Srikanth Sastry

Wait-free dining under eventual weak exclusion

We present a wait-free solution to the generalized dining philosophers problem under eventual weak exclusion in environments subject to crash faults. Wait-free dining guarantees that every correct hungry process eventually eats, regardless of process crashes. Eventual weak exclusion (◊WX) actually allows scheduling mistakes, whereby mutual exclusion may be violated finitely-many times; for each run, however, there must exist a convergence point after which live neighbors never eat simultaneously. Wait-free dining under ◊WX is particularly useful for synchronization tasks where eventual safety is sufficient for correctness (e.g., duty-cycle scheduling, self-stabilizing daemons, and contention managers). Unfortunately, wait-free dining is unsolvable in asynchronous systems. As such, we characterize sufficient conditions for solvability under partial synchrony by presenting a wait-free dining algorithm for ◊WX using a local refinement of the eventually perfect failure detector ◊P1.

Eventually perfect failure detectors using ADD channels

We present a novel implementation of the eventually perfect failure detector (⋄P) from the original hierarchy of Chandra-Toueg oracles. Previous implementations of ⋄P have assumed models of partial synchrony where point-to-point message delay is bounded and/or communication is reliable. We show how to implement this important oracle under even weaker assumptions using Average Delayed/Dropped (ADD) channels. Briefly, all messages sent on an ADD channel are privileged or non-privileged. All non-privileged messages can be arbitrarily delayed or even dropped. For each run, however, there exists an unknown window size w, and two unknown upper-bounds d and r, where d bounds the average delay of the last w privileged messages, and r bounds the ratio of non-privileged messages to privileged messages per window.

Fast track article: Reliable networks with unreliable sensors

Wireless sensor networks (WSNs) deployed in hostile environments suffer from a high rate of node failure. We investigate the effect of such failure rate on network connectivity. We provide a formal analysis that establishes the relationship between node density, network size, failure probability, and network connectivity. We show that large networks can maintain connectivity despite a significantly high probability of node failure. We derive mathematical functions that provide lower bounds on network connectivity in WSNs. We compute these functions for some realistic values of node reliability, area covered by the network, and node density, to show that, for instance, networks with over a million nodes can maintain connectivity with a probability exceeding 95% despite node failure probability exceeding 53%.

Leader election using loneliness detection

We consider the problem of leader election (LE) in singlehop radio networks with synchronized time slots for transmitting and receiving messages. We assume that the actual number n of processes is unknown, while the size u of the ID space is known, but possibly much larger. We consider two types of collision detection: strong (SCD), whereby all processes detect collisions, and weak (WCD), whereby only non-transmitting processes detect collisions. We introduce loneliness detection (LD) as a key subproblem for solving LE in WCD systems. LD informs all processes whether the system contains exactly one process or more than one. We show that LD captures the difference in power between SCD and WCD, by providing an implementation of SCD over WCD and LD. We present two algorithms that solve deterministic and probabilistic LD in WCD systems with time costs of O(log u/n) and O(min(log u/n, log(1/e)/n)), respectively, where e is the error probability. We also provide matching lower bounds. We present two algorithms that solve deterministic and probabilistic LE in SCD systems with time costs of O(log u) and O(min(log u, log log n+ log(1/e))), respectively, where e is the error probability. We provide matching lower bounds.

Crash fault detection in celerating environments

Failure detectors are a service that provides (approximate) information about process crashes in a distributed system. The well-known “eventually perfect” failure detector, ◊P, has been implemented in partially synchronous systems with unknown upper bounds on message delay and relative process speeds. However, previous implementations have overlooked an important subtlety with respect to measuring the passage of time in “celerating” environments, in which absolute process speeds can continually increase or decrease while maintaining bounds on relative process speeds. Existing implementations either use action clocks, which fail in accelerating environments, or use real-time clocks, which fail in decelerating environments. We propose the use of bichronal clocks, which are a composition of action clocks and real-time clocks. Our solution can be readily adopted to make existing implementations of ◊P robust to process celeration, which can result from hardware upgrades, server overloads, denial-of-service attacks, and other system volatilities.

Asynchronous leader election and MIS using abstract MAC layer

We study leader election (LE) and computation of a maximal independent set (MIS) in wireless ad-hoc networks. We use the abstract MAC layer proposed in [14] to divorce the algorithmic complexity of solving these problems from the low-level issues of contention and collisions. We demonstrate the advantages of such a MAC layer by presenting simple asynchronous deterministic algorithms to solve LE and MIS and proving their correctness. First, we present an LE algorithm for static single-hop networks in which each process sends no more than three messages to its neighbors in the system. Next, we present an algorithm to compute an MIS in a static multi-hop network in which each process sends a constant number of messages to each of its neighbors in the communication graph.

Asynchronous failure detectors

Failure detectors - oracles that provide information about process crashes - are an important abstraction for crash tolerance in distributed systems. Although current failure-detector theory provides great generality and expressiveness, it also poses significant challenges in developing a robust hierarchy of failure detectors. We address some of these challenges by proposing a variant of failure detectors called asynchronous failure detectors and an associated modeling framework. Unlike the traditional failure-detector framework, our framework eschews real time completely. We show that asynchronous failure detectors are sufficiently expressive to include several popular failure detectors. Additionally, we show that asynchronous failure detectors satisfy many desirable properties: they are self-implementable, guarantee that stronger asynchronous failure detectors solve more problems, and ensure that their outputs encode no information other than process crashes. We introduce the notion of a failure detector being representative of a problem to capture the idea that some problems encode the same information about process crashes as their weakest failure detectors do. We show that a large class of problems, called finite problems, do not have representative failure detectors.

The weakest failure detector for wait-free dining under eventual weak exclusion

Dining philosophers is a classic scheduling problem for local mutual exclusion on arbitrary conflict graphs. We establish necessary conditions to solve wait-free dining under eventual weak exclusion in message-passing systems with crash faults. Wait-free dining ensures that every correct hungry process eventually eats. Eventual weak exclusion permits finitely many scheduling mistakes, but eventually no live neighbors eat simultaneously; this exclusion criterion models scenarios where scheduling mistakes are recoverable or only affect performance. Previous work showed that the eventually perfect failure detector (◊P) is sufficient to solve wait-free dining under eventual weak exclusion; we prove that ◊P is also necessary, and thus ◊P is the weakest oracle to solve this problem. Our reduction also establishes that any such dining solution can be made eventually fair. Finally, the reduction itself may be of more general interest; when applied to wait-free perpetual weak exclusion, our reduction produces an alternative proof that the more powerful trusting oracle (T) is necessary (but not sufficient) to solve the problem of Fault-Tolerant Mutual Exclusion (FTME).

Wait-Free Stabilizing Dining Using Regular Registers

Dining philosophers is a scheduling paradigm that determines when processes in a distributed system should execute certain sections of their code so that processes do not execute ‘conflicting’ code sections concurrently, for some application-dependent notion of a ‘conflict’. Designing a stabilizing dining algorithm for shared-memory systems subject to process crashes presents an interesting challenge: classic stabilization relies on all processes continuing to execute actions forever, an assumption which is violated when crash failures are considered. We present a dining algorithm that is both wait-free (tolerates any number of crashes) and is pseudo-stabilizing. Our algorithm works in an asynchronous system in which processes communicate via shared regular registers and have access to the eventually perfect failure detector \(\diamondsuit \mathcal{P}\). Furthermore, with a stronger failure detector, the solution becomes wait-free and self-stabilizing. To our knowledge, this is the first such algorithm. Prior results show that \(\diamondsuit \mathcal{P}\) is necessary for wait-freedom.

Reliable networks with unreliable sensors

Wireless sensor networks (WSNs) deployed in hostile environments suffer from a high rate of node failure. We investigate the effect of such failure rate on network connectivity. We provide a formal analysis that establishes the relationship between node density, network size, failure probability, and network connectivity. We show that as network size and density increase, the probability of network partitioning becomes arbitrarily small. We show that large networks can maintain connectivity despite a significantly high probability of node failure. We derive mathematical functions that provide lower bounds on network connectivity in WSNs. We compute these functions for some realistic values of node reliability, area covered by the network, and node density, to show that, for instance, networks with over a million nodes can maintain connectivity with a probability exceeding 99% despite node failure probability exceeding 57%.