Probe scheduling for efficient detection of silent failures

Abstract

Most discovery systems for silent failures work in two phases: a continuous monitoring phase that detects presence of failures through probe packets and a localization phase that pinpoints the faulty element(s). We focus on the monitoring phase, where the goal is to balance the probing overhead with the cost associated with longer failure detection times.We formulate a general model for the underlying fundamental subset-test scheduling problem. We unify the treatment of schedulers and cost objectives and make several contributions: We propose Memoryless schedulesa natural subclass of stochastic schedules which is simple and suitable for distributed deployment. We show that the optimal memoryless schedulers can be efficiently computed by convex programs (for SUM objectives, which minimize average detection time) or linear programs (for MAX objectives, which minimize worst-case detection time), and surprisingly perhaps, are guaranteed to have expected detection times that are not too far off the (NP hard) stochastic optima. We study Deterministic schedules, which provide a guaranteed bound on the maximum (rather than expected) cost of undetected faults, but like general stochastic schedules, are NP hard to optimize. We develop novel efficient deterministic schedulers with provable approximation ratios.Finally, we conduct an experimental study, simulating our schedulers on real networks topologies, demonstrates a significant performance gains of the new memoryless and deterministic schedulers over previous approaches.

Scheduling Subset Tests: One-Time, Continuous, and How They Relate

“…These ratios significantly improve over previous results [6] with approximation ratios that depend logarithmically on the number of tests containing an element, which can be exponential in the number of elements. Indeed, experimentally in [6] we observed that we needed to artificially restrict the set of tests to obtain good schedules using the previous approaches.…”

“…We follow notation from [6]. For an element e, M t [e|σ] is the maximum over time t of the cover time of e at time t, and E t [e|σ] is the (limit of) the average over time t of the cover time of e at time t. For a time t, M e [t|σ] = max e p e T (e, t|σ) is the (weighted) maximum over elements and E e [t|σ] = e p e T (e, t|σ) is the weighted sum over the elements of the cover time of e at t. The weighting, in both cases, is according to the priorities p. When clear from context, we omit the reference to the schedule σ in the notation.…”

“…With stochastic schedules, we redefine T (e, t|σ) to be the expected number of steps until e is covered [6].…”

“…A recently studied application is silent failure detection in networks [14,12,13,6]: Elements correspond to physical or logical network elements (links, nodes, or forwarding rules in the software defined network) and tests corresponding to routing paths. Invoking a test translated to sending a probe packet.…”

“…We recently studied continuous schedules [6], and related stochastic and deterministic schedules and presented deterministic approximation algorithms based on derandomizing optimal memoryless schedules (memoryless schedules are a subclass of stochastic schedules which can be optimized by an LP or convex programs). Our work here builds on the results in [9,6] which are discussed in more detail in Section 2.…”