This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. We first %DIFDELCMD < {\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 %DIFDELCMD < {\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 %DIFDELCMD < {\it %%% collision effect between nodes prevails over the %DIFDELCMD < {\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%DIFDELCMD < {\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%DIFDELCMD < {\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 %DIFDELCMD < {\it %%% L\'evy \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances,%DIFDELCMD < {\it %%% leaning tendency, and%DIFDELCMD < {\it %%% directional unfairness .
This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. We first %DIFDELCMD < {\it %%% 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 %DIFDELCMD < {\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 %DIFDELCMD < {\it %%% collision effect between nodes prevails over the %DIFDELCMD < {\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 %DIFDELCMD < {\it %%% 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 %DIFDELCMD < {\it %%% 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 %DIFDELCMD < {\it %%% L\'evy \alpha-stable distribution with \alpha \in (1,2) %DIFDELCMD < {\it %%% %DIFDELCMD < {\it %%% .
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establish
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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
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entropy
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collision
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Poissonian aggregation
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per-packet backoff has a truncated
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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
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directional
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unfairness