1. Efficient Algorithms for Distributed Snapshots and Global Virtual Time Approximation Author: Friedermann Mattern Presented By: Shruthi Koundinya

2. Overview Introduction Models and Definitions Consistent Cut Algorithm Distributed Monotonic Computation Scheme Distributed Simulation Global Virtual Time Summary

3. 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)

4. 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

5. 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

6. Consistent Cut Algorithm 2 4 3 1 Initiator - 1

7. Consistent Cut Algorithm 2 4 3 1 Initiator - 1 Control Messages & a Red message sent

8. Consistent Cut Algorithm 2 4 3 1 Initiator - 1 Red Message Received at 2

9. Consistent Cut Algorithm 2 4 3 1 Initiator - 1 3 sends white Mesg to 1 Ctrl Mesg from 1 reaches 3

10. Consistent Cut Algorithm 2 4 3 1 Initiator - 1 White Mesg received at 1 Red Ctrl Mesg received

11. 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.

12. Catching Messages In Transit Vector Counter Principle Every process P i counts the number of white messages it has sent to P j 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.

13. 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.

14. 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’)

15. 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?

16. 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.

17. GVT Approximation Rules: Each process has a local clock & a vector counter Send Message Receive Message Control Message reaches P i Control Message reaches P init

18. Summary 1. Consistent Cut 2. Get Transit message 3. Monotonic Functions4. GVT

19. Q/A