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Quasi-Linearizability: relaxed consistency for improved concurrency<br />Y. Afek, G. Korland, E. Yanovsky Tel-Aviv University<br />

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Motivation<br />Linearizability Intuitive & clear <br />BUT, requires strong synchronization <br />  limited scalability<br />

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Motivation SEDA<br /><ul><li>Highly concurrent server application

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Thread pools

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A task queue and a set of consumer threads</li></li></ul><li>Motivation SEDA cont.<br />Typically, task queue is a linearizable queue <br />  May become a contention point<br />Head<br />Tail<br />Task<br />Task<br />Task<br />Task<br />Task<br />Task Consumers<br />Task Producers<br />

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Motivation Shared Counter<br /><ul><li>Statistical Counter

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ID generator </li></li></ul><li>Motivation HashTable<br /><ul><li>Web Cache</li></li></ul><li>Motivation Cont.<br /><ul><li>What about Stack?

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What about Tree?

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What about Priority Queue?</li></li></ul><li>The Solution<br /><ul><li>Relaxthe linearizability requirement

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Back to the SEDA example…</li></ul>Strict FIFO order is not a must<br />Replace FIFO with Loose-FIFO.<br />

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Example IEventual consistency<br />Given a sufficiently long period of timeover which no updates<br /> are sent, we can expect <br /> that during this period, <br /> all updates will, <br /> eventually, propagate <br /> through the system and<br /> all the replicas will be consistent. <br />

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Example IIQuiescent consistency<br />Operations whose occurrence is <br /> separated by a quiescent state <br /> should appear in the order of their occurrence. <br />An object is in a quiescent state if currently there is no pending or executing operation on that object.<br />

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The Solution cont.<br /><ul><li>Relax the linearizability requirement

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Back to the SEAD example…</li></ul>Strict FIFO order is not a must<br /><ul><li>Replace FIFO with Loose-FIFO.</li></ul>“Quasi-FIFO”<br /><ul><li>When a task is executed, no more than K tasks that were inserted prior to it, are pending execution.</li></li></ul><li>Quasi FIFO Queue<br /><ul><li>Random Dequeue</li></ul>Task<br />k<br />Tail<br />Head<br />Task<br />Task<br />Task<br />Task<br />Task<br />Task<br />Task<br />Algorithm idea:<br /><ul><li>do

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Pick a node at randomfrom the first Knodes

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dequeueits element if possible.

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If already dequeued, and the queue is not empty, repeat.</li></li></ul><li>Quasi FIFO Example<br />enq(x)<br />enq(z)<br />T1:<br />enq(y)<br />T2:<br />QUASILINEARIZABLE<br />NOTLINEARIZABLE<br />deq(z)<br />deq(y)<br />deq(x)<br />T3:<br />NotLegal Sequential history<br />enq(y)<br />enq(x)<br />enq(z)<br />deq(z)<br />deq(y)<br />deq(x)<br />enq(x)<br />enq(z)<br />deq(z)<br />deq(y)<br />deq(x)<br />enq(y)<br />Legal Sequential history<br />Distance 2 <br />

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Quasi Linearizable Definition<br />Parallel <br />Histories<br />Legal<br />Sequential<br />Histories<br />

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Quasi Linearizable Definition<br />H’<br />1<br />2<br />3<br />4<br />5<br />6<br />H<br />4<br />1<br />2<br />3<br />5<br />6<br />Distance 3 <br />

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Quasi Linearizable Definition<br />Example<br />

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Quasi Linearizable Definition<br />

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Quasi Linearizable Definition<br />

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Quasi Linearizable Definition<br />

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Quasi Linearizable Definition<br />Parallel <br />Histories<br />Q-Quasi-Sequential <br />Legal<br />Sequential<br />Histories<br />

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Quasi LinearizableFIFO Queue<br />Q(deq op)= 0 (cannot move dequeue operations).<br />Q(enq op)= K (move enqueue up to distance K).<br />==<br />Q(deq not empty op)= K (move dequeue up to distance K).<br />Q(deq empty op) = 0 (except dequeueempty).<br />Q(enq op)= 0 (cannot move enqueue operations).<br />

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Segmented Queue<br /><ul><li>Segmented Quasi-Linearizable queue

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do

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Pick a randomelement from corresponding segment

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If empty-segment (Full-segment) remove it (Add new)

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repeat </li></ul>Each segment size == K.<br />

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Appendix <br />

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Counting Network (Thanks to “Art of Multiprocessor Programming, Herlihy & Shavit”)<br />1<br />

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Counting Network <br />1<br />2<br />

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Counting Network <br />1<br />2<br />3<br />

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Counting Network <br />1<br />2<br />3<br />4<br />

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Counting Network <br />1<br />5<br />2<br />3<br />4<br />

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Counting Network <br />

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Bitonic[k] not Linearizable<br />

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Bitonic[W] is not Linearizable<br />

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Bitonic[W] is not Linearizable<br />2<br />

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Bitonic[W] is not Linearizable<br />0<br />2<br />

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Bitonic[W] is not Linearizable<br />0<br />Problem is:<br /><ul><li>Red finished before Yellow started

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Red took 2

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Yellow took 0</li></ul>But it is “Quiescently Consistent”<br />2<br />

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Bitonic[W] Counting Network<br />Is it K-Quasi LinearizableCounter?<br />Yes, for K≥N*W (N-Num of threads)<br />