We think that scrutinizing and understanding the application features in the services are quite important, in order to obtain some meaningful results from the performance analysis. Specifically, in the considered system, each user follows several others and wants to retrieve the most recent messages generatedbythefollowed persons,which emphasizesthe timecriticality of messages. Considering the time-criticality and the fact that not all the massages are guaranteed to be delivered in ICMN, the more recently created message should be given a higher priority in message relaying. Therefore, we adopted a new relaying scheme Last-Create-First-Relay, which is much different from traditional relaying schemes in other types of networks. Although being different, the scheme is quite meaningful to the considered Twitter-like subscriber/publisher services, as it satisfies the application-level user demands. According to our knowledge, few existing work discussed the performance under such a relaying scheme, which results in that the analytical methods proposed by the existing work are inapplicable to the considered system and some different conclusive results are open to be obtained. The results of our work fill the knowledge gap of the system performance under the novel relaying scheme.