准Po2方案不同，当$\epsilon > 1/2$且$\lambda$充分小时，该误差模型下的Po2方案性能可能劣于随机方案。在负载无关误差模型中，新作业以与采样服务器负载无关的固定概率$\epsilon$被分配到负载最大的服务器。针对该模型，我们证明仅当$\epsilon \leq 1/2$时Po2方案的性能优势得以保留；当$\epsilon > 1/2$时，系统稳定域缩小，其性能显著劣于随机方案。