Application of AI and MLTechniques to FaultTolerant Routing - PowerPoint PPT Presentation

Title: Application of AI and MLTechniques to FaultTolerant Routing


1
Application of AI- and ML-Techniques to
Fault-Tolerant Routing
Arjun Rao CS 717 November 16 and 18, 2004
2
Papers Covered

• 1 Loh, Peter K.K., Artificial Intelligence
  Search Techniques as Fault-Tolerant Routing
  Strategies
• 2 Loh, Shaw., A Genetic-Based Fault-Tolerant
  Routing Strategy for Multiprocessor Networks

3
Papers Covered (cont.)

• 3 Loh, Schröder, Hsu., Fault-Tolerant Routing
  on Complete Josephus Cubes (not AI-related but
  interesting nevertheless)
• If time permits, also
• 4 Bradley, Tyrrell., Immunotronics Hardware
  Fault Tolerance Inspired by the Immune System

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The Problem of Routing

• Communication between nodes
• Servers
• Microprocessors
• Desire shortest, most efficient paths
• Multiprocessor network topologies, e.g.
  hypercubes, Josephus cubes, etc.
• Desire availability of paths
• What to do when links/nodes fail?
• How to remain (close to) optimal?

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Intro to Fault-Tolerant Routing

• Current algorithms adaptive but non-minimal
• Misrouting
• Routing strategies tied to specific topologies
• k-ary, n-cubes, meshes, etc. Regular structures
  and symmetry
• Constrained by fault number and types
• More general strategies vulnerable to deadlock
  and livelock

6
Turn Model Glass, Ni

• Widest application scope
• k-ary, n-cubes, nD-meshes, torus geometries, etc.
• West-First algorithm (on 2D-mesh)
• Messages prevented from turning west again
• Prevents cycles?deadlocks
• Routing along virtual channels in strictly
  decreasing or increasing order

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Turn Model and Channel Numbering
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Turn Model (cont.)

• Three examples of routing
• F FAILURE
• Full adaptation w/o deadlock and livelock
  requires more global info?more overhead

9
AI Search Techniques

• Arbitrary topology ? Search space
• Search space ? Search tree(s)
• Adaptive but still non-minimal
• Characteristic recursion impractical on
  loosely-coupled, distributed network

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AI Logical Abstraction

• Abstraction
• S Problem space
• O Set of objectives
• P Search paths
• S (O, P), where oi ? O and pj ? P, each pj
  connects tuple (ok, ol), k ? l
• Abstraction used to model

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Multiprocessor Network w/ Generic Topology

• Network
• N Nodes
• L Links between nodes
• G (N, L), where ni ? N and lj ? L, each lj
  connects tuple (nk, nl), k ? l
• Objective ? Node
• Search path ? Link

12
Abstract Routing Model

• Search ?
• ?(os, ot) S x S ? S, where S (O, P) and S
  (O, P)
• ox,oy ? O and ox,oy ? O ? Successful search
• ox,oy ? O and ox ? O, oy ? O ? Unsuccessful ?
• Routing attempt R
• R(ns, nd) G x G ? G, where G (N, L) and G
  (N, L)
• ni,nj ? N and ni,nj ? N ? Complete route
• ni,nj ? N and ni ? N, nj ? N ? Incomplete ?

13
Routing Analogy

• AI search equivalent to routing attempt
• Successful search ? Route between source and
  destination nodes
• Unsuccessful search ? Incomplete route to
  destination

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Caveats of Analogy

• No specific search algorithm ? No routing
  strategy
• No optimality constraints
• Nothing about deadlocks/livelocks
• Nothing about fault tolerance!!

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Fault-Tolerant Routing Model

• Model considers two aspects
• Routing system configuration
• Must be generic enough!
• Message propagation protocols and policies
• Following slides introduce what is needed for AI
  searches (w/ physical message backtracking)

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FT Routing Model (cont.)
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FT Routing Model (cont.)

• Eager readership of input messages
• Single input buffer to avoid polling
• Multiple output buffers to accommodate different
  delivery rates
• Router process
• AI/FT routing strategy implemented here
• Physical message backtracking ? Increased message
  sizes
• Increased message sizes/overhead ? Requires
  communications router at each node

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Communications Router
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Communications Router (cont.)

• Communication router constitutes router process
  and connections
• Main components LCM and CP
• ROM Stores link management and routing software
• RAM Stores routing table, link status table,
  associated link lists

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CR Data Structure Routing Table
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CR Routing Table

• For each node, up to n links
• For each link
• Connected with status OK and node ID of neighbor
• Not connected with status NC and node ID 1
• Link fault represented by timeout
• Status reset to NC
• Processor fault represented by timeouts in
  neighbors

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CR Data Structures Link Status Table, Lists
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Message Packets

• Six fields
• Router Control (4 bits) Type of message,
  including NORMAL and BACKTRACK
• Destination Node ID (10 bits) Supports network
  of size up to 1024 nodes
• Pending Nodes (20 bytes) Stack of node IDs that
  may receive packet but have not yet
• Traversed Nodes (20 bytes) Stack of nodes
  traversed, with most recent on top

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Message Packets (cont.)

• Traversed Nodes Index (10 bits) Index to
  previous traversed nodes field. Supports
  simulation of physical message backtracking
• Data Field (n-bit pointer) Points to
  information content of packet

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(Finally) AI Search Strategies

• Brute Force
• Depth-First Search
• Random Climbing
• Heuristic
• Hill Climbing
• Best-First Search
• A

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AI Search Strategies (cont.)

• In presence of network faults
• Prevent cycles ? No deadlocks
• Prevent more than two traversals of nodes/links ?
  No livelocks and necessary for AI searches
• Adaptations of search algorithms
• Problems
• Recursion? Nope (PMB)
• Overhead? Fixed (Well, mostly)

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Common Beginning

• Extracts header and disassembles it
• IF Destination Node is reached, pass packet to
  host processor
• ELSE
• IF Router Control is BACKTRACK
• IF Pending Nodes top node is directly linked
• Route packet to that node
• Set Router Control to NORMAL
• ELSE
• Backtrack packet to previous node in
  traversed
• Pop current node ID from Pending Nodes
• Push current node ID onto Traversed Nodes

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Depth-First Search

• Travel as far as possible
• Do not consider alternative paths just yet
• If fault or dead-end, backtrack to most recent
  possible path

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DFS (cont.)

• Following common beginning
• Look for directly linked successor nodes
• IF they are already traversed, ignore
• ELSE IF they are in Pending Nodes, ignore
• ELSE push them onto Pending Nodes
• Read top node of Pending Nodes
• IF directly linked (no fault), route packet to it
• ELSE Set BACKTRACK and route to last traversed
  node
• END

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DFS Example
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DFS Example (cont.)
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Random Climbing

• Following the common beginning
• ELSE
• Select a successor node randomly
• Push unselected successor nodes onto Pending
  Nodes

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Hill Climbing

• Heuristic Estimated remaining distance
• Following common beginning
• ELSE
• Sort successor nodes according to est. remaining
  distance
• Push sorted nodes onto Pending Nodes

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Best-First Search

• Resumes partial routes not previously considered
• Looks at immediate neighbors, neighbors of
  predecessors
• Sorts by est. remaining distance
• Leads to non-minimal routes!

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BFS (cont.)

• ELSE
• Push (directly linked successor nodes) onto
  Pending Nodes
• Sort Pending Nodes according to est. remaining
  distance

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A

• Two heuristics
• Estimated remaining distance h
• Path length traversed g
• Partial paths sorted by f g h
• When no faults, always finds minimal route

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A (cont.)

• After current ID processing
• Record path length traversed, g
• ELSE
• Calculate and store f for new successor nodes
• Push them onto Pending Nodes sorted by f

38
Performance Testing

• Simulated 125-node multiprocessor network
• Max 8 links per node (maps to many topologies)
• Faulty links and processors
• Pre-specified or dynamically generated
• Testing
• Messages between every pair of nodes
• 20 trials at 0, 5, 10, 15, 20 faulty links
• 125 x 125 x 20 x 6 1,875,000 tests (??)

39
Test Results

• As faults increase, heuristic strategies fair
  better (esp. gt 15)
• A best search technique but slow
• Hill climbing and BFS do not consider nodes
  traversed
• Hill climbing considers only immediate neighbors

40
Test Results (cont.)
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Main Point

• Using AI search techniques, we abstract from
  routing in networks to searching in trees
  (topology-independent, quantity and type of
  faults irrelevant)

42
Next Paper

• 1 Loh, Peter K.K., Artificial Intelligence
  Search Techniques as Fault-Tolerant Routing
  Strategies
• 2 Loh, Shaw., A Genetic-Based Fault-Tolerant
  Routing Strategy for Multiprocessor Networks

43
Our Little Problem

• AI search techniques topology- and fault-type
  independent
• but non-minimal routes utilized
• Follow-up work shows how genetic algorithms
  (combined with heuristics) can find minimal
  routes in presence of network faults

44
Genetic Algorithms Overview

• Optimization strategy
• Population of potential solutions evolve over
  series of generations
• Each element of population is chromosome each
  unit of chromosome is gene
• Chromosomes undergo crossover and mutation
• Most fit chromosomes selected for next
  generation, based upon fitness function

45
Abstract Model

• Same as before (including definitions of S and G)
• Pure abstraction suffers from same caveats as
  before
• Basic idea Instead of AI search for adaptive
  route, optimize over population of routes to find
  best

46
Message Packets

• Simplified version

47
Chromosome

• Route ? Chromosome
• Node on route ? Gene in chromosome
• Length of route ? Size of chromosome
• Chromosome size directly reflects routing
  performance!
• Distance traversed basis of fitness

48
Population Creation
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Mutation and Crossover

• Mutation Swap and/or shift
• Normal crossover destroys routes, messes with
  source and destination problem w/ different
  lengths
• Use one-point random crossover

50
Fitness Function

• F (Dmax Droute) / Dmax ?
• Dmax Maximum distance between source and
  destination
• Droute Distance traveled by specific route
• ? Predefined value to ensure non-zero fitness
• Higher value ? More fit

51
Selection Scheme

• Roulette Wheel
• Sum of fitness values random value from 0,1
• Select chromosomes with fitness greater than
  product
• Tournament Selection
• Most fit chromosomes selected
• Stochastic Remainder
• Probabilities used to select route
• Which scheme has best performance selecting
  optimal route?

52
Reroute
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Genetic Hybrid Algorithm