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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 4362652, 15 pages
https://doi.org/10.1155/2017/4362652
Research Article

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

1College of Information and Communications, Korea University, Anam-dong 5-ga, Seongbuk-gu, Seoul 136-713, Republic of Korea
2Department of Computer Engineering, Hongik University, 72-1 Sangsoo-dong, Mapo-gu, Seoul 121-791, Republic of Korea

Correspondence should be addressed to Seung Jun Baek

Received 1 June 2017; Accepted 30 October 2017; Published 21 November 2017

Academic Editor: Haipeng Peng

Copyright © 2017 Seung Jun Baek and Joon-Sang Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a scheduling problem for a two-hop queueing network where the queues have randomly varying connectivity. Customers arrive at the source queue and are later routed to multiple relay queues. A relay queue can be served only if it is in connected state, and the state changes randomly over time. The source queue and relay queues are served in a time-sharing manner; that is, only one customer can be served at any instant. We propose Join the Shortest Queue-Longest Connected Queue (JSQ-LCQ) policy as follows: (1) if there exist nonempty relay queues in connected state, serve the longest queue among them; (2) if there are no relay queues to serve, route a customer from the source queue to the shortest relay queue. For symmetric systems in which the connectivity has symmetric statistics across the relay queues, we show that JSQ-LCQ is strongly optimal, that is, minimizes the delay in the stochastic ordering sense. We use stochastic coupling and show that the systems under coupling exist in two distinct phases, due to dynamic interactions among source and relay queues. By careful construction of coupling in both phases, we establish the stochastic dominance in delay between JSQ-LCQ and any arbitrary policy.