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

Optimism Transactions (Txs) proceed until a conflict occurs  T 1 conflicts with an on-going T 2 if T 1 tries to write to a data item previously accessed by T 2  one transaction aborts or waits for the other to complete  If no conflict occurs, they run in parallel

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

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

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?

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

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

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 :

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

Lower Bound: Workload The proof uses s 2 /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

Lower Bound: First Requests Work conserving CM must select an independent set of s Txs E.g., column 1. s…ssss/2  …………  6…6663 4…4442 2…2221 s-1… s/2  …………  5…5553 3…3332 1…1111 …321

Lower Bound: Second Requests s…sss,1s/2  …………  6…666,13 4…444,12 2…222,11 s-1… s-1,2s/2  …………  5…555,23 3…333,22 1…111,21 s/2…321 Odd Txs all ask for 2 Even Txs all ask for 1 Only two Txs can complete

Lower Bound: Next Set s…2ks,3s,1s/2  …………  6…66,36,13 4…44,34,12 2…22,32,11 s-1… s-1,4s-1,2s/2  …………  5…55,45,23 3…33,43,22 1…11,41,21 s/2…321 Similarly… Only two Txs can complete from the second independent set of s Txs

Lower Bound: Repeat s,s-1…s,5s,3s,1s/2  …………  6,s-1…6,56,36,13 4,s-1…4,54,34,12 2,s-1…2,52,32,11 s-1,s…s-1,6s-1,4s-1,2s/2  …………  5,s…5,65,45,23 3,s…3,63,43,22 1,s…1,61,41,21 s/2…321 In general, at most two Txs from each independent set can complete

Makespan of Non-Clairvoyant Scheduler After aborting, all Txs request the same data item Makespan ≈ s,s-1…s,5s,3s,1s/2  …………  6,s-1…6,56,36,13 4,s-1…4,54,34,12 2,s-1…2,52,32,11 s-1,s…s-1,6s-1,4s-1,2s/2  …………  5,s…5,65,45,23 3,s…3,63,43,22 1,s…1,61,41,21 s/2…321

Makespan of Clairvoyant Scheduler Schedule an extended diagonal together s/2 independent Txs complete Makespan ≈ s s,s-1…s,5s,3s,1s/2  …………  6,s-1…6,56,36,13 4,s-1…4,54,34,12 2,s-1…2,52,32,11 s-1,s…s-1,6s-1,4s-1,2s/2  …………  5,s…5,65,45,23 3,s…3,63,43,22 1,s…1,61,41,21 s/2…321 Competitive ratio ≈ s

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 commit property has O(s) competitive ratio at any time, some running transaction will execute uninterrupted until it commits

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 k+1 134k … [Attiya & Milani. OPODIS 09]

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 Extending the lower bound to read- dominated workload Theorem 3. There is a read-dominated workload, s.t. the competitive ratio of any deterministic CM is Ω(s)

Lower Bound : Workload 12 … q 1 R 1 R q R q+1 W q+1 … 2 R 1 R q R q+2 W q+2 … … i R 1 R q R q+i W q+i … … q R 1 R q R 2q W 2q … 1 R 1 R 2 … R q-1 R q … 2 … … m-q R 1 R 2 … R q-1 R q … … … … … … …… ……

Makespan of Non-Clairvoyant Scheduler 12 … q 1 R 1 R q R q+1 W q+1 … 2 R 1 R q R q+2 W q+2 … … i R 1 R q R q+i W q+i … … q R 1 R q R 2q W 2q … q+1 R 1 R 2 … R q-1 R q … q+ 2 R 1 R 2 … R q-1 R q … … m … … … … … … …… …… Work conserving CM must select an independent set of m Txs e.g., 1 row plus m-q read-only Txs

Makespan of Non-Clairvoyant Scheduler 12 … q 1 R 1 R q R q+1 W q+1 … 2 R 1 R q R q+2 W q+2 … … i R 1 R q R q+i W q+i … … q R 1 R q R 2q W 2q … q+1 R 1 R 2 … R q-1 R q … q+ 2 R 1 R 2 … R q-1 R q … … m … … … … … … …… …… Only one Tx in a given row can commit Restarted Txs all request the same data item

Makespan of Non-Clairvoyant Scheduler 12 … q 1 R 1 …R q R 1 W 1 … 2 … … i … … q … q+1 … q+ 2 … … m … … … … …… …… At time q, still  q 2 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 [R 1 …R q R 1 W 1 ]

Makespan of the Clairvoyant Scheduler 12 … q 1 R 1 R q R q+1 W q+1 … 2 R 1 R q R q+2 W q+2 … … i R 1 R q R q+i W q+i … … q R 1 R q R 2q W 2q … q+1 R 1 R 2 … R q-1 R q … q+ 2 R 1 R 2 … R q-1 R q … … m … … … … … … …… …… Each column is an independent set of Txs At time q, all Txs are committed q=s/2  Makespan s Competitive ratio s

Theorem 4. There is a late-write workload,such that the competitive ratio of any deterministic conservative scheduler is Ω(m) 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

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

CAR-STM scheduler T1 T2 Conflict T3 T2 Txs in execution Enqueued Txs T3 T1 is a writing Tx T2 and T3 and T5 are read-only Txs T5 T4 T6 T5T6 T5 T4 Serialize the execution of read-only Txs

Bimodal scheduler T1 T2 Conflict T3 T2 Txs in execution Enqueued Txs T3 Read-only queue T1 is a writing Tx T2 and T3 and T5 are read-only Txs T5 T4 T6 T5T6 T5 T2 T3 T5

 (s) [Attiya et al.]  (s)  (m) CAR-STM, ATS, SoA  (m) O(s) Bimodal  (s) derived from [Attiya et al.] O(m) trivial “Conservative” schedulerAny schedulerWORKLOADS WRITE- DOMINATED Early write BIMODAL : Early write + read-only READ- DOMINATED : Late write + read-only Summary &  “Conservative” schedulers decrease performance w/ read-dominated WL Can a “smarter” scheduler do better? At what cost? 3 & &  123 late-write Txs are more difficult to handle than read-only Txs