Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 61, Issue 4, Pages 1687-1701Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2015.2404795
Keywords
Point process theory; regular variation theory; 802.11; mean field theory
Funding
- Centre for Quantifiable Quality of Service in Communication Systems
- Centre of Excellence
- Research Council
- NTNU
- UNINETT
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This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. A simplistic principle founded upon regular variation theory is that the backoff time has a truncated Pareto-type tail distribution with an exponent of (log gamma)/log m (m is the multiplicative factor and gamma is the collision probability). This reveals that the per-node backoff process is heavy-tailed in the strict sense for gamma > 1/m(2), and paves the way for the following unifying result. The state-of-the-art theory on the superposition of the heavy-tailed processes is applied to establish a dichotomy exhibited by the aggregate backoff process, putting emphasis on the importance of time-scales on which we view the backoff processes. While the aggregation on normal time-scales leads to a Poisson process, it is approximated by a new limiting process possessing long-range dependence (LRD) on coarse time-scales. This dichotomy turns out to be instrumental in formulating short-term fairness, extending existing formulas to arbitrary population, and to elucidate the absence of LRD in practical situations. A refined wavelet analysis is conducted to strengthen this argument.
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