Delay-Optimal Scheduling for Two-Hop Relay Networks with Randomly Varying Connectivity: Join the Shortest Queue-Longest Connected Queue Policy

Figure 3

Example of the system in water-filling majorization (WFM) phase. The SQ under has an excess of customers compared to that under , which satisfies (40). The RQs at time under JSQ-LCQ are not necessarily better balanced than those under ; we observe that , if we compare the system in the upper left and the bottom left. However, if we construct by performing a “water-filling” routing of customers from to , we observe that is better balanced than , if we compare the queues in the upper right and the bottom right. Thus, we have , which satisfies (41).