Fault-Tolerant Computing: COTS-Based Algorithm Design & Robust Data Structures - Prof. B. , Study Guides, Projects, Research of Electrical and Electronics Engineering

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Dec. 2006

Algorithm Design Methods

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Fault-Tolerant Computing^ SoftwareDesignMethods

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Algorithm Design Methods

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About This Presentation Edition^

Released

Revised

Revised

First^

Dec. 2006

This presentation has been prepared for the graduatecourse ECE 257A (Fault-Tolerant Computing) byBehrooz Parhami, Professor of Electrical and ComputerEngineering at University of California, Santa Barbara.The material contained herein can be used freely inclassroom teaching or any other educational setting.Unauthorized uses are prohibited. © Behrooz Parhami

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Algorithm Design Methods

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Algorithm Design Methods

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Multilevel Model of Dependable Computing

Component

Logic

Service

Result

Information

System

Level^ →

Low-Level Impaired

Mid-Level Impaired

High-Level Impaired

Unimpaired

Entry Legend:

Deviation

Remedy

Tolerance

Ideal

Defective

Faulty

Erroneous

Malfunctioning

Degraded

Failed

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Algorithm Design Methods

Slide 7

Some History: The SIFT Experience

SIFT (software-implemented fault tolerance), developed at Stanford inearly 1970s using mostly COTS components, was one of two competing“concept systems” for fly-by-wire aircraft control The other one, FTMP (fault-tolerant multiprocessor), developed at MIT,used a hardware-intensive approach System failure rate goal: 10

–9^ /hr over a 10-hour flight

SIFT allocated tasks for execution on multiple, loosely synchronizedCOTS processor-memory pairs (skew of up to 50

μs was acceptable);

only the bus system was custom designed Some fundamental results on, and methods for, clock synchronizationemerged from this project To prevent errors from propagating, processors obtained multiple copiesof data from different memories over different buses (local voting)

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Algorithm Design Methods

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Limitations of the COTS-Based Approach Some modern microprocessors have dependability features built in: Parity and other codes in memory, TLB, microcode store Retry at various levels, from bus transmissions to full instructions Machine check facilities and registers to hold the check results According to Avizienis, however: These are often not documented enough to allow users to build on them Protection is nonsystematic and uneven Recovery options are limited to shutdown and restart Description of error handling is scattered among a lot of other detail There is no top-down view of the features and their interrelationships Manufacturers can incorporate both more advanced and new features,and at times have experimented with a number of mechanisms, but thelow volume of the application base has hindered commercial viability

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Algorithm Design Methods

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Recoverable Linear Linked Lists

Simple linked list: 0-detectable, 0-correctable Circular list, with node count and unique ID: 1-detectable, 0-correctable

ID^

ID^

ID^

ID^

ID

Size Doubly linked list, with node count and ID: 2-detectable, 1-correctable

ID^

ID^

ID^

ID^

ID

Size Cannot recover from even one erroneous link Add skip links to make this 3-detectable, 1-correctable

Skip

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Algorithm Design Methods

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Other Robust Data Structures

Trees, FIFOs, stacks (LIFOs), heaps, queues In general, a linked data structure is 2-detectable and 1-correctable iffthe link network is 2-connected Robust data structures provide fairly good protection with little designeffort or run-time overhead^ Audits can be performed during idle time^ Reuse possibility makes the method even more effective Robustness features to protect the structure can be combined withcoding methods (such as checksums) to protect the content

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Algorithm Design Methods

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Algorithm-Based Error Tolerance

M^ =r^

M^ =f^

2

M^ =

Matrix M^ =c^

M^

Row checksum matrix

Column checksum matrix

Full checksum matrix

Error coding applied to data structures, rather than at the level of atomicdata elements Example: mod-8checksums usedfor matrices If^ Z^ =^

X^ ×^ Y

then Z =^ X f^

×^ Y c r In^ M , any singlef error is correctableand any 3 errorsare detectable Four errors maygo undetected

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Algorithm Design Methods

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Matrix Multiplication Using ABET

X^ =

If^ Z^ =^

X^ ×^ Y

then Z =^ X f^

×^ Y c r

Column checksummatrix for

X 2

Y^ =

46 + 20 + 42 = 108 = 4 mod 8 20 + 41 + 30 = 91 = 3 mod 8

35 = 3 mod 8

36 = 4 mod 8

×^ Row checksum matrix for

Y

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Algorithm Design Methods

Cell 6 Slide 16

Cell 1^

Cell 2^

Cell 3^

Cell 4^

Cell 5

Recomputing with Shift in Space

Linear array with an extra cell can redo the same pipelined computationwith each step of the original computation shifted in space Each cell

i^ + 1 compares the result of step

i^ that it received from the left

in the first computation to the result of step

i^ that it obtains in the second

computation With two extra cells in the linear array, three computations can bepipelined and voting used to derive highly reliable results

1

2

3

4

5

1 ′^

2 ′^

3 ′^

4 ′^

5 ′

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Algorithm Design Methods

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COTS-Based Reliable Distributed Systems Distributed systems, built from COTS nodes (processors plus memory)and interconnects, have redundancy and allow software-based faulttolerance implementation Interconnect malfunctions are dealt with by synthesizing reliablecommunication primitives ( Node malfunctions are modeled differently, with the more generalmodels requiring greater redundancy to deal with

Byzantine Timing Omission Crash Node stops (does notundergo incorrect transitions)

Node does not respondto some inputs

Node responds eithertoo early or too late

Totally arbitrary behavior

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Algorithm Design Methods

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Reliable Group Membership Service

A group of processes may be cooperating for solving a problem The group’s membership may expand and contract owing to changingprocessing requirements or because of malfunctions and repairs Reliable multicast:

message guaranteed to be received by all

members within the group ECE 254C:

Advanced Computer Architecture – Distributed Systems (course devoted to distributed computing and its reliability issues)

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Algorithm Design Methods

Slide 20

Data Replication

Resilient objects using the primary site approach Active replicas: the state-machine approach Request is sent to all replicas All replicas are equivalent and any one of them can service the request Ensure that all replicas are in same state (e.g., via atomic broadcast) Read and write quorumsExample: 9 replicas, arranged in 2D gridRows constitute write quorumsColumns constitute read quorumsA read quorum contains the latest update Maintaining replica consistency very difficult under Byzantine faults Will discuss Byzantine agreement next time

Mostup-to-datereplicasPossibleread quorum