Fault tolerance-omer-rana
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This document discusses fault tolerance and distributed systems concepts. It defines key terms like failure, error and fault. It describes different types of faults like hard and soft faults. It discusses failure detection metrics like MTBF, MTTD and MTTR. It also covers different failure models like fail-stop, Byzantine and omission failures. The document then discusses distributed algorithms, their properties of safety and liveness, and timing models like synchronous, asynchronous and partial synchrony. It covers distributed consensus algorithms and how they ensure agreement, validity and termination properties. It provides examples of synchronous fail-stop and Byzantine consensus algorithms.
Fault tolerance-omer-rana
- 3. Basic Definitions • Failure: deviation of a system from behaviour described in its specification. • Error: part of the state which is incorrect. • Fault: an error in the internal states of the components of a system or in the design of a system.
- 4. … and Donald Rumsfeld said: There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know.
- 5. Types of Faults • Hard faults – Permanent Resulting failures are called hard failures • Soft faults – Transient or intermittent – Account for more than 90% of all failures Resulting failures are called soft failures
- 7. Failure Detection MTBF: Mean Time Between Failure MTTD: Mean Time To Discovery MTTR: Mean Time to Repair
- 9. Distributed Algorithms • Primary focus in Distributed Systems is on a number of concurrently running processes • Distributed system is composed of n processes • A process executes a sequence of events – Local computation – Sending a message m – Receiving a message m • A distributed algorithm makes use of more than one process.
- 10. Properties of Distributed Algorithms • Safety – Means that some particular “bad” thing never happens. • Liveness – Indicates that some particular “good” thing will (eventually) happen. Timing/failure assumptions affect how we reason about these properties and what we can prove
- 11. Timing Model • Specifies assumptions regarding delays between – execution steps of a correct process – send and receipt of a message sent between correct processes • Many gradations. Two of interest are: Synchronous Known bounds on message and execution delays. Asynchronous No assumptions about message and execution delays (except that they are finite). • Partial synchrony is more realistic in distributed system
- 12. Synchronous timing assumption • Processes share a clock • Timestamps mean something between processes – Otherwise processes are synchronised using a time server • Communication can be guaranteed to occur in some number of clock cycles CSC469 11/30/13
- 13. Asynchronous timing assumption • Processes operate asynchronously from one another. • No claims can be made about whether another process is running slowly or has failed. • There is no time bound on how long it takes for a message to be delivered.
- 14. Partial synchrony assumption • “Timing-based distributed algorithms” • Processes have some information about time – Clocks that are synchronized within some bound – Approximate bounds on message-deliver time – Use of timeouts
- 15. Failure Model • A process that behaves according to its I/O specification throughout its execution is called correct • A process that deviates from its specification is faulty • Many gradations of faulty. Two of interest are: Fail-Stop failures A faulty process halts execution prematurely. Byzantine failures No assumption about behavior of a faulty process.
- 16. Errors as failure assumptions • Specific types of errors are listed as failure assumptions – Communication link may lose messages – Link may duplicate messages – Link may reorder messages – Process may die and be restarted
- 17. Fail-Stop failure • A failure results in the process, p, stopping – Also referred to as crash failure – p works correctly until the point of failure • p does not send any more messages • p does not perform actions when messages are sent to it • Other processes can detect that p has failed
- 18. Fault/failure detectors • A perfect failure detector – No false positives (only reports actual failures). – Eventually reports failures to all processes. • Heartbeat protocols – Assumes partially synchronous environment – Processes send “I’m Alive” messages to all other processes regularly – If process i does not hear from process j in some time T = Tdelivery + Theartbeat then it determines that j has failed – Depends on Tdelivery being known and accurate
- 19. Other Failure Models • Omission failure • Process fails to send messages, to receive incoming messages, or to handle incoming messages • Timing failure • process‘s response lies outside specified time interval • Response failure • Value of response is incorrect
- 20. Byzantine failure • Process p fails in an arbitrary manner. • p is modeled as a malevolent entity – Can send the messages and perform the actions that will have the worst impact on other processes – Can collaborate with other “failed” processes • Common constraints – Incomplete knowledge of global state – Limited ability to coordinate with other Byzantine processes
- 21. Setup of Distributed Consensus • N processes have to agree on a single value. – Example applications of consensus: • Performing a commit in a replicated/distributed database. • Collecting multiple sensor readings and deciding on an action • Each process begins with a value • Each process can irrevocably decide on a value • Up to f < n processes may be faulty – How do you reach consensus if no failures?
- 22. Properties of Distributed Consensus • Agreement – If any correct process believes that V is the consensus value, then all correct processes believe V is the consensus value. • Validity – If V is the consensus value, then some process proposed V. • Termination – Each process decides some value V. • Agreement and Validity are Safety Properties • Termination is a Liveness property.
- 23. Synchronous Fail-stop Consensus • FloodSet algorithm run at each process i – Remember, we want to tolerate up to f failures • S is a set of values • Decide(x) can be Si {initial value} various functions for k = 1 to f+1 send Si to all processes receive Sj from all j != i Si Si Sj (for all j) end for Decide(Si) • E.g. min(x), max(x), majority(x), or some default • Assumes nodes are connected and links do not fail
- 24. Analysis of FloodSet • Requires f+1 rounds because process can fail at any time, in particular, during send • Agreement: Since at most f failures, then after f+1 rounds all correct processes will evaluate Decide(Si) the same. • Validity: Decide results in a proposed value (or default value) • Termination: After f+1 rounds the algorithm completes
- 25. Example with f = 1, Decide() = min() 1 End of round 1 End of round 2 S1 = {0} 2 S2 = {1} {1} {0,1} decide 0 {0,1} {0,1} decide 0 3 S3 = {1}
- 26. Synchronous/Byzantine Consensus • Faulty processes can behave arbitrarily – May actively try to trick other processes • Algorithm described by Lamport, Shostak, & Pease in terms of Byzantine generals agreeing whether to attack or retreat. Simple requirements: – All loyal generals decide on the same plan of action • Implies that all loyal generals obtain the same information – A small number of traitors cannot cause the loyal generals to adopt a bad plan – Decide() in this case is a majority vote, default action is “Retreat”
- 27. Byzantine Generals • Use v(i) to denote value sent by ith general • Traitor could send different values to different generals, so can’t use v(i) obtained from i directly. New conditions: – Any two loyal generals use the same value v(i), regardless of whether i is loyal or not – If the ith general is loyal, then the value that she sends must be used by every loyal general as the value of v(i). • Re-phrase original problem as reliable broadcast: – General must send an order (“Use v as my value”) to lieutenants – Each process takes a turn as General, sending its value to the others as lieutenants – After all values are reliably exchanged, Decide()
- 28. Synchronous Byzantine Model Theorem: There is no algorithm to solve consensus if only oral messages are used, unless more than two thirds of the generals are loyal. • In other words, impossible if n ≤ 3f for n processes, f of which are faulty • Oral messages are under control of the sender – sender can alter a message that it received before forwarding it • Let’s look at examples for special case of n=3, f=1
- 29. Case 1 • Traitor lieutenant tries to foil consensus by refusing to participate “white hats” == loyal or “good guys” “black hats” == traitor or “bad guys” Round 1: Commanding General sends “Retreat” Commanding General 1 Round 2: L3 sends “Retreat” to L2, but L2 sends nothing Decide: L3 decides “Retreat” Lieutenant 2 CSC469 R Loyal lieutenant obeys commander. (good) R Lieutenant 3 R decides to retreat 11/30/13
- 30. Case 2a • Traitor lieutenant tries to foil consensus by lying about order sent by general Round 1: Commanding General sends “Retreat” Commanding General 1 Round 2: L3 sends “Retreat” to L2; L2 sends “Attack” to L3 R Decide: L3 decides “Retreat” Loyal lieutenant obeys commander. (good) R Lieutenant 3 Lieutenant 2 R decides to retreat A CSC469 11/30/13
- 31. Case 2b • Traitor lieutenant tries to foil consensus by lying about order sent by general Round 1: Commanding General sends “Attack” Commanding General 1 Round 2: L3 sends “Attack” to L2; L2 sends “Retreat” to L3 A Decide: L3 decides “Retreat” Loyal lieutenant disobeys commander. (bad) A Lieutenant 3 Lieutenant 2 A decides to retreat R CSC469 11/30/13
- 32. Case 3 • Traitor General tries to foil consensus by sending different orders to loyal lieutenants Round 1: General sends “Attack” to L2 and “Retreat” to L3 Commanding General 1 Round 2: L3 sends “Retreat” to L2; L2 sends “Attack” to L3 A Decide: L2 decides “Attack” and L3 decides “Retreat” Loyal lieutenants obey commander. (good) Decide differently (bad) R Lieutenant 3 Lieutenant 2 R decides to attack decides to retreat A CSC469 11/30/13
- 33. Byzantine Consensus: n > 3f • • • Oral Messages algorithm, OM(f) Consists of f+1 “phases” Algorithm OM(0) is the “base case” (no faults) 1) Commander sends value to every lieutenant 2) Each lieutenant uses value received from commander, or default “retreat” if no value was received • CSC469 Recursive algorithm handles up to f faults 11/30/13
Editor's Notes
- #11: <number> Different aspects of the system can exhibit different degrees of synchrony/types of failures -Processor synchrony -Communication synchrony --Ordered messages --Broadcast ability or point-to-point --Atomic receive/send or distinct operations -Link failures can be considered independently from process failures.
- #20: <number> These form a hierarchy of failure models from most (failstop) to least (byzantine) benign. Failures up to response failure can be considered relatively benign (can be detected and handled, need not result in corruption). A server that returns an incorrect response, or deviates from the specified behavior internally is hard to detect, as are arbitrary failures, which can lead to serious errors in the distributed system.
- #22: <number> e.g. for sensors, robot soccer team – each robot has sensors to detect the environment around it. Team of robots must agree on a strategy (e.g. defense or offense), based on reaching agreement about whether team controls the ball, or other team does. Each robot begins with a value based on its sensors (team_has_ball := I_have_ball). After some consensus alg, each robot decides whether the team has the ball or not. Q: Every process sends its initial value to every other process. Every process then runs same function to decide a value based on those proposed. Assuming no failures, every process starts with the same inputs, computes same function, decides on same value consensus. Once you allow failures, multiple rounds of communication are needed to reach agreement.
- #23: <number> - Validity is hard to define and hard to understand. Lamport, Shostak & Pease don’t use the term “validity” in the Byzantine Generals paper, but instead require that “all correct processes decide on a reasonable value” (their actual phrase is “a small number of traitors cannot cause the loyal generals to adopt a bad plan”, but we haven’t gotten into the Byzantine situation yet, and they sort of sidestep defining what a bad plan would be. Another alternate definition is “If all processes begin with the same input, then any value decided by a correct process must be that input”.
- #24: <number> Link failure could cause the perceived failure of multiple nodes (maybe more than f) or could create partitioned sets of nodes, which could each decide the other was failed and come to consensus among themselves, but decide different values.
- #25: <number> Requires f+1 rounds because process can fail at any time during the send operation i.e. process i can send Wi to process j, but not process k … then, set of values S at j and k will be different and they could Decide() different values. But, in next round, j and k exchange their complete sets so far, so the differences are resolved.
- #26: <number>
- #29: <number> Oral messages represent the typical unsigned message delivery in computer systems. This allows a faulty process to lie about the messages that were sent to it in a previous round.
- #30: <number> Remember, this is synchronous timing assumption, so L3 knows when to stop waiting for a message from L2.
- #31: <number> L3 has no clear majority in this case (1 attack, 1 retreat)… Two possible ways to decide: always obey general in absence of majority, or always decide on safe default (retreat). In this case, they lead to same result, let’s assume our default action in absence of majority is to retreat.
- #32: <number> L3 again has no clear majority in this case (1 attack, 1 retreat)… This time, however, our safe default of “retreat” leads to loyal lieutenant disobeying loyal general. Bad. So it looks like our default in absense of majority should be to obey the general. But what if the general can’t be trusted?
- #33: <number> Neither L2 nor L3 has a majority in the values they received (both have 1 attack, 1 retreat). Decision to obey commander leads to violation of consensus in this case. But, from the perspective of any loyal lieutenant, this is indistinguishable from Case 2, so other default action (always retreat if no majority) could lead to loyal lieutenant disobeying a loyal general, which also violates the requirements