In optical burst switching (OBS) networks, a key problem is to schedule as many bursts as possible on wavelength channels so that the throughput is maximized and the burst loss is minimized. Most of the current research on OBS has been concentrated on reducing burst loss in an ldquoaverage-caserdquo sense, and little effort has been devoted to understanding the worst case performance. Since OBS itself is an open-loop control system, it may exhibit a worst case behavior when adversely synchronized. On the other hand, most commercial systems require an acceptable worst case performance. In this paper, we use competitive analysis to analyze the worst case performance of a large set of scheduling algorithms, called best-effort online scheduling algorithms, for OBS networks and establish a number of interesting upper and lower bounds on the performance of such algorithms. Our analysis shows that the performance of any best-effort online algorithm is closely related to a few factors, such as the range of offset time, maximum-to-minimum burst-length ratio, and the number of data channels. A surprising discovery is that the worst case performance of any best-effort online scheduling algorithm is primarily determined by the maximum-to-minimum burst-length ratio, followed by the range of offset time. Furthermore, if all bursts have the same burst length and offset time, all best-effort online scheduling algorithms generate the same optimal solution, regardless of how different they may look. Our analysis can also be extended to some non-best-effort online scheduling algorithms, such as the well-known Horizon algorithm, and establish similar bounds. Based on the analytic results, we give guidelines for several widely discussed OBS problems, including burst assembly, offset time setting, and scheduling algorithm design, and propose a new channel reservation protocol called virtual fixed offset-time (VFO) to improve the worst case performance. Our simulation shows that VFO can also reduce the average burst loss rate.