U∞ 1S On the Instability of Slotted Aloha with Capture

Yingqun Yu, Georgios B Giannakis, Xiaodong Cai

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We analyze the stability properties of slotted Aloha with capture for random access over fading channels with infinitely-many users. We assume that each user node knows only its own uplink channel gain, and uses this decentralized channel state information (CSI) to perform power control and/or probability control. The maximum stable throughput (MST) for a general capture model is obtained by means of drift analysis on the backlog Markov chain. We then specialize our general result to a signal-to-interference-plus-noise ratio (SINR) capture model. Our analysis shows that if the channels of all users are identical and independently distributed (i.i.d.) with finite means, the system is unstable under any kind of power and probability control mechanism that is based only on decentralized CSI.

Original languageEnglish (US)
Pages (from-to)257-261
Number of pages5
JournalIEEE Transactions on Wireless Communications
Issue number2
StatePublished - Feb 2006

Bibliographical note

Funding Information:
Manuscript received January 12, 2004; revised July 28, 2004; accepted February 14, 2005. The editor coordinating the review of this paper and approving it for publication was Li-Chun Wang. Work in this paper was prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. Part of the work in this paper was presented at the Proc. of WCNC, Atlanta, March 21-25, 2004.


  • SINR capture model
  • Slotted Aloha
  • maximum stable throughput
  • stability


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