Mathematical Problems in Engineering / 2017 / Article / Fig 3

Research Article

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).

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at help@hindawi.com to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.