Performance Guarantee Under Longest-Queue-First Schedule in Wireless Networks

• Published in: IEEE transactions on information theory Vol. 58; no. 9; pp. 5878 - 5889
• Main Authors: Li, Bo, Boyaci, Cem, Xia, Ye
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Electric noise; Exact sciences and technology; Graphs; Information theory; Information, signal and communications theory; Interference; Interference graphs; local pooling; longest-queue-first (LQF) policy; Matrix; Optimization; Schedules; Scheduling; stability; Stability analysis; Streams; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teletraffic; Thermal stability; Vectors; Wireless networks; wireless networks scheduling; Performance evaluation; Optimal algorithm; Wireless telecommunication; Interference; Teletraffic; Scheduling; longest-queue-first (LQF) policy; wireless networks scheduling; Queueing system; Diagonal matrix; Traffic management; NP hard problem; Traffic control; local pooling; Wireless network; Queue; stability
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2012.2201691

Efficient link scheduling in a wireless network is challenging. Typical optimal algorithms require solving an NP-hard subproblem. To meet the challenge, one stream of research focuses on finding simpler suboptimal algorithms that have low complexity but high efficiency in practice. In this paper, we study the performance guarantee of one such scheduling algorithm, the longest-queue-first (LQF) algorithm. It is known that the LQF algorithm achieves the full capacity region, \Lambda , when the interference graph satisfies the so-called local pooling condition. For a general graph G , LQF achieves (i.e., stabilizes) a part of the capacity region, \sigma ^{\ast }(G) \Lambda , where \sigma ^{\ast }(G) is the overall local pooling factor of the interference graph G and \sigma ^{\ast }(G) \leq 1 . It has been shown later that LQF achieves a larger rate region, \Sigma ^{\ast }(G) \Lambda , where \Sigma ^{\ast }(G) is a diagonal matrix. The contribution of this paper is to describe three new achievable rate regions, which are larger than the previously known regions. In particular, the new regions include all the extreme points of the capacity region and are not convex in general. We also discover a counterintuitive phenomenon in which increasing the arrival rate may sometime help to stabilize the network. This phenomenon can be well explained using the theory developed in this paper.