It is important to accurately evaluate and reduce jitter accumulation in long-haul digital repeatered lines. Jitter accumulation caused by random pattern signals has already been analyzed. However, periodic pattern signals such as pseudorandom signals are usually used to measure jitter accumulation. This paper describes the difference between the jitter accumulation for both signals and the necessary conditions to accurately estimate jitter accumulation for random pattern signals by using periodic pattern signals. First, it is shown theoretically that systematic jitter for periodic signals saturates, showing a ripple pattern. The limit of increase is determined by the ratio of tank bandwidth and pattern repetition frequency. Up to a certain number of regenerators determined by the ratio, systematic jitter increases in rough proportion to the\sqrt{N}slope. It is also shown that the equation to estimate random pattern jitter accumulation is determined by the measured value for periodic pattern signals. Second, jitter characteristics are simulated by optical signal circulating experiments. The results are in agreement with the analysis. In addition, the reduction effects on periodic signal jitter accumulation caused by timing signal delay and nonlinearity of the limiter in the timing circuit are shown.