The Power of Two Choices with Load Comparison Errors

Abstract

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}.