advanced25 min studyLesson 229 in Engineering

Failure domains beyond path count

Evaluate shared dependencies and degraded capacity instead of multiplying independent failure probabilities by habit.

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What you’ll understand

  • Identify common dependencies that correlate nominally redundant paths.
  • Calculate a conditional common-cause failure model.
  • Distinguish reachability after failure from sufficient remaining capacity.

Two physical-looking paths are not necessarily two independent ways to keep a job running. They may share power, a chassis, a control plane, a conduit, software configuration, or the same endpoint. Redundancy must be evaluated against named failures and the workload's degraded requirements. A fabric can remain reachable while losing enough capacity that synchronized jobs exceed deadlines. Treat failure independence and adequate remaining service as separate claims requiring evidence.

Draw the dependency map

Start at each endpoint and trace links, transceivers, switches, power feeds, and management or routing dependencies. Mark where paths meet. Diversity at one layer can hide a shared lower-layer resource, such as two logical interfaces behind one adapter or two switches on one power domain. Software rollout and configuration can also fail several devices together. A useful failure-domain map includes operational dependencies rather than only the forwarding diagram shown during normal conditions.

Define the event being modeled: loss of reachability for a flow, loss of all job participants, degraded throughput, or a deadline miss. Those events have different dependency structures. An apparently independent link-failure probability cannot be substituted for the probability that an entire distributed job misses its iteration target. State the observation window and conditional assumptions before combining probabilities. Historical incident correlations can challenge the model, but finite data cannot prove future independence.

P(A∩B)=P(A)P(B∣A)P(A\cap B)=P(A)P(B\mid A)
The identity applies to failure events A and B with P(A)>0. Replacing the conditional probability by P(B) requires independence. All probabilities are dimensionless and refer to the same specified observation window.↔ Scroll wide equations horizontally.

Common causes dominate an optimistic product

Consider a common event that removes both paths, plus separate path failures conditional on that event not occurring. Count the common case once, then add the conditional joint failure case. Multiplying two unconditional small percentages can miss a much larger shared risk. The model can still be incomplete if supposedly separate failures share repair resources or environmental conditions. Present it as a declared scenario and sensitivity analysis rather than a measured reliability guarantee.

Failure recovery changes traffic placement. If one of two equal paths disappears, existing work may hash onto the remaining path, reconnect, or wait for a timeout. Routing convergence and transport recovery are different intervals. Even after convergence, the residual capacity can be smaller than offered demand. Check post-failure queue growth and application deadlines, and include maintenance states in which redundancy is already reduced. A normal-state capacity test does not establish an acceptable failure budget.

Pboth=q+(1−q)p2P_{\rm both}=q+(1-q)p^2
q is a declared common-cause probability removing both paths. Conditional on no common event, each path fails independently with probability p during the same window. This simplified model excludes further correlations and repair dynamics.↔ Scroll wide equations horizontally.

Exercise failures at the application boundary

Use controlled fault tests with documented scope, observation, rollback, and useful-work checks. Disable or degrade a chosen path and observe convergence, retries, correctness, and time to steady completion. Test a shared dependency separately from a single link. A partially failing or high-error link can be more disruptive than a clean removal because traffic continues selecting it. Correlate application symptoms with both active probes and device telemetry rather than relying on one link-state bit.

The reliability lab counts up replicas and a majority threshold, not network path diversity. Reset and set both n=5, k=2; predict three available and a majority of three, then inspect. Reset and re-set n=5, k=3; predict only two available. Play changes illustration state, not failure probabilities or routing. The lesson is limited: counting reachable resources does not prove independent failure domains, adequate bandwidth, or replica consistency. Those properties require a separate dependency and protocol argument.

A shared risk changes the result

During one hypothetical observation window, a shared power event removes both paths with probability 0.01. Conditional on no power event, each path fails independently with probability 0.001.

  1. The conditional joint separate-failure probability is 0.001²=0.000001. The no-common-event probability is 0.99.

  2. Combine disjoint cases:0.01+0.99×0.000001=0.01000099, or 1.000099%. The shared case dominates this assumed model.

  3. Ignoring the common cause and simply squaring 0.001 would give 0.0001%, a very different number. Neither estimate is a measured guarantee; validate the power dependency, event window, and conditional independence before using it for planning.

The result

Redundant path count cannot justify independent-risk multiplication when a common dependency can remove every path together.

Explore the model

Interactive lab

Interactive lab · reliability

Available counts are not independent paths

Reset and set n=5, k=2; predict up 3 and majority 3. Reset and re-set n=5, k=3; predict up 2. This replica-count model does not simulate path failures, probabilities, routing, or capacity and does not prove consistency.

Available counts are not independent pathsA replica count and a majority threshold, without a consensus protocol. Playback highlights fixed replica states. Having a majority alone does not establish linearizability, durability or failure independence. Current readings: Available replicas: 4 of 5; Majority needed: 3; Majority available?: Yes. All parameters are adjustable with the labeled controls below.Majority available · need 3 of 5Playback highlights fixed statesR1 · upR2 · upR3 · upR4 · upR5 · downCyan mark: majority threshold
AvailableUnavailableMajority threshold
Available replicas
4 of 5
Majority needed
3
Majority available?
Yes
t = 0 s

A replica count and a majority threshold, without a consensus protocol. Playback highlights fixed replica states. Having a majority alone does not establish linearizability, durability or failure independence. Parameter changes pause playback and recompute the model at the current elapsed time. Reset restores both parameters and returns time to zero. Playback starts paused. Adjust either parameter, then choose Play or Step.

Look forA count of available resources is one input to a design, not proof of independent failure domains or enough remaining service.

Check your understanding

Two paths use separate switches but share one power feed. Which assumption is least justified?

Try it yourself

A workload offers 150 Gbit/s across two independent 100 Gbit/s paths in normal operation. One path fails and the other remains reachable. Calculate the steady excess offered rate if the workload does not adapt, and explain why reachability is not enough.

Take a moment to make a prediction or work it out on paper. Open a hint when you need one.

Give me a hint

Compare unchanged demand with the surviving capacity, not with the original aggregate.

Compare with the solution

Normal aggregate capacity is 200 Gbit/s. After failure only 100 Gbit/s remains, so excess offered demand is 50 Gbit/s. Queues or upstream waiting grow until demand adapts, traffic is rejected, or loss changes sending. The fabric can pass packets yet fail the application's latency or throughput requirement; routing convergence alone does not resolve that capacity gap.

Take it with you

  • Redundancy must be evaluated against shared physical and operational dependencies.
  • Failure independence is an assumption to test, not a consequence of path count.
  • Degraded reachability and degraded workload capacity are different acceptance criteria.

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