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.
A class of tree-based algorithms for contention resolution is proposed in @cite_26 . Work in @cite_71 addresses the case of heterogeneous packet sizes. The case where packets can arrive dynamically is examined in @cite_69 @cite_17 @cite_18 .
@cite_69 @cite_26 @cite_18 @cite_71 @cite_17
2493870798 2116736083 2014455962 2490780450
In this paper, we consider the classical contention resolution problem in which an unknown subset of n possible nodes are activated and connected to a shared channel. The problem is solved in the first round that an active node transmits alone (thus breaking symmetry). Contention resolution has been an active research topic for over four decades. Accordingly, tight upper and lower bounds are known for most major model assumptions. There remains, however, an important case that is unresolved: contention resolution with multiple channels and collision detection. (Tight bounds are known for contention resolution with multiple channels, and contention resolution with collision detection, but not for the combination of both assumptions.) Recent work proved the first non-trivial lower bound for randomized solutions to this problem in this setting. The optimality of this lower bound was left an open question. In this paper, we answer this open question by describing and analyzing new contention resolution algorithms that match, or come within a log factor of matching, this bound for all relevant parameters. By doing so, we help advance our understanding of an important longstanding problem. Of equal importance, our solutions introduce a novel new technique in which we leverage a distributed structure we call coalescing cohorts to simulate a well-known parallel search strategy from the structured PRAM CREW model in our unstructured distributed model. We conjecture that this approach is relevant to many problems in the increasingly important setting of distributed computation using multiple shared channels. The multiaccessing of a broadcast communication channel by independent sources is considered. Previous accessing techniques suffer from long message delays, low throughput, and or congestion instabilities. A new class of high-speed, high-throughput, stable, multiaccessing algorithms is presented. Contentions resolving tree algorithms are introduced, and they are analyzed for specific probabilistic source models. It is shown that these algorithms are stable (in that all moments of delay exist) and are optimal in a certain sense. Furthermore, they have a maximum throughput of 0.430 packets slut and have good delay properties. It is also shown that, under heavy traffic, the optimally controlled tree algorithm adaptively changes to the conventional time-division multiple access protocol. As the size of High Performance Computing clusters grows, so does the probability of interconnect hot spots that degrade the latency and effective bandwidth the network provides. This paper presents a solution to this scalability problem for real life constant bisectional-bandwidth fat-tree topologies. It is shown that maximal bandwidth and cut-through latency can be achieved for MPI global collective traffic. To form such a congestion-free configuration, MPI programs should utilize collective communication, MPI-node-order should be topology aware, and the packet routing should match the MPI communication patterns. First, we show that MPI collectives can be classified into unidirectional and bidirectional shifts. Using this property, we propose a scheme for congestion-free routing of the global collectives in fully and partially populated fat trees running a single job. The no-contention result is then obtained for multiple jobs running on the same fat-tree by applying some job size and placement restrictions. Simulation results of the proposed routing, MPI-node-order and communication patterns show no contention which provides a 40 throughput improvement over previously published results for all-to-all collectives. In this paper, we study upper and lower bounds for contention resolution on a single hop fading channel; i.e., a channel where receive behavior is determined by a signal to interference and noise ratio (SINR) equation. The best known previous solution solves the problem in this setting in O(log2 n log log n) rounds, with high probability in the system size n. We describe and analyze an algorithm that solves the problem in O(log n + log R) rounds, where R is the ratio between the longest and shortest link, and is a value upper bounded by a polynomial in n for most feasible deployments. We complement this result with an Ω(log n) lower bound that proves the bound tight for reasonable R. We note that in the classical radio network model (which does not include signal fading), high probability contention resolution requires Ω(log 2 n) rounds. Our algorithm, therefore, affirms the conjecture that the spectrum reuse enabled by fading should allow distributed algorithms to achieve a significant improvement on this log2 n speed limit. In addition, we argue that the new techniques required to prove our upper and lower bounds are of general use for analyzing other distributed algorithms in this increasingly well-studied fading channel setting.