Fundamentals of the Backoff Process in 802.11: Dichotomy of the Aggregation

Abstract

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 γ)/ log m (m is the multiplicative factor and γ is the collision probability). This reveals that the per-node backoff process is heavy-tailed in the strict sense for γ > 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.

The Cost of Mitigating Power Law Delay in Random Access Networks

“…Moreover, following Corollary 1, we see that E[X n ] for EB is finite if P c < 1 r n and infinite if P c ≥ 1 r n . This is consistent with the results in [3] and [5]. Notice that Theorem 1 is more general in that it applies even if the limit in the LHS of (31) does not exist 2 .…”

“…In the literature, Q1 has been partly addressed. [5] first finds that the medium access delay distribution of EB is heavytailed when retry limit K is infinite, regardless of the backoff exponent r. [3] later proves that the medium access delay indeed follows a power law distribution, the slope of which is obtained as a function of the backoff exponent and the collision probability. Noticeably, the effect of power law delay cannot be eliminated even if a finite retry limit K is enforced in practical systems.…”

Improving Performance of Ieee 802.11 by a Dynamic Control Backoff Algorithm Under Unsaturated Traffic Loads

“…As mentioned above, the backoff algorithm for IEEE 802.11 is very important for controlling channel access to maximize throughput and fairness [3]. There are several methods for extending or proposing backoff algorithms.…”

Delay analysis and optimality of the renewal access protocol

“…Thus, we see that the medium access delay is light-tailed whatever distribution it uses as the selection distribution in the RAP. It is shown that the exponential backoff (EB) scheme, which are adopted in the IEEE 802.11 DCF, may cause heavy-tailed medium access delay for some backoff multiplier values (Bi and Zhang 2012;Cho and Jiang 2009;Sakurai and Vu 2007) (with no retransmission limit and infinite maximum backoff stage). In other words, expanding the backoff window after a collision makes the medium access delay have large higher moments.…”

“…Furthermore, the probability generating functions of the medium access delay were derived in Sakurai and Vu (2007), Tadayon et al (2012), Zanella and De Pellegrini (2005). It was also shown that the exponential backoff (EB) scheme, which is used in the IEEE 802.11 DCF, makes the medium access delay distribution be heavytailed (Bi and Zhang 2012;Cho and Jiang 2009;Sakurai and Vu 2007) and a scheme called polynomial backoff was proposed in Bi and Zhang (2012) to mitigate the heavy-tailedness of medium access delay. For unsaturated condition, to handle the variation in the number of contending terminals, fixed point analysis (Dai and Sun 2013;Felemban and Ekici 2011;Garetto and Chiasserini 2005;Tickoo and Sikdar 2008) and Markovian framework (Foh et al 2007;Liu et al 2010) were utilized.…”