Quasi-Linearizability: relaxed consistency for improved

concurrency

Y. Afek, G. Korland, E. Yanovsky Tel-Aviv University

Motivation

• Linearizability Intuitive & clear

• BUT, requires strong synchronization

limited scalability

Motivation SEDA

• Highly concurrent server application

• Thread poolso A task queue and a set of consumer threads

Motivation SEDA cont.

• Typically, task queue is a linearizable queue

May become a contention point

Head Tail

Task TaskTask TaskTask

Task ProducersTask Consumers

Motivation Shared Counter

• Statistical Counter

• ID generator

Motivation HashTable

• Web Cache

Motivation Cont.

• What about Stack?• What about Tree?• What about Priority Queue?

The Solution

• Relax the linearizability requirement

• Back to the SEDA example…• Strict FIFO order is not a must

Replace FIFO with Loose-FIFO.

Example I

Eventual consistency

• Given a sufficiently long period of time over which no updates

are sent, we can expect

that during this period,

all updates will,

eventually, propagate

through the system and

all the replicas will be consistent.

Example II

Quiescent consistency

• Operations whose occurrence is

separated by a quiescent state

should appear in the order of their occurrence.

• An object is in a quiescent state if currently there is no pending or executing operation on that object.

The Solution cont.

• Relax the linearizability requirement

• Back to the SEAD example…• Strict FIFO order is not a musto Replace FIFO with Loose-FIFO.

• “Quasi-FIFO”o When a task is executed, no more than K tasks

that were inserted prior to it, are pending execution.

Quasi FIFO Queue

– Random Dequeue

HeadTail

Task TaskTask Task Task

Algorithm idea:• do

• Pick a node at random from the first K nodes • dequeue its element if possible.

• If already dequeued, and the queue is not empty, repeat.

Task Task

kTask

Quasi FIFO Example

T1:

T2:

T3:

enq(x) enq(z)

enq(y)

deq(z) deq(y) deq(x)NOT LIN

EARIZABLE

enq(y)enq(x) enq(z) deq(z) deq(y) deq(x)

Not Legal Sequential history

enq(y)enq(x) enq(z) deq(z) deq(y) deq(x)

Legal Sequential history

QUASI LIN

EARIZABLE

Distance 2

Quasi Linearizable Definition

Parallel Histories

LegalSequentialHistories

Quasi Linearizable Definition

1 2 3 4 5 6

4 1 2 3 5 6

H’

H

Distance 3

Q-Quasi-Sequential

Quasi Linearizable Definition

Parallel Histories

LegalSequentialHistories

Segmented Queue– Segmented Quasi-Linearizable queue

• do• Pick a random element from corresponding segment • If empty-segment (Full-segment) remove it (Add new)

• repeat

Each segment size == K.

Appendix

Counting Network (Thanks to “Art of Multiprocessor Programming, Herlihy & Shavit”)

1

Counting Network

2

1

Counting Network

3

2

1

Counting Network

3

2

1

4

Counting Network

3

2

1

4

5

Counting Network

Bitonic[k] not Linearizable

Bitonic[W] is not Linearizable

Bitonic[W] is not Linearizable

2

Bitonic[W] is not Linearizable

2

0

Bitonic[W] is not Linearizable

2

0

Problem is:• Red finished before Yellow started• Red took 2• Yellow took 0

But it is “Quiescently Consistent”

Bitonic[W] Counting Network

Is it K-Quasi Linearizable Counter?

Yes, for K≥N*W (N-Num of threads)