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Efficient Algorithms for Distributed Snapshots and Global Virtual Time Approximation. Author: Friedermann Mattern Presented By: Shruthi Koundinya. Overview. Introduction Models and Definitions Consistent Cut Algorithm Distributed Monotonic Computation Scheme Distributed Simulation

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efficient algorithms for distributed snapshots and global virtual time approximation

Efficient Algorithms for Distributed Snapshots and Global Virtual Time Approximation

Author: Friedermann Mattern

Presented By: Shruthi Koundinya

overview
Overview
  • Introduction
  • Models and Definitions
  • Consistent Cut Algorithm
  • Distributed Monotonic Computation Scheme
  • Distributed Simulation
  • Global Virtual Time
  • Summary
introduction
Introduction
  • Efficient snapshot algorithms to get global state of the system under non FIFO conditions and without acknowledgments
  • Assumptions:
    • Processes and channels form a strongly connected finite graph
    • Messages are assumed to be delivered correctly with arbitrary delay, but not necessarily in the same order.
    • 3 types or events – Send , Receive and internal
  • Applications
    • Detecting stable properties like termination detection, detection of deadlocks.
    • Used to compute monotonic functions of the global state such as lower bounds of simulation time (Global Virtual Time)
models and definitions
Models and Definitions
  • Causally Consistent Global state
    • State of the channels – Messages still in transit
    • Local states of processes
  • Monotonic Functions of the Global State
    • F is monotonic function from a partial ordered set: f(s(c))<f(s(c’)) where s( c) is a particular global state.
  • Infimum
    • Greatest lower bound, the infimum of a subset of some set is the greatest element that is smaller than all other elements of the subset
consistent cut algorithm
Consistent Cut Algorithm
  • Algorithm
    • There are 2 colors for each process Red and White. Initially all processes are white
    • A process becomes red when the local snapshot is taken.
    • Messages carry the process color along with the basic message
    • Every process takes a local snapshot when feasible before a red message is received.
    • A single process initiates the snapshot algorithm, sends virtual broadcast messages to the rest of the processes.

*Messages are non-FIFO

One can receive red messages before receiving a red control message to initiate a local timestamp

consistent cut algorithm1
Consistent Cut Algorithm

3

Initiator - 1

4

2

1

consistent cut algorithm2
Consistent Cut Algorithm

3

Initiator - 1

4

2

1

Control Messages & a Red message sent

consistent cut algorithm3
Consistent Cut Algorithm

3

Initiator - 1

4

2

Red Message Received at 2

1

consistent cut algorithm4
Consistent Cut Algorithm

3

Initiator - 1

3 sends white Mesg to 1

Ctrl Mesg from 1 reaches 3

4

2

1

consistent cut algorithm5
Consistent Cut Algorithm

3

Initiator - 1

4

2

Red Ctrl Mesg received

1

White Mesg received at 1

catching messages in transit
Catching Messages in Transit
  • Counting Method
    • Each process has a counter storing (white) sent messages during local snapshot these are sent to the initiator
    • Initiator has total white message count and waits until they are all received.
catching messages in transit1
Catching Messages In Transit
  • Vector Counter Principle
    • Every process Pi counts the number of white messages it has sent to Pj on jth component of a Vector
    • A control message, with control vector circulates the ring.
    • Round 1-Send control message across the ring and increment the control vector C:= C+V[i]
    • Reset V[i] to zero
    • C[i] = number of white message
    • Round 2- Process C[i]> 0 for all i revisited and control message waits at each process until count goes to 0.
distributed monotonic computing scheme
Distributed Monotonic Computing Scheme
  • Internal events – xi only increases
  • Send event xi >= current value of xi
  • Receive event
    • xi >= to value of xi before the receive event
    • xi >= to X-stamp of the received message.
  • A global infimum function tells one how far the computation has progressed.
how to handle inconsitent message closure c
How to handle inconsitent message- Closure C*
  • DMC allows messages

FUTURE  PAST

  • FUTURE  PAST doesn’t affect global infimum of the system
  • Global consistent cut reached through closure for cut C
  • C* = C U {e’ Є E| e Є C: e’  e}
  • F(C) is the lower bound :

f(c )<=f(c*)<=f(c’)

distributed simulation
Distributed Simulation

A distributed discrete simulation system has a set of sequential event driven simulators implemented by autonomous processes which interact by messages

  • Chronology is essential in Simulations
  • Optimistic Scheme: Simulator may directly execute the earliest event. If the event message with an earlier timestamp arrives, the simulator rolls back.
  • How long to keep the memory around for rollback?
gvt approximation
GVT Approximation
  • GVT is also called distributed infimum approximation
  • GVT is calculated along the cut C’
  • Messages sent between C and C’ are used to determine the GVT
  • Consistent cut algorithm and Vector Counter Implementation are used to device the algorithm.
gvt approximation1
GVT Approximation
  • Rules: Each process has a local clock & a vector counter

Send Message

Receive Message

Control Message reaches Pinit

Control Message reaches Pi

summary
Summary

2. Get Transit message

1. Consistent Cut

3. Monotonic Functions

4. GVT