Seven OâClock: A New Distributed GVT Algorithm using Network Atomic Operations

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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.

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### 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.
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.

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)

Sequentially consistent memory model ensures proper causal order

• Limited to shared memory architecture
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

*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.

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

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
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 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
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”

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.
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
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

GVT

7

LVT: 7

9

GVT: min(5,7)

LVT: min(5,9)

LVT: 5

5

10

NAO

A

B

C

D

E

GVT

7

LVT: 7

9

GVT: min(5,7)

LVT: min(5,9)

LVT: 5

5

10

NAO

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

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
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

Maximize distribution (round robin among nodes) VERSUS

Maximize parallelization (use all CPUs before using additional nodes)

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.

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