Randomized binary exponential backoff (BEB) is a popular algorithm for coordinating access to a shared channel. With an operational history exceeding four decades, BEB is currently an important component of several wireless standards. Despite this track record, prior theoretical results indicate that under bursty traffic (1) BEB yields poor makespan and (2) superior algorithms are possible. To date, the degree to which these findings manifest in practice has not been resolved. To address this issue, we examine one of the strongest cases against BEB: @math packets that simultaneously begin contending for the wireless channel. Using Network Simulator 3, we compare against more recent algorithms that are inspired by BEB, but whose makespan guarantees are superior. Surprisingly, we discover that these newer algorithms significantly underperform. Through further investigation, we identify as the culprit a flawed but common abstraction regarding the cost of collisions. Our experimental results are complemented by analytical arguments that the number of collisions -- and not solely makespan -- is an important metric to optimize. We believe that these findings have implications for the design of contention-resolution algorithms.
Work in @cite_46 addresses saturated throughput (each station always has a packet ready to be transmitted) of exponential backoff; roughly, this is the maximum throughput under stable packet arrival rates. Custom simulations are used to confirm these findings.
@cite_46
2017653216 2011032476 1965978478 2102391321
In the paper, we analyze the stochastic behavior of backoff protocols for multiple access channels such as the Ethernet. In particular, we prove that binary exponential backoff is unstable if the arrival rate of new messages at each station is λ N for any number of stations N exceeding 1 and any overall arrival rate λ exceeding .567 + 1 4 N - 2. More importantly, we also prove that any superlinear polynomial backoff protocol (e.g., quadratic backoff) is stable for any set of arrival rates that sum to less than one, and any number of stations. The results significantly extend the previous work in the area, and provide the first examples of acknowledgement based protocols known to be stable for a nonnegligible overall arrival rate distributed over an arbitrarily large number of stations. The results also disprove a popular assumption that exponential backoff is the best choice among acknowledgement based protocols for systems with large overall arrival rates. Finally, we prove that any linear or sublinear backoff protocol is unstable if the arrival rate at each station is λ N for any fixed λ and sufficiently large N . Binary exponential backoff is a randomized protocol for regulating transmissions on a multiple-access broadcast channel. Ethernet, a local-area network, is built upon this protocol. The fundamental theoretical issue is stability: Does the backlog of packets awaiting transmission remain bounded in time, provided the rates of new packet arrivals are small enough? It is assumed n ≥ 2 stations share the channel, each having an infinite buffer where packets accumulate while the station attempts to transmit the first from the buffer. Here, it is established that binary exponential backoff is stable if the sum of the arrival rates is sufficiently small. Detailed results are obtained on which rates lead to stability when n = 2 stations share the channel. In passing, several other results are derived bearing on the efficiency of the conflict resolution process. Simulation results are reported that, in particular, indicate alternative retransmission protocols can significantly improve performance. This paper analyzes the worst-case performance of randomized backoff on simple multiple-access channels. Most previous analysis of backoff has assumed a statistical arrival model.For batched arrivals, in which all n packets arrive at time 0, we show the following tight high-probability bounds. Randomized binary exponential backoff has makespan Θ(nlgn), and more generally, for any constant r, r-exponential backoff has makespan Θ(nloglgr n). Quadratic backoff has makespan Θ((n lg n)3 2), and more generally, for r>1, r-polynomial backoff has makespan Θ((n lg n)1+1 r). Thus, for batched inputs, both exponential and polynomial backoff are highly sensitive to backoff constants. We exhibit a monotone superpolynomial subexponential backoff algorithm, called loglog-iterated backoff, that achieves makespan Θ(nlglg n lglglg n). We provide a matching lower bound showing that this strategy is optimal among all monotone backoff algorithms. Of independent interest is that this lower bound was proved with a delay sequence argument.In the adversarial-queuing model, we present the following stability and instability results for exponential backoff and loglog-iterated backoff. Given a (λ,T)-stream, in which at most n=λT packets arrive in any interval of size T, exponential backoff is stable for arrival rates of λ=O(1 lgn) and unstable for arrival rates of λ=Ω(lglgn lgn); loglog-iterated backoff is stable for arrival rates of λ=O(1 (lglgn )) and unstable for arrival rates of λ=Ω(1 lgn). Our instability results show that bursty input is close to being worst-case for exponential backoff and variants and that even small bursts can create instabilities in the channel. Goodman, Greenberg, Madras and March gave a lower bound of n-Ω(log n) for the maximum arrival rate for which the n-user binary exponential backoff protocol is stable. Thus, they showed that the protocol is stable as long as the arrival rate is at most n-Ω(log n). We improve the lower bound, showing that the protocol is stable for arrival rates up to O(n-.9).