Seven O’Clock: A New Distributed GVT Algorithm using Network Atomic Operations

1. Seven O’Clock: A New Distributed GVT Algorithm using Network Atomic Operations David Bauer, Garrett Yaun Christopher Carothers Computer Science Murat Yuksel Shivkumar Kalyanaraman ECSE

2. Global Virtual Time Defines a lower bound on any unprocessed event in the system. Defines the point beyond which events should not be reclaimed. • Imperative that GVT computation operate as efficiently as possible.

3. Simultaneous Reporting Problem Transient Message Problem Key Problems arises “because not all processors will report their local minimum at precisely the same instant in wall-clock time”. message is delayed in the network and neither the sender nor the receiver consider that message in their respective GVT calculation. Asynchronous Solution: create a synchronization, or “cut”, across the distributed simulation that divides events into two categories: past and future. Consistent Cut:a cut where there is no message scheduled in the future of the sending processor, but received in the past of the destination processor.

4. Mattern’s GVT Algorithm Construct cut via message-passing Cost: O(log n) if tree, O(N) if ring • If large number of processors, then free pool exhausted waiting for GVT to complete

5. Fujimoto’s GVT Algorithm Construct cut using shared memory flag Cost: O(1) Sequentially consistent memory model ensures proper causal order • Limited to shared memory architecture

6. Memory Model Sequentially consistent does not mean instantaneous Memory events are only guaranteed to be causally ordered Is there a method to achieve sequentially consistent shared memory in a loosely coordinated, distributed environment?

7. GVT Algorithm Differences *cost of algorithm much higher

8. Network Atomic Operations Goal: each processor observes the “start” of the GVT computation at the same instance of wall clock time Definition: An NAO is an agreed upon frequency in wall clock time at which some event is logically observed to have happened across a distributed system.

9. Update Tables Update Tables Update Tables Update Tables Update Tables Update Tables Update Tables Compute GVT Compute GVT Compute GVT Compute GVT Compute GVT Compute GVT Compute GVT wall-clock time wall-clock time Network Atomic Operations Definition: An NAO is an agreed upon frequency in wall clock time at which some event is logically observed to have happened across a distributed system. Goal: each processor observes the “start” of the GVT computation at the same instance of wall clock time possible operations provided by a complete sequentially consistent memory model

10. Clock Synchronization • Assumption: all processors share a highly accurate, common view of wall clock time. • Basic building block: CPU timestamp counter • Measures time in terms of clock cycles, so a gigahertz CPU clock has granularity of 109 secs • Sending events across network is much larger granularity depending on tech: ~106 secs on 1000base/T

11. Clock Synchronization • Issues: clock synchronization, drift and jitter • Ostrovsky and Patt-Shamir: • provably optimal clock synchronization • clocks have drift and the message latency may be unbounded • Well researched problem in distributed computing – we used simplified approach • simplified approach helpful in determining if system working properly

12. Max Send Dt • Definition: max_send_delta_t is maximum of • worst case bound on the time to send an event through the network • twice synchronization error • twice max clock drift over simulation time • add a small amount of time to the NAO expiration • Similar to sequentially consistent memory • Overcomes: • Transient message problem, clock drift/jitter and clock synchronization error

13. Max Send Dt: clock drift • Clock drift causes CPU clocks to become unsynchronized • Long running simulations may require multiple synchs • Or, we account for it in the NAO • Max Send Dt overcomes clock drift by ensuring no event “falls between the cracks”

14. Dmax Dmax GVT tmax LP2 LP1 tmax Dmax Dmax GVT wallclock time Max Send Dt • What if clocks are not well synched? • Let Dmax be the maximum clock drift. • Let Smax be the maximum synchronization error. • Solution: Re-define tmax as t’max = max(tmax , 2*Dmax , 2*Smax) • In practice both Dmax and Smax are very small in comparison to tmax.

15. Transient Message Problem • Max Send Dt: worst case bound on time to send event in network • guarantees events are accounted for by either sender of receiver

16. Simultaneous Reporting Problem • Problem arises when processors do not start GVT computation simultaneously • Seven O’Clock does start simultaneously across all CPUs, therefore, problem cannot occur

17. GVT 7 LVT: 7 9 GVT: min(5,7) LVT: min(5,9) LVT: 5 5 10 NAO A B C D E

18. GVT 7 LVT: 7 9 GVT: min(5,7) LVT: min(5,9) LVT: 5 5 10 NAO

19. GVT #2 GVT #1 NAO NAO Simulation: Seven O’Clock GVT Algorithm • Assumptions: • Each processor has a highly accurate clock • A message passing interface w/o ack is available • The worst case bound on the time to transmit a message through the network tmax is known. • Properties: • a clock-based algorithm for distributed processors • creates a sequentially consistent view of distributed memory tmax tmax 7 12 LP4 LVT=min(7,9) LP3 9 cut point GVT=min(5,7) LP2 10 LVT=min(5,9) LP1 5 NAO wallclock time

20. Limitations • NAOs cannot be “forced” • agreed upon intervals cannot change • Simulation End Time • worst-case, complete NAO and only one event remaining to process • amortized over entire run-time, cost is O(1) • Exhausted Event Pool • requires tuning to ensure enough optimistic memory available

21. Uniqueness • Only real-time based GVT algorithm • Zero-cost consistent-cut  truly scalable • O(1) cost  optimal • Only algorithm which is entirely independent of available event memory • Event memory loosely tied to GVT algorithm

22. r-PHOLD PHOLD with reverse computation Modified to control percent remote events (normally 75%) Destinations still decided using a uniform random number generator  all LPs possible destination TCP-Tahoe TCP-TAHOE ring of Campus Networks topology Same topology design as used by PDNS in MASCOTS ’03 Model limitations required us to increase the number of LAN routers in order to simulate the same network Performance Analysis: Models

23. Performance Analysis: Clusters

24. Itanium Cluster: r-PHOLD, CPUs allocated round-robin

25. Maximize distribution (round robin among nodes) VERSUS Maximize parallelization (use all CPUs before using additional nodes)

26. NetSim Cluster: Comparing 10- and 25% remote events (using 1 CPU per node)

27. NetSim Cluster: Comparing 10- and 25% remote events (using 1 CPU per node)

28. TCP Model Topology Single Campus 10 Campus Networks in a Ring Our model contained 1,008 campus networks in a ring, simulating > 540,000 nodes.

29. Itanium Cluster: TCP results using 2- and 4-nodes

30. Sith Cluster: TCP Model using 1 CPU per node and 2 CPU per node

31. Future Work & Conclusions • Investigate “power” of different models by computing spectral analysis • GVT now in frequency domain • Determine max length of rollbacks • Investigate new ways of measuring performance • Models too large to run sequentially • Account for hardware affects (even in NOW there are fluctuations in HW performance) • Account for model LP mapping • Account for different cases, ie, 4 CPUs distributed across 1, 2, and 4 nodes