This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. We first {\it establish} that the so-called mean field technique, which spins off a fixed point equation, is mathematically valid for use in performance analysis of 802.11. On the basis of this, succinct equations describing the backoff distribution as a function of the collision probability \gamma are derived , which also shed light on a controversy in the field . In addition, the observation that the {\it 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 {\it collision} effect between nodes prevails over the {\it 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 per-packet backoff has a truncated {\it 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 {\it   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 {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. We first {\it establish} that the so-called mean field technique, which spins off a fixed point equation, is mathematically valid for use in performance analysis of 802.11. On the basis of this, succinct equations describing the backoff distribution as a function of the collision probability \gamma are derived . In addition, the observation that the {\it 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 {\it collision} effect between nodes prevails over the {\it 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 per-packet backoff has a truncated {\it 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 the{\it long-range dependence in 802.11 and 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 {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
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, which also shed light on a controversy in the field
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identify the
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long-range dependence
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in 802.11 and