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

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.

Key Problems Simultaneous Reporting Problem Transient Message Problem 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.

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

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

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?

GVT Algorithm Differences Fujimoto7 O’ClockMatternSamadi Cost of Cut Calculation O(1) O(N) or O(log N) O(N) or O(log N) * Parallel / Distributed PP+D Global Invariant Shared Memory Flag Real Time Clock Message Passing Independent of Event Memory NYNN * cost of algorithm much higher

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.

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. wall-clock time Compute GVT wall-clock time Update Tables possible operations provided by a complete sequentially consistent memory model

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 10 9 secs –Sending events across network is much larger granularity depending on tech: ~10 6 secs on 1000base/T

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

Max Send  t 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

Max Send  t: 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  t overcomes clock drift by ensuring no event “falls between the cracks”

Max Send  t What if clocks are not well synched? –Let  D max be the maximum clock drift. –Let  S max be the maximum synchronization error. Solution: Re-define  t max as  t’ max = max(  t max, 2*  D max, 2*  S max ) In practice both  D max and  S max are very small in comparison to  t max. LP 1 wallclock time LP 2 GVT  t max GVT  D max  t max

Transient Message Problem Max Send  t: worst case bound on time to send event in network –guarantees events are accounted for by either sender of receiver

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

NAO 7 5 GVT 109 LVT: 7LVT: 5 LVT: min(5,9) GVT: min(5,7) ABCDE

NAO 7 5 GVT 109 LVT: 7LVT: 5 LVT: min(5,9) GVT: min(5,7)

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  t max is known. cut point LP 1 LP 2 wallclock time LP 3 LP 4 GVT #1  t max GVT # NAO LVT=min(5,9) LVT=min(7,9) 12 GVT=min(5,7) –Properties: a clock-based algorithm for distributed processors creates a sequentially consistent view of distributed memory

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

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

Performance Analysis: Models 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: Clusters Itanium Cluster Location: RPI Total Nodes: 4 Total CPU: 16 Total RAM: 64GB CPU: Quad Itanium-2 1.3GHz Network: Myrinet 1000base/T NetSim Cluster Location: RPI Total Nodes: 40 Total CPU: 80 Total RAM: 20GB CPU: Dual Intel 800MHz Network: ½ 100base/T, ½ 1000base/T Sith Cluster Location: Georgia Tech Total Nodes: 30 Total CPU: 60 Total RAM: 180GB CPU: Dual Itanium-2 900MHz Network: ethernet 1000base/T

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

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

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

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

TCP Model Topology Single Campus10 Campus Networks in a Ring Our model contained 1,008 campus networks in a ring, simulating > 540,000 nodes.

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

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

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