[PPT] - Title How FIFO is Your Concurrent FIFO Queue? Andreas Haas , PowerPoint Presentation

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Title

RACES Workshop, October 2012

How FIFO is Your Concurrent FIFO Queue?

Andreas Haas, Christoph M. Kirsch, Michael Lippautz, Hannes Payer

University of Salzburg

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Strict vs. Relaxed FIFO Queues

strict FIFO queue implementations relaxed FIFO queue implementations

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Strict vs. Relaxed FIFO Queues

linearizable with respect to strict FIFO queue semantics strict FIFO queue implementations relaxed FIFO queue implementations

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Strict vs. Relaxed FIFO Queues

linearizable with respect to strict FIFO queue semantics strict FIFO queue implementations linearizable with respect to relaxed FIFO queue semantics relaxed FIFO queue implementations

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Strict vs. Relaxed FIFO Queues

linearizable with respect to strict FIFO queue semantics strict FIFO queue implementations linearizable with respect to relaxed FIFO queue semantics relaxed FIFO queue implementations bounded

ut-of-order treatment
f queue elements

possible

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Strict vs. Relaxed FIFO Queues

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 2 10 20 30 40 50 60 70 80

perations/ms (more is better)

number of threads LB MS FC

linearizable with respect to strict FIFO queue semantics strict FIFO queue implementations linearizable with respect to relaxed FIFO queue semantics relaxed FIFO queue implementations bounded

ut-of-order treatment
f queue elements

possible

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Strict vs. Relaxed FIFO Queues

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 2 10 20 30 40 50 60 70 80

perations/ms (more is better)

number of threads LB MS FC US k-FIFO (k=80)

linearizable with respect to strict FIFO queue semantics strict FIFO queue implementations linearizable with respect to relaxed FIFO queue semantics relaxed FIFO queue implementations bounded

ut-of-order treatment
f queue elements

possible

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Strict vs. Relaxed FIFO Queues

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 2 10 20 30 40 50 60 70 80

perations/ms (more is better)

number of threads 2RA Scal (p=80) LB MS FC US k-FIFO (k=80) RR Scal (p=80)

linearizable with respect to strict FIFO queue semantics strict FIFO queue implementations linearizable with respect to relaxed FIFO queue semantics relaxed FIFO queue implementations bounded

ut-of-order treatment
f queue elements

possible

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How FIFO are Relaxed FIFO Queues?

Some people say relaxed FIFO queues are not enough FIFO. No applications for relaxed FIFO queues.

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How FIFO are Relaxed FIFO Queues?

We say relaxed FIFO queue implementations can be even more FIFO than strict FIFO queue implementations. Some people say relaxed FIFO queues are not enough FIFO. No applications for relaxed FIFO queues.

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Example

time a enq b enq a deq b deq

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Example

linearization point time a enq b enq a deq b deq

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Example

linearization point time a enq b enq a deq b deq linearizable

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Example

linearization point time a enq b enq a deq b deq time a enq b enq a deq b deq linearizable

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Example

linearization point time a enq b enq a deq b deq time a enq b enq a deq b deq linearizable not linearizable

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Example

linearization point time a enq b enq a deq b deq time a enq b enq a deq b deq linearizable not linearizable

ut-of-order execution
f overlapping operations
ut-of-order treatment
f queue elements

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Key Idea

Record concurrent histories of various FIFO queue implementations. Analyze these concurrent histories using only the invocation times of operations. 2.) 1.)

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Key Idea

Record concurrent histories of various FIFO queue implementations. Analyze these concurrent histories using only the invocation times of operations. 2.) 1.)

Ideally operations would take zero time

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Key Idea

Record concurrent histories of various FIFO queue implementations. Analyze these concurrent histories using only the invocation times of operations. 2.) 1.)

Ideally operations would take zero time Independent of the execution time of operations

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Element-Fairness

time a enq b enq a deq b deq

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Element-Fairness

time a enq b enq a deq b deq

zero-time linearization

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Element-Fairness

time a enq

element

vertakes element

a b

b enq a deq b deq

zero-time linearization

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Element-Fairness

time a enq

element

vertakes element

a b

b enq a deq b deq

element-fairness = number of overtakings in the zero-time linearization Definition zero-time linearization

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Experiments

for 10.000 iterations dequeue element { } enqueue unique element all threads do in parallel

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Experiments

for 10.000 iterations calculate Pi dequeue element { } enqueue unique element calculate Pi all threads do in parallel

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Experiments

for 10.000 iterations calculate Pi dequeue element { } enqueue unique element calculate Pi all threads do in parallel No dequeues in the first 200 iterations to avoid empty checks. No enqueues in the last 200 iterations to empty the queue.

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Element-Fairness per Element

0.1 1 10 100 1000 1000 2000 4000 8000 16000 32000 64000 element-fairness per element (logscale, less is better) computational load (logscale) 80 threads

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Element-Fairness per Element

0.1 1 10 100 1000 1000 2000 4000 8000 16000 32000 64000 element-fairness per element (logscale, less is better) computational load (logscale) 80 threads LB MS FC

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Element-Fairness per Element

0.1 1 10 100 1000 1000 2000 4000 8000 16000 32000 64000 element-fairness per element (logscale, less is better) computational load (logscale) 80 threads LB MS FC US k-FIFO (k=80)

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Element-Fairness per Element

0.1 1 10 100 1000 1000 2000 4000 8000 16000 32000 64000 element-fairness per element (logscale, less is better) computational load (logscale) 80 threads LB MS FC US k-FIFO (k=80) RR Scal (p=80) 2RA Scal (p=80)

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Operation-Fairness

Measure the out-of order execution of single operations

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Operation-Fairness

Observation: Linearization points induce a strict order on the queue operations Measure the out-of order execution of single operations

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Operation-Fairness

time a enq b enq a deq b deq

Observation: Linearization points induce a strict order on the queue operations Measure the out-of order execution of single operations

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Operation-Fairness

time a enq b enq a deq b deq

Observation: Linearization points induce a strict order on the queue operations Measure the out-of order execution of single operations

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a enq b enq

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a enq b enq

peration enq

a b

vertakes operation enq

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a enq b enq

peration enq

a b

vertakes operation enq
peration-fairness =

number of overtakings in a concurrent history Definition

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Operation-Age and Operation-Lateness

age (op) = number of operations op overtakes Definition

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Operation-Age and Operation-Lateness

age (op) = number of operations op overtakes Definition

a enq b enq

age(enq a ) = 0 age(enq b ) = 1

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Operation-Age and Operation-Lateness

age (op) = number of operations op overtakes lateness (op) = number of operations which overtake op Definition Definition

a enq b enq

age(enq a ) = 0 age(enq b ) = 1

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Operation-Age and Operation-Lateness

age (op) = number of operations op overtakes lateness (op) = number of operations which overtake op Definition Definition

a enq b enq

age(enq a ) = 0 age(enq b ) = 1 lateness(enq a ) = 1 lateness(enq b ) = 0

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Experiments (2)

Only for strict FIFO queue implementations at the moment. Measuring relaxed implementations is future work.

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Experiments (2)

for 10.000 iterations enqueue unique element { } calculate Pi all threads do in parallel Only for strict FIFO queue implementations at the moment. Measuring relaxed implementations is future work.

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Experiments (2)

for 10.000 iterations enqueue unique element { } calculate Pi all threads do in parallel Only for strict FIFO queue implementations at the moment. Measuring relaxed implementations is future work. dequeue all elements sequentially

ne thread does

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Maximum Operation-Age

1 10 100 1000 2000 4000 8000 16000 32000 64000 maximum operation-age (logscale, less is better) computational load (logscale) 80 threads LB MS FC

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Maximum Operation-Lateness

10 100 1000 10000 100000 1000 2000 4000 8000 16000 32000 64000 maximum operation-lateness (logscale, less is better) computational load (logscale) 80 threads LB MS FC

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Number of Overtaking Operations

20 40 60 80 100 1000 2000 4000 8000 16000 32000 64000 % of enqueue operations with operation-age > 0 (less is better) computational load (logscale) 80 threads LB MS FC

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Number of Overtaken Operations

20 40 60 80 100 1000 2000 4000 8000 16000 32000 64000 % of enqueue operations with operation-lateness > 0 (less is better) computational load (logscale) 80 threads LB MS FC

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Conclusion

Future work Measure operation-fairness of relaxed FIFO queue implementations. Use element-fairness to analyze implementation of other data structures, e.g. stacks. We introduced metrics to compare the behavior of various FIFO queue implementations. Relaxed implementation can appear more FIFO than strict implementations.

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Thank You

For more information about the queue implementations see http://scal.cs.uni-salzburg.at/ Additional measurement results can be seen on http://scal.cs.uni-salzburg.at/races12/