Adaptive and Distributed SystemLevel Diagnosis

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Adaptive and Distributed System-Level Diagnosis
Computer Science Department, University of Pisa

• Seminars for the PhD in Computer Science
• Luiz Carlos Pessoa Albini

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Adaptive Diagnosis

• Introduced by Nakajima in 1981
• Centralized
• The central diagnoser chooses the order of the
  tests to be executed by the units during the
  diagnosis process
• Complete testing graph
• Any unit is capable of testing any other unit
• Objective identify one faultfree unit which
  will be used as a tester of the rest of the
  system.
• Main Idea
• Units decide the next tests based-on previous
  tests results.

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Distributed Diagnosis

• Does not exist a central diagnoser
• Units that perform the tests achieve diagnosis
• Algorithm is executed on many or all units
  simultaneously
• The complexity of a distributed diagnosis
  algorithm depends on the test and communication
  interconnection
• If the system test graph satisfies only the
  diagnosability requirements the distributed
  diagnosis algorithm will probably be complex
• If the interconnection network is regular then
  the distributed diagnosis algorithm may be
  simplified by making use of the structure of the
  system.

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SELF

• Kuhl and Reddy in 1981 introduce the distributed
  system-level diagnosis
• SELF algorithm
• Tests are fixed (non-adaptive)
• Each unit tests its pre-designated neighbors
• Broadcast the test results
• Each unit performs the diagnosis based on its own
  tests and on the received testing results
• Diagnosis can be incorrect because broadcasts can
  be routed by faulty units.

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New_SELF

• Proposed by Hosseini, Kuhl and Reddy in 1984
• New_SELF
• First algorithm for distributed diagnosis of
  distributed systems
• Works correctly if the number of faults is no
  more than t
• Fixed test assignment (non-adaptive)
• Each unit independently determines the state of
  the system based on the results of its own tests
  and on the results received from other units
• Failures and repairs are accepted, but a unit
  cannot fail and then recovery without its failure
  being detected
• Ensures the accuracy of the test-results by
  restricting the forwarding of testing results to
  fault-free units

• Requires that every fault-free unit receives all
  test results from other fault-free units.

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Somani and Agarwal

• Distributed local diagnosis approach for regular
  structures proposed by Somani and Agarwal in
  1989
• For most regular structures, all fault sets of
  size up to t are uniquely diagnosed by the
  algorithm in linear time complexity
• For large regular structures, most fault sets of
  size up to O(log N) and
• O( ) are uniquely diagnosed

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Algorithm Evaluation

• Latency
• Maximum time interval for all fault-free units
  diagnose an event
• Normally expressed in number of testing rounds.
• Maximum Number of Tests
• Number of tests performed by all fault-free
  units
• Normally expressed in number of tests per testing
  round.
• Diagnosability
• Limit for the number of fault units in the
  system.
• Testing round
• Maximum time interval needed by the fault-free
  units to finish their tests
• Can be different for different algorithms.

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Adaptive-DSD

• Adaptive-DSD - Adaptive Distributed System-Level
  Diagnosis Algorithm.

• Characteristics
• Fully-connected systems
• A fault-free unit performs tests until it finds
  another fault-free unit, or testing all units as
  faulty
• Diagnositc graph is a circle when all units are
  fault-free
• A fault-free unit is tested at most once per
  testing round
• Testing round maximum time interval needed by
  the fault-free units to test another fault-free
  unit, or test all units as faulty.

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Adaptive-DSD

• Latency
• O(N) testing rounds.
• Maximum Number of Tests
• O(N) tests in the worst case.
• Diagnosability
• (N-1)-diagnosable.

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Hi-ADSD

• Characteristics
• Fully-connected system
• Units are grouped in clusters
• A fault-free unit performs tests until it finds
  another fault-free unit, or testing all units as
  faulty
• Diagnostic graph is a hypercube when all units
  are fault-free

• When a fault-free unit tests another fault-free
  unit, it gets diagnostic information from the
  tested unit about the entire cluster
• Testing round maximum time interval needed by
  the fault-free units to test another fault-free
  unit, or test all units as faulty.

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Hi-ADSD

• Latency
• Log2 N testing rounds.

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Hi-ADSD

• Maximum Number of Tests
• O(N2) in the worst case.

• Diagnosability
• (N-1)-diagnosable.

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Hi-ADSD with Detours

• Characteristics
• Fully-connected systems
• Units are grouped in clusters
• When a faulty unit is tested the tester uses
  detours to get the information about this blocked
  cluster, instead of perform other tests
• Detours are alternative paths that are used when
  the original path is faulty with the same
  diagnostic distance
• Diagnostic Distance Size of the shortest path
  between two units in the diagnostic graph
• If the original path and the detours are faulty
  the algorithm works as the Hi-ADSD and performs
  more tests
• Testing round Maximum time interval needed for
  the fault-free units to execute the normal test
  plus the extra tests needed.

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Hi-ADSD with Detours

• Latency
• Log2 N testing rounds.
• Maximum Number of Tests
• N logN tests per logN testing rounds in the worst
  case
• Worst case example No faulty units.
• Diagnosability
• (N-1)-diagnosable.

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Hi-ADSD with Timestamps

• Characteristics
• Fully-connected systems
• Units are grouped in clusters
• All clusters with N/2 units
• Units can be in more than one cluster
• Event diagnosis
• Diagnosis of dynamic fault and repair events
• Timestamps
• State changing counters of each unit of the
  system
• Used to date the information
• Testing round Maximum time interval needed for
  the fault-free units to execute the normal test
  plus the extra tests needed.

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Hi-ADSD with Timestamps

• Latency
• Smaller than other algorithms in average
• Log2 N testing rounds in the worst case.
• Maximum Number of Tests
• N logN tests per logN testing rounds in the worst
  case.
• Diagnosability
• (N-1)-diagnosable.

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Broadcast Comparison

• Will be presented latter

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Generalized Model for Distributed Comparison

• Tests are made through comparisons of tasks
  results
• A unit sends a task to two units

• After executing the task the two units send their
  outputs to the tester
• The tester compares the outputs

• If the comparison produces a match
• The two tested units are considered fault-free

• If the comparison produces a mismatch
• The tester knows that at least one of the tested
  units is faulty, but does not know which one.

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Generalized Model for Distributed Comparison

• Assumptions
• A fault-free unit comparing outputs produced by
  two fault-free units always produces a match
• A fault-free unit comparing outputs produced by a
  faulty unit and any other unit, faulty or
  fault-free, always produces a mismatch
• The time for a fault-free unit to produce na
  output for a task is bounded
• After a unit is tested in a certain testing
  round, its state does not change until the end of
  the testing round.

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Hi-Comp

• Characteristics
• Fully-connected systems
• Units are grouped in clusters
• All clusters with N/2 units
• Units can be in more than one cluster
• Event diagnosis
• Diagnosis of dynamic fault and repair events
• Together, with the output of a test, the tested
  unit sends to the tester the diagnostic
  informations
• The tester keeps this information until it
  determines the state of the tested unit
• If fault-free The tester updates its own
  information
• If faulty The tester discard the information
• Testing round Time interval need for all
  fault-free units to get diagnostic information
  about all units in the system
• By the end of a testing round all units are
  classified as faulty or fault-free.

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Hi-Comp
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Hi-Comp

• Latency
• Log N testing rounds in the worst case.
• Maximum Number of Tests
• N3 testing rounds in the worst case.
• Diagnosability
• (N-1)-diagnosable.

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Conclusions

• Without a central observer
• Some algorithms needs a fully-connected system
• Local area networks
• In fully-connected systems
• At the end of a testing round the diagnosis is
  complete
• Sometimes incorrect, depends on the number of
  testing rounds elapsed from the event.
• Algoriths are not comparable based on the testing
  round as they use different definitions of
  testing round.