Is Our Model for Contention Resolution Wrong?

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: $n$ 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.Comment: Accepted to the 29th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2017

Adversarial Analyses of Window Backoff Strategies for Simple Multiple-Access Channels

Backoff strategies have typically been analyzed by making statistical assumptions on the distribution of problem inputs. Although these analyses have provided valuable insights into the efficacy of various backoff strategies, they leave open the question as to which backoff algorithms perform best in the worst case or on inputs, such as bursty inputs, that are not covered by the statistical models. This paper analyzes randomized backoff strategies using worst-case assumptions on the inputs. Specifically, we analyze algorithms for simple multiple-access channels, where the only feedback from each attempt to send a packet is a single bit indicating whether the transmission succeeded or the packet collided with another packet. We analyze a class of strategies, called window strategies, where each packet partitions time into a sequence (W₁, W₂,...) of windows. Within each window, the packet makes an access attempt during a single randomly selected slot. If its transmission is unsuccessful, it waits for its slot in the next window before retrying. We use delay-sequence arguments to show that for the batch problem, in which n packets all arrive at time 0, if every window has size W = Θ(n), then with high probability, all packets successfully transmit with makespan n lg lg n ± O(n). We use this result to analyze window backoff strategies with varying window sizes. Specifically, we show that the familiar binary exponential backoff algorithm, where Wk = Θ(2k), has makespan Θ(n lg n), and that more generally, for any constant r > 1, the r-exponential backoff algorithm in which Wk = Θ(rk) has makespan Θ(n lglg rn). We also show that for any constant r > 1, the r-polynomial backoff algorithm, in which Wk = Θ(kr), has makespan Θ((n/lg n)¹⁺¹/r). All of these batch strategies are monotonic, in the sense that the window size monotonically increases over time. We exhibit a monotonic backoff algorithm that achieves makespan Θ(n lg lg n/lg lg lg n). We prove that this algorithm, whose backoff is superpolynomial and subexponential, is optimal over all monotonic backoff schemes. In addition, we exhibit a simple backoff/backon algorithm, having window sizes that vary nonmonotonically according to a "sawtooth" pattern, that achieves the optimal makespan of Θ(n). We study the online setting using an adversarial queueing model. We define a (λ,T)-stream to be an input stream of packets in which at most n = λT packets arrive during any time interval of size T. In this model, to evaluate a given backoff algorithm (which does not know λ or T), we analyze the worst-case behavior of the algorithm over the class of (λ,T)-streams. Our results for the online setting focus on exponential backoff. We show that for any arrival rate λ, there exists a sufficiently large interval size T such that the throughput goes to 0 for some (λ,T)-stream. Moreover, there exists a sufficiently large constant c such that for any interval size T, if λ ⥠c lg lg n/lg n, the system is unstable in the sense that the arrival rate exceeds the throughput in the worst case. If, on the other hand, we have λ ⤠c/lg n for a sufficiently small constant c, then the system is stable. Surprisingly, the algorithms that guarantee smaller makespans in the batch setting require lower arrival rates to achieve stability than does exponential backoff, but when they are stable, they have better response times.Singapore-MIT Alliance (SMA

Contention management for distributed data replication

PhD ThesisOptimistic replication schemes provide distributed applications with access to shared data at lower latencies and greater availability. This is achieved by allowing clients to replicate shared data and execute actions locally. A consequence of this scheme raises issues regarding shared data consistency. Sometimes an action executed by a client may result in shared data that may conflict and, as a consequence, may conflict with subsequent actions that are caused by the conflicting action. This requires a client to rollback to the action that caused the conflicting data, and to execute some exception handling. This can be achieved by relying on the application layer to either ignore or handle shared data inconsistencies when they are discovered during the reconciliation phase of an optimistic protocol. Inconsistency of shared data has an impact on the causality relationship across client actions. In protocol design, it is desirable to preserve the property of causality between different actions occurring across a distributed application. Without application level knowledge, we assume an action causes all the subsequent actions at the same client. With application knowledge, we can significantly ease the protocol burden of provisioning causal ordering, as we can identify which actions do not cause other actions (even if they precede them). This, in turn, makes possible the client’s ability to rollback to past actions and to change them, without having to alter subsequent actions. Unfortunately, increased instances of application level causal relations between actions lead to a significant overhead in protocol. Therefore, minimizing the rollback associated with conflicting actions, while preserving causality, is seen as desirable for lower exception handling in the application layer. In this thesis, we present a framework that utilizes causality to create a scheduler that can inform a contention management scheme to reduce the rollback associated with the conflicting access of shared data. Our framework uses a backoff contention management scheme to provide causality preserving for those optimistic replication systems with high causality requirements, without the need for application layer knowledge. We present experiments which demonstrate that our framework reduces clients’ rollback and, more importantly, that the overall throughput of the system is improved when the contention management is used with applications that require causality to be preserved across all actions

Performance analysis of general backoff protocols

In this paper, we analyze backoff protocols, such as the one used in Ethernet. We examine a general backoff function (GBF) rather than just the binary exponential backoff (BEB) used by Ethernet. Under some mild assumptions we find stability and optimality conditions for a wide class of backoff protocols with GBF. In particular, it is proved that the maximal throughput rate over the class of backoff protocols is a fixed function of the number of stations (N) and the optimal average service time is about Ne for large N. The reasons of the instability of the BEB protocol (for a big enough input rate) are explained. Additionally, the paper introduces novel procedure for analyzing bounded backoff protocols, which is useful for creating new protocols or improving existing, as no protocol can use unbounded counters

Singletons for Simpletons: Revisiting Windowed Backoff with Chernoff Bounds

Backoff algorithms are used in many distributed systems where multiple devices contend for a shared resource. For the classic balls-into-bins problem, the number of singletons - those bins with a single ball - is important to the analysis of several backoff algorithms; however, existing analyses employ advanced probabilistic tools to obtain concentration bounds. Here, we show that standard Chernoff bounds can be used instead, and the simplicity of this approach is illustrated by re-analyzing some well-known backoff algorithms