Transactional Contention Management as a Non-Clairvoyant Scheduling Problem

1. Transactional Contention Managementas a Non-Clairvoyant Scheduling Problem [Attiya et al. PODC 06] [Attiya and Milani OPODIS 09] Alessia Milani

2. Optimism • Transactions (Txs) proceed until a conflict occurs • T1conflicts with an on-going T2 if T1 tries to write to a data item previously accessed by T2 • one transaction aborts or waits for the other to complete • If no conflict occurs, they run in parallel

3. Conflict ABORT Write((Z)) Read(X)0 T1 T2 Read(Y) Write(X)1 COMMIT Conservative approach • A conflict does not imply a violation of serializability • T1 and T2 can both commit without violating strict serializability

4. Contention manager mediates conflicts • Decides which transaction aborts • E.g., the Greedy contention manager [Guerraoui et al. PODC 05] • Each Tx is assigned a unique timestamp reflecting Txs real-time order • If Txs T1 and T2 conflict, the Tx with the smaller timestamp aborts / waits • Decides when to restart aborted Txs • E.g., CAR-STM [Dolev et al. PODC 08] • the aborted Tx is not executed until the completion of the conflicting Tx  unrelated Txs may be executed serially

5. Need for a “clever” contention manager • Complete the work quickly  makespan : Worst-case total time to complete all transactions • Not waste work  do not repeate conflicts  • What Works and Why?

6. What Works and Why? In Practice [Scherer and Scott, CSJP 04] • Extensive testing • Backoff • Aging • Randomized • Various priority • … • None dominates on all benchmarks

7. What Works and Why? In Theory • Contention Management as a Scheduling problem • Evaluate the throughput, measured by the makespan of a finite set of transactions • Worst-case total time to complete all transactions • Relative to the makespan guaranteed by an optimal off-line scheduler

8. Non-Clairvoyant Scheduling • A scheduler A does not know Txs characteristics a priori • Txs arrive one by one, and their duration is unknown • Evaluated in comparison with an optimal, clairvoyant scheduler • knows the set of Txs, their data set, their release times and duration • Competitive ratio:

9. A lower bound for CM [Attiya et al. PODC 06] Even if the contention manager is : • centralized Theorem 1. The competitive ratio of any work conserving CM is Ω(s) It always lets a maximal set of non-conflicting transactions run

10. Lower Bound: Workload • The proof uses s2/2 transactions • s is the number of shared data items • Each transactions access two data items • All transactions • are available at time 0 • have the same duration • may have a different data set if executed at different times or restarted

11. 1 2 3 … s/2 1 1 1 1 … 1 2 3 3 3 … 3 3 5 5 5 … 5  … … … …  s/2 s-1 s-1 s-1 … s-1 1 2 2 2 … 2 2 4 4 4 … 4 3 6 6 6 … 6  … … … …  s/2 s s s … s Lower Bound: First Requests Work conserving CM must select an independent set of s Txs E.g., column 1.

12. 1 2 3 … s/2 1 1,2 1 1 … 1 2 3,2 3 3 … 3 3 5,2 5 5 … 5  … … … …  s/2 s-1,2 s-1 s-1 … s-1 1 2,1 2 2 … 2 2 4,1 4 4 … 4 3 6,1 6 6 … 6  … … … …  s/2 s,1 s s … s Lower Bound: Second Requests Odd Txs all ask for 2 Even Txs all ask for 1 Only two Txs can complete

13. 1 2 3 … s/2 1 1,2 1,4 1 … 1 2 3,2 3,4 3 … 3 3 5,2 5,4 5 … 5  … … … …  s/2 s-1,2 s-1,4 s-1 … s-1 1 2,1 2,3 2 … 2 2 4,1 4,3 4 … 4 3 6,1 6,3 6 … 6  … … … …  s/2 s,1 s,3 2k … s Lower Bound: Next Set Similarly… Only two Txs can complete from the second independent set of s Txs

14. 1 2 3 … s/2 1 1,2 1,4 1,6 … 1,s 2 3,2 3,4 3,6 … 3,s 3 5,2 5,4 5,6 … 5,s  … … … …  s/2 s-1,2 s-1,4 s-1,6 … s-1,s 1 2,1 2,3 2,5 … 2,s-1 2 4,1 4,3 4,5 … 4,s-1 3 6,1 6,3 6,5 … 6,s-1  … … … …  s/2 s,1 s,3 s,5 … s,s-1 Lower Bound: Repeat In general, at most two Txs from each independent set can complete

15. 1 2 3 … s/2 1 1,2 1,4 1,6 … 1,s 2 3,2 3,4 3,6 … 3,s 3 5,2 5,4 5,6 … 5,s  … … … …  s/2 s-1,2 s-1,4 s-1,6 … s-1,s 1 2,1 2,3 2,5 … 2,s-1 2 4,1 4,3 4,5 … 4,s-1 3 6,1 6,3 6,5 … 6,s-1  … … … …  s/2 s,1 s,3 s,5 … s,s-1 Makespan of Non-Clairvoyant Scheduler After aborting, all Txs request the same data item Makespan ≈

16. 1 2 3 … s/2 1 1,2 1,4 1,6 … 1,s 2 3,2 3,4 3,6 … 3,s 3 5,2 5,4 5,6 … 5,s  … … … …  s/2 s-1,2 s-1,4 s-1,6 … s-1,s 1 2,1 2,3 2,5 … 2,s-1 2 4,1 4,3 4,5 … 4,s-1 3 6,1 6,3 6,5 … 6,s-1  … … … …  s/2 s,1 s,3 s,5 … s,s-1 Makespan of Clairvoyant Scheduler Schedule an extended diagonal together s/2 independent Txs complete Makespan ≈ s Competitive ratio ≈s

17. at any time, some running transaction will execute uninterrupted until it commits A matching Upper Bound • Proved for the Greedy CM [Attiya et al. PODC 06] • Relies on the fact that Txs write most of the time Theorem 2.Any work conserving CM with the pending commitproperty has O(s) competitive ratio

18. … 1 3 4 k Read-Dominated Workloads • Existing results hold for write-dominated workloads • Transactions need exclusive access for most of their duration (early-write transactions) [Guerraoui et al. PODC 05, Attiya et al. PODC 06] • What about read-dominated workloads? • Read-only transactions • Late-write transactions [Attiya & Milani. OPODIS 09] k+1

19. Extending the lower bound to read-dominated workload • It holds also for CM that has a more careful approach than being conservative • Transactions : • have the same duration, are available at time 0 • But may have a different data set if executed at different times or restarted Theorem 3. There is a read-dominated workload, s.t. the competitive ratio of any deterministic CM is Ω(s)

20. Lower Bound : Workload … … … … … … … … …

21. Makespan of Non-Clairvoyant Scheduler Work conserving CM must select an independent set of m Txs e.g., 1 row plus m-q read-only Txs … … … … … … … … …

22. Makespan of Non-Clairvoyant Scheduler Only one Tx in a given row can commit Restarted Txs all request the same data item … … … … … … … … …

23. Makespan of Non-Clairvoyant Scheduler At time q, still  q2 late-write Txs to be executed We have to execute them serially q=s/2 Makespan … … … … … … To remove the work-conserving assumption : A Tx that starts after time q is [R1…Rq R1 W1] …

24. Makespan of the Clairvoyant Scheduler Each column is an independent set of Txs At time q, all Txs are committed q=s/2 Makespan s … … … … … … … … … Competitive ratio s

25. A lower bound for conservative CM • The makespan is not competitive even relative to a clairvoyant online scheduler[Dragojevic et al. PODC 09] • It has complete information on a transaction as it arrives Theorem 4. There is a late-write workload,such that the competitive ratio of any deterministic conservative scheduler is Ω(m)

26. On Bimodal Workloads • If a transaction writes, it writes from the very beginning • Recent contention managers try to avoid repeated conflicts by serializing conflicting Txs • CAR-STM, Steal On Abort, ATS • They are conservative • Ω(m)competitive ratio for read-dominated workloads (by Theorem 4) • also Ω(m)competitive ratio for bimodal workloads

27. Conflict CAR-STM scheduler Txs in execution T4 T1 T5 T2 T6 T3 T4 T6 T5 T2 Enqueued Txs T3 T5 Serialize the execution of read-only Txs • T1 is a writing Tx • T2 and T3 and T5 are read-only Txs

28. Conflict Bimodal scheduler T3 Txs in execution T2 T1 T5 T2 T3 T5 T6 T6 T4 T5 T2 Enqueued Txs T3 T5 Read-only queue • T1 is a writing Tx • T2 and T3 and T5 are read-only Txs

29. “Conservative” schedulers decrease performance w/ read-dominated WL Can a “smarter” scheduler do better? At what cost? Summary late-write Txs are more difficult to handle than read-only Txs & &  &  1 1 2 2 3 1 (s) [Attiya et al.] 3 (s) derived from [Attiya et al.] (m) CAR-STM, ATS, SoA O(s) Bimodal 2 (s) (m) O(m) trivial