1. ECE 753: FAULT-TOLERANT COMPUTING
4/7/2019
ECE 753: FAULT-TOLERANT COMPUTING
Kewal K.Saluja
Department of Electrical and Computer Engineering
Reconfiguration

2. ECE 753 Fault Tolerant Computing
4/7/2019
Overview
Introduction and basic concept
Fault model and fault coverage
Two example architectures
n-cubes
de Bruijn networks
Summary
ECE 753 Fault Tolerant Computing

3. Introduction and basic concept
4/7/2019
Introduction and basic concept
References
Text and some other material
Basic concept
Must avoid using the faulty unit(s) – whether it be a process, processor, program, data, link between a pair of units, etc.
Two types of re-configurations
Fault tolerance via degraded performance
fault tolerance provided by sufficient redundancy at design stage
ECE 753 Fault Tolerant Computing

4. Fault model and fault coverage
4/7/2019
Fault model and fault coverage
Candidate architectures
Bus bases systems
Crossbar based systems
Mash connected systems
Hypercube networks
de Bruijn Networks
Tree networks
Hexagonal networks
Other regular architectures
ECE 753 Fault Tolerant Computing

5. Fault model and Fault coverage (contd.)
4/7/2019
Fault model and Fault coverage (contd.)
System Model
Units are represented as nodes
Interconnects are represented as links between nodes
Failure models
Nodes may fail or go down – the corresponding unit unable to interact with other units
Interconnect may fail or go down – no units can communicate using the failed or down link
ECE 753 Fault Tolerant Computing

6. Fault model and Fault coverage (contd.)
4/7/2019
Fault model and Fault coverage (contd.)
Objective of fault tolerance
Any pair of units must be able to interact in the presence of
Node failures
Link failures
Performance metrics
How many faults (node or link failures) can be tolerated (fault coverage)
Impact on the route length – number of hops between pairs of nodes (same as the length of the shortened path between a pair of nodes)
Can pay attention to the worst case scenario or impact on the average length of the paths
ECE 753 Fault Tolerant Computing

7. Two example architectures
4/7/2019
Two example architectures
Hypercube architecture
A n-cube
Contains 2n nodes
Encode the 2n nodes as n-tuples
Two nodes are connected using a bi-directional link if and only if the Hamming distance between them is exactly 1
3-cube
2-cube 00 01 10 11
ECE 753 Fault Tolerant Computing

8. Two example architectures (contd.)
4/7/2019
Two example architectures (contd.)
Hypercube architecture (contd.)
A method of sending message between a pair of nodes
Find a route between two nodes
An algorithm for finding a route between nodes n1 and n2
Use binary encoding of n1 and n2 Let it be
a1 a2 … ak and b1 b2 … bk
Determine the locations these two string differ and complement one bit at a time to find a route between the two nodes
Length of such a path can be no larger than k
ECE 753 Fault Tolerant Computing

9. Two example architectures (contd.)
4/7/2019
Two example architectures (contd.)
Hypercube architecture (contd.)
Finding a route in the presence of a faulty node
Consider an example – find path between nodes 0011 and 0101 in the presence of 0111 being faulty
A possible path is 0011  0001  0101
Result: between every pair of nodes there are k node disjoint paths
The paths are
Complement one bit at a time starring from the left most bit and keeping it that way. Thus we will have n starts and these will lead to n disjoint paths with some careful construction of paths
ECE 753 Fault Tolerant Computing

10. Two example architectures (contd.)
4/7/2019
Two example architectures (contd.)
Hypercube architecture (contd.)
In a hypercube of dimension k, upto k-1 node faults can be tolerated
Some faults cause a degradation as the path length starts to increase after certain faults
Number of link faults that can be tolerated is at least the number of tolerable node faults
Problems that have been addresses in literature
Centralized observer (as discussed above)
Distributed algorithm in which every node knows the location of the faulty node
Distributed algorithms in which only the neighbors of faulty node know its status
ECE 753 Fault Tolerant Computing

11. Two example architectures (contd.)
4/7/2019
Two example architectures (contd.)
de Bruijn networks
Contains 2n nodes
Encode the 2n nodes as n-tuples
Two nodes are connected using a bi-directional link if and only if the second node can be derived by logical left or right shift of the first node
An example de Bruijn network for k-3 is given next
ECE 753 Fault Tolerant Computing

12. Two example architectures (contd.)
4/7/2019
Two example architectures (contd.)
de Bruijn networks (contd.)
000
001
100
111
011
110
010
101
ECE 753 Fault Tolerant Computing

13. Two example architectures (contd.)
4/7/2019
Two example architectures (contd.)
de Bruijn networks (contd.)
There are at least two node disjoint paths between any pair of node
Hence, in the presence of a single node failure nodes can continue to interact
Many such results are known for de Bruijn networks
ECE 753 Fault Tolerant Computing

14. ECE 753 Fault Tolerant Computing
4/7/2019
Summary
Described two network architectures in which messages can be re-configured to maintain the network connectivity in the presence of faulty nodes and/or links
ECE 753 Fault Tolerant Computing