## 4 Simulation Results and Discussion
Notably, in Figure 3a,b, the compensation characteristics in the all-random distribution are generally better than those in the random-follow. This result suggests that the case number of making the dispersion distribution close to symmetric with respect to the midway OPC is greater in the all-random distribution than in the random-follow distribution. In contrast, the random-follow distribution deviates significantly from symmetry because the dispersion map of the latter half is the same as that of the former half. In Figure 3, \"descending order number\" is used for convenience of comparison, but all of three random distribution cases were performed 50 times with different random arrays. The pattern numbers were assigned in the order in which simulations were performed. Figure 4 compares pattern number 48 with the largest difference in performance between the EOP and timing jitter and pattern number 49 with the smallest difference in random-inverse  
Figure 3: The maximum launch power of the worst channel. (**a**) Resulting 1-dB EOP, (**b**) resulting 2.5 ps timing jitter. distribution. It can be seen from Figure 4 that, depending on the random distribution pattern of RDPS, the variation of timing jitter is larger than that of the EOP. This can be confirmed in Figure 4, where the difference in the launch power, which produces 2.5 ps timing jitter, is larger than the difference in launch power that produces a 1-dB EOP. The flexibility is included in the quality evaluation factor for the design of optical transmission links. The effective NRD range can be used as a measure to evaluate the flexibility of the dispersion-managed link. In the analysis, the NRD was fixed at 10 ps/nm because this value can induce the best compensation. However, it was confirmed through the previous studies that NRD can obtain the valid compensation even if it has value larger or smaller than 10 ps/nm. Thus, the effective NRD range can be defined as the range from the minimum NRD to the maximum NRD at which the 1-dB EOP can be achieved. Figure 5 shows the effective NRD range in each random distribution for which the best compensation is obtained. To be more specific, the results obtained for pattern number 28 in random-inverse distribution and pattern number 48 in random-follow and all-random distributions are represented in Figure 5. As can be seen intuitively, the effective NRD range shown in Figure 5 has a closed curve shape. It can be seen that the larger the area of the closed curve, the greater the flexibility of the link design. Consistent with the results obtained above, it can be confirmed that the flexibility of the dispersion-managed link design is excellent and is in the order of random-inverse, all-random, and random-follow. Figure 4: The EOP and timing jitter of pattern number 49 and 48 as a function of the launch power in case of random-inverse distribution. Figure 5: The effective NRD ranges versus the launch power. In terms of performance, the area of the closed curve, i.e., the area of the effective NRD range, is equivalent to the product of NRD and launch power. We evaluated the effective NRD range for a total of 150 RDPS distribution patterns. However, it is difficult to express and analyze the effective NRD range with one graph, since the number of data is too large. An easy and convenient way to compare flexibility is to use the product of NRD and launch power for each random pattern. Figure 6 shows the product of NRD and launch power for all distributions investigated in this study. It can be confirmed that random-inverse distribution is the best in terms of the flexibility of the dispersion-managed link design. Moreover, it can be seen that the product of NRD and launch power for all random-inverse distribution patterns is larger than the conventional scheme (333.6 (ps/nm) dBm). As a result of the analysis of the product of NRD and launch power, it can be confirmed that the effective NRD range and the maximum launch power resulting in a 1-dB EOP may not be simultaneously large even if the product is larger.