In this paper, we analyze the effects of erroneous load comparisons on the performance of the Po2 scheme. Specifically, we consider {\em load-dependent} and {\em 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 an error 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，具体研究了依赖负载与独立负载两类误差模型。在依赖负载的误差模型中，若两个采样服务器的队列长度差不超过常数$g$，则新到达任务以错误概率$\epsilon$被分配给队列长度较大的服务器；当队列长度差大于$g$时则不产生错误。针对此类误差，我们证明只要系统规模足够大且负载参数$\lambda$充分接近1，Po2方案的优势仍能保持。此外，我们发现与标准Po2方案不同，当$\epsilon > 1/2$且$\lambda$足够小时，此类误差下的Po2方案性能可能劣于随机方案。在独立负载的误差模型中，新到达任务不依赖采样服务器负载，以固定错误概率$\epsilon$被分配给负载最大的采样服务器。对于该模型，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。