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Efficient link scheduling in a wireless network is challenging. Typical optimal algorithms require solving an NP-hard sub-problem. To meet the challenge, one stream of research focuses on finding simpler sub-optimal algorithms that have low complexity but high efficiency in practice. In this paper, we study the performance guarantee of one such scheduling algorithm, the Longest-Queue-First (LQF) algorithm. It is known that the LQF algorithm achieves the full capacity region, $\Lambda$, when the interference graph satisfies the so-called local pooling condition. For a general graph $G$, LQF achieves (i.e., stabilizes) a part of the capacity region, $\sigma^*(G) \Lambda$, where $\sigma^*(G)$ is the overall local pooling factor of the interference graph $G$ and $\sigma^*(G) \leq 1$. It has been shown later that LQF achieves a larger rate region, $\Sigma^*(G) \Lambda$, where $\Sigma^ (G)$ is a diagonal matrix. The contribution of this paper is to describe three new achievable rate regions, which are larger than the previously-known regions. In particular, the new regions include all the extreme points of the capacity region and are not convex in general. We also discover a counter-intuitive phenomenon in which increasing the arrival rate may sometime help to stabilize the network. This phenomenon can be well explained using the theory developed in the paper., Comment: 27 pages, 7 figures