This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. We first make a simplistic Palm interpretation of the Bianchi's formula and on the basis of which, succinct equations describing the backoff distribution as a function of the collision probability \gamma are derived, which also correct a possible misunderstanding in the field. The observation that the entropy of the backoff process in 802.11 increases with the number of nodes leads us to see through a Poissonian character inherent in 802.11. However, it is also found that the collision effect between nodes prevails over the Poissonian aggregation effect in spite of its tendency to increase with the number of nodes. Based on these findings, we formulate the principle about the inter-transmission probability that lays a foundation for the short-term fairness analysis. Another principle discovered upon regular variation theory is that the backoff times have a truncated Pareto-type tail distribution with an exponent of (\log \gamma)/\log m (m is the multiplicative factor  ). This reveals that the  backoff process is heavy-tailed in the strict sense for m^2 \gamma>1 , essentially due to collision. Moreover, we identify long-range dependence in 802.11 through both of mathematical and empirical wavelet-based analyses and answer a riddle: the absence of long range dependence in aggregate total load. We also show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or L\'evy \alpha-stable distribution with \alpha \in (1,2) .
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-scale 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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We first make a simplistic Palm interpretation of the Bianchi's formula and on the basis of which, succinct equations describing the backoff distribution as a function of the collision probability \gamma are derived, which also correct a possible misunderstanding in the field. The observation that the entropy of the backoff process in 802.11 increases with the number of nodes leads us to see through a Poissonian character inherent in 802.11. However, it is also found that the collision effect between nodes prevails over the Poissonian aggregation effect in spite of its tendency to increase with the number of nodes. Based on these findings, we formulate the principle about the inter-transmission probability that lays a foundation for the short-term fairness analysis. Another principle discovered
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in 802.11 through both of mathematical and empirical wavelet-based analyses and answer a riddle:
(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
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long range dependence in aggregate total load. We also show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or L\'evy \alpha-stable distribution with \alpha \in (1,2)
LRD in practical situations. A refined wavelet analysis is conducted to strengthen this argument