Serializability of global history

Transcription

1 Serializability of global history Global history serializable? r1(a) r4(c) w2(d) r3(d) w3(a) c3 r2(d) c2 c3 w1(b) c1 w4(b) w4(e) c4 c4 s1: r1(a) w3(a) c3 w1(b) c1 w4(b) c4 s2: r4(c) w2(d) r3(d) c3 r2(e) c2 w4(e) c4 s1: t1 < t3, t1 < t4 t1 t3 t4 s2 : t2 < t4, t2 < t3 t2 t3 t4 Global history is serializable: t1 < t2 < t3 < t4 t1 t2 t3 t4 by chance! Local serializability does NOT imply global serializability HS-2010 HS / TA-DCC-2-15

2 Serializablity of global history Counterexample with serializable local histories and conservative scheduling of t1,t2 without a serializable global one S1 = {a}, S2= {b,c} Global TA: t1 = r(a), w(b), t2 = w(a) r(c) Local TA t3 = r(b) w(c) Note: without local TA serializable Local histories: S1: r1(a) w2(a) S2: r3(b) w1(b) r2(c) w3(c) local histories serializable: t1, t2 and t2 t3 t1 global history is not: t1 t2 t3?? # t2 t3 t1?? # HS-2010 HS / TA-DCC-2-16

3 Global histories Consequence: Serializability of global TA without locals not sufficient to guarantee global serializability in heterogeneous federations Reason: indirect conflict between t1 and t2 at S2 caused by local TA t3: r3(b) w1(b) r2(c) w3(c) Solution in principle: Global TA manager has to guarantee same serialization sequence of global TAs also in case of indirect conflicts HS-2010 HS / TA-DCC-2-17

4 Global histories Even read-only transactions may be in conflict (!) s1= {a,b}, S2 = {c,d } S1: r1(a) r3(a) r3(b) w3(a) w3(b) r2(b) S2: r2(c) r4(c) r4(d) w4(c) w4(d) r1(d) Global transactions t1 and t2 (both read-only!) are serialized differently at either site. t1 t3 t2 t2 t4 t1 HS-2010 HS / TA-DCC-2-18 t4

5 3.4 Conflicts in heterogeneous DDB Let S i be a local history, and let t, t TAs active in S i, t t' t and t are in a direct conflict in C i if there are two data operations p t and q t in s i that access the same data item and at least one of them is a write. t and t are in an indirect conflict in S i if there exists a sequence t1,..., tr of transactions with operations in S i such that t is in S i in a direct conflict with t1, tj is in S i in a direct conflict with tj+1, 1 <= j<= r-1, and tr is in S i in a direct conflict with t. t and t are in conflict in s i if they are in a direct or an indirect conflict HS-2010 HS / TA-DCC-2-19

6 Global serializability in heterogeneous DDB Global conflict graph: Union of all local conflict graphs which include direct and indirect conflicts Schedule is globally conflict serializable global conflict graph (serialization graph) cycle free. How to achieve global serializability? HS-2010 HS / TA-DCC-2-20

7 Global serializability Reasonable assumption: Servers guarantee local conflict serializability Question: how should global TA manager schedule global TAs in order to avoid indirect conflicts? Hint: TAs in indirect conflict but not in direct conflict may commute: Let t3 < t1 and t2 < t3, then t1 and t2 may be exchanged as long as t3 < t1, t2 < t3 still holds HS-2010 HS / TA-DCC-2-21

8 Global serializability Example S1: r1(a) w2(a) S2: r3(b) w1(b) r2(c) w3(c) In Site 1, t1 and t2 are in direct conflict. In Site 2, they are in indirect conflict. Note: t1 and t2 do commute at S2, but that leaves their indirect conflict unchanged. HS-2010 HS / TA-DCC-2-22

9 Serialization in Multidatabases: : Questions (1) Properties of local schedulers which guarantee global serializability? Which ones? (2) If local schedulers can only guarantee local conflict serializability e.g. by using 2PL locking, how can a global scheduler notice conflict? (3). what can global Scheduler do to enforce global conflict serializability? HS-2010 HS / TA-DCC-2-23

10 Global serializability in heterogeneous MDB Goal: find properties of local schedulers in order to guarantee global serializability Reasonable assumption: Local schedulers guarantee conflict serializable schedules e.g. 2PL, TO, not sufficient, as we know Stronger protocol: rigorousness (RG) If there is a conflict pair op k (X) < op j (X), then transaction k commits (or aborts) before the op j (X) is executed strict and no overwrite (of values read by t k ) HS-2010 HS / TA-DCC-2-24

11 Global serializability Assume all local scheduler produce rigorous schedules A necessary condition,... but not quite sufficient Counterexample s1 = w1(a) c1 r3(a) r3(b) c3 w2(b) c2 with t1 < t2 s2 = w2(c) c2 r4(c) r4(d) c4 w1(d) c1 with t2 < t1 is RG, is RG, Problem: w1(d) c1 "too late", or w1(a) c1 "too early" but note: not a global conflict between t1 and t2 HS-2010 HS / TA-DCC-2-25

12 Global serializability t is commit-deferred if its commit operation is sent by the GTM to respective local sites only after all of t s local operations have been acknowledged. Let s be a global history for s1,..., sn. If each si is in RG and all global transactions are commit-deferred, then s is globally serializable. Because t1 t2 tj-1 tj == t1 If not csr there must be a cycle connecting (cycle-free) local graphs Rigorous in s1,..., sn t1 must have been committed at one site, but still active at another. # HS-2010 HS / TA-DCC-2-26

13 Global serializability Rigorous serializability not exotic: Strict 2PL - all locks are released at commit if write and read locks: rigorousness established Consequence: Heterogeneous transactional servers can be built with local servers using strict 2PL HS-2010 HS / TA-DCC-2-27

14 Global serializability in heterogeneous environments Suppose servers do not have "nice" properties (e.g. strict 2PL) How could the local / global transaction managers check for cycles? S1 ={a,b }, S2 = {c,d}, global TA: t1, t2. S1: r1(a) c1 w3(a) w3(b) c3 r2(b) c2 -> -> t1 t1 t3 t2 S2: w4(c) r1(c) c1 r2(d) c2 w4(d) c4 -> -> t2 t2 t4 t1 Avoid the 'grey' continuation Global TMgr should wait until no cycle involving t2 is possible any more (t4 must end). Not an option: GTMgr does not know, when local TA t4 ends. Serial execution of global TAs? HS-2010 HS / TA-DCC-2-28

15 Global serializability S1={a}, S2 ={b,c} S1: r 1 (a) w 2 (a) S2: r 3 (b) w 1 (b) c1 r 2 (c) w 3 (c) c 3 Serial execution of global transactions is not : t1 t2 t3 t1 If global TM schedules t2 after t1 (serial execution of TAs) and t1 writes an (artificial) object which t2 reads (at each local site) then serialization is either "t1 t2" or a local conflict will be detected! HS-2010 HS / TA-DCC-2-29

16 3.5 Global serializability using tickets Example from above: S1={a}, S2 ={b,c} S1: r 1 (a) w 2 (a) S2: r 3 (b) w 1 (b) c1 r 2 (c) w 3 (c) c 3 Take a site ticket! (I1 or I2) : Make conflicts visible! S1: r1(i1) w1(i1+1) r1(a) c1 r2(i1) w2(i1+1) w2(a) c2 S2: r3(b) r1(i2) w1(i2+1) w1(b) c1 r2(i2) w2(i2+1) r2(c) c2 w3(c) t1, not serializable! Conflict detected! t3 < t1, t1 < t2 (forced!) t2 < t3 But serial execution of global TAs not a smart solution... HS-2010 HS / TA-DCC-2-30

17 Global serializability using tickets Ticket: e.g. counter at each site, e.g. timestamp Basic idea: each global TA takes ticket and guarantees a particular serialization order (at this site!): If t1 takes a ticket at S before t2, then t1 < t2 at S In order to check global serializability Global TM must know the relative "ticket orders": global ticket graph. Global TM receives ticket order from each local server ticket graph acyclic globally serializable HS-2010 HS / TA-DCC-2-31

18 Global serializability using tickets Alternative to global ticket graph? Yes: if local servers S guarantee conflict serializability and avoid cascading abort, resulting global histories are conflict serializable! Show: if there is an incompatible serialization order at s i and s j, e.g. t1 < t2 at s i and t2 < t1 at s j then t2 cannot read ticket at s i before t1 commits (and vice versa). No cascading abort! Total ordering of commits assumed: # No global ticket graph, serialization conflicts are detected completely locally HS-2010 HS / TA-DCC-2-32

19 Summary Homogeneous federations No fundamental change of model(s) concurrency control needs global synchronization emphasis is on transparency Heterogeneous federations the more important ones, allow for a component-based approach built from (strong) local properties and the ticket method emphasis is on autonomy Next: concurrency control methods HS-2010 HS / TA-DCC-2-33