In pull-based peer-to-peer (P2P) live streaming systems, peers contribute a fixed amount of memory space to buffer the multimedia content downloaded from their neighbor peers; at the same time, the peers periodically notify neighbor peers of buffered content by exchanging buffer maps. However, the relationship between buffer size (BS) and buffer map exchange period (BMEP) is still not clearly revealed. Towards this issue, we develop a simulator to evaluate the impact of BS and BMEP on system performance, such as startup delay and playback fluency. It is observed that the system performance can be improved by increasing BS only when BS is in certain range; however, shortening the BMEP can continuously improve the system performance. Further, we compare the system performance of PPLive and PPStream in the flash crowd scenario by this simulator. Though these two systems have different BS and BMEP, the playback continuity of these two systems is almost the same but the startup delay of PPStream is much smaller than that of PPLive. Shortening BMEP is effective to improve system performance but causes much additional signaling overhead. Towards this issue, we introduce Run-Length Encoding to compress the buffer map and the compression ratio can be as high as 11:1. What we have done is benefit to not only the optimization but also the modeling of P2P live streaming protocols.