CSCI 633: Advanced Operating Systems- II Dept. of Computer Science CSU San Marcos

1. 1 CSCI 633: Advanced Operating Systems- IIDept. of Computer ScienceCSU San Marcos Fall 2003 Kayhan Erciyes

2. 2 Theory

3. 3 Model Distributed system model: n processes connected by a communications network imperfectly synchronized clocks, thus no exact notion of �what time it is� at other processes reliable message delivery may or may not bound message delivery time depending on what problem we�re examining depending on how practical we want solution to be no shared memory

4. 4 Fundamental Limitations Distributed systems are assumed to have no global clock Distributed systems have no shared memory These limitations force us to be creative in solving the following fundamental problems (among others) Ordering events Capturing a global state Ensuring mutual exclusion

5. 5 Time in Distributed Systems Three notions of time: Time seen by external observer: A global clock of perfect accuracy Time seen on clocks of individual hosts: Each has its own clock, and clocks may drift out of sync Logical time: event a occurs before event b and this is detectable because information about a may have reached b b is causally dependent on a

6. 6 External Time The �gold standard� against which many protocols are defined Not implementable with non-zero transmission speeds GPS helps, but there is still latency �and GPS only works outside. ?

7. 7 Internal Clocks Most workstations have reasonable clocks But clocks drift apart and software resynchronization is inaccurate Workstation clocks are appropriate only for coarse-grained notion of time Unpredictable speeds a feature of all computing systems Thus: can�t reliably predict how long events will take Example: how long for message transmission Example: how long to compute n! Scheduling issues, daemon processes, other applications �Artificially� choose bounds which trade off performance for safety �If I don�t receive a response in 15 seconds, server is down�

8. 8 Logical Time Abstraction Doesn�t provide a clock in the sense of wall clock time Focus is on definition of the �happens before� relationship between events �Could what�s happening in this event have been influenced by what happened in that event?� Events are: message sends message receptions local events

9. 9 Logical Time: The Picture

10. 10 Happened-Before Relation The happened before relation ( � ) captures the causal relationships between events: a � b if a and b are events in the same process and a occurred before b a � b if a is the send event of a message m and b is the corresponding receive event � is a transitive relation Event a potentially causally affects event b if a � b Event a is concurrent with event b if neithera � b nor b � a

11. 11 Three Important Schemes Lamport�s logical clocks clock is a single integer Vector clocks clock is a vector of integers with length n n = number of processes Matrix clocks clock is an n x n matrix of integers n = number of processes Useful for ordered multicast�covered later Optimizations for the latter two schemes to reduce overheads are important!

12. 12 Lamport�s Clocks Lamport�s clocks captures partial ordering defined by the � relation Lamport�s logical clocks: Each process i maintains a counter Ci whose current value is attached to each message sent Internal events in a process cause the counter Ci to be incremented When a message is received by a process i, Ci is set to max(m.Cj, Ci) + 1

13. 13 Happened before relation: a -> b : Event a occurred before event b. Events in the same process. a -> b : If a is the event of sending a message m in a process and b is the event of receipt of the same message m by another process. a -> b, b -> c, then a -> c. �->� is transitive. Causally Ordered Events a -> b : Event a �causally� affects event b Concurrent Events Only one is true: a -> b (or) b -> a (or) a || b. Lamport�s Clock

14. 14 Space-time Diagram

15. 15 Logical Clocks Conditions satisfied: Ci is clock in Process Pi. If a -> b in process Pi, Ci(a) < Ci(b) a: sending message m in Pi; b : receiving message m in Pj; then, Ci(a) < Cj(b). Implementation Rules: R1: Ci = Ci + d (d > 0); clock is updated between two successive events. R2: Cj = max(Cj, tm + d); (d > 0); When Pj receives a message m with a time stamp tm (tm assigned by Pi, the sender; tm = Ci(a), a being the event of sending message m).

16. 16 Space-time Diagram

17. 17 Limitation of Lamport�s Clock

18. 18 Vector Clocks Keep track of transitive dependencies among processes for recovery purposes. Ci[1..n]: is a �vector� clock at process Pi whose entries are the �assumed�/�best guess� clock values of different processes. Ci[j] (j != i) is the best guess of Pi for Pj�s clock. Vector clock rules: Ci[i] = Ci[i] + d, (d > 0); for successive events in Pi For all k, Cj[k] = max (Cj[k],tm[k]), when a message M is received by Pj from Pi.

19. 19 Vector Clock �

20. 20 Causal Ordering of Messages

21. 21 Message Ordering � Not really worry about maintaining clocks. Order the messages sent and received among all processes in a distributed system. Send(M1) -> Send(M2), M1 should be received ahead of M2 by all processes. This is not guaranteed by the communication network since M1 may be from P1 to P2 and M2 may be from P3 to P4. Message ordering: Deliver a message only if the preceding one has already been delivered. Otherwise, buffer it up.

22. 22 BSS Algorithm BSS: Birman-Schiper-Stephenson Protocol Broadcast based: a message sent is received by all other processes. Deliver a message to a process only if the message preceding it immediately, has been delivered to the process. Otherwise, buffer the message. Accomplished by using a vector accompanying the message.

23. 23 BSS Algorithm ...

24. 24 BSS Algorithm �

25. 25 SES Algorithm SES: Schiper-Eggli-Sandoz Algorithm. No need for broadcast messages. Each process maintains a vector V_P of size N - 1, N the number of processes in the system. V_P is a vector of tuple (P�,t): P� the destination process id and t, a vector timestamp. Tm: logical time of sending message m Tpi: present logical time at pi

26. 26 SES Algorithm Sending a Message: Send message M, time stamped tm, along with V_P1 to P2. Insert (P2, tm) into V_P1. Overwrite the previous value of (P2,t), if any. Any future message carrying (P2,tm) in V_P1 cannot be delivered to P2 until tm < tP2. Delivering a message If V_M (in the message) does not contain any pair (P2, t), it can be delivered. /* (P2, t) exists */ If t > Tp2, buffer the message. (don�t deliver) else deliver it

27. 27 SES Algorithm �

28. 28 SES Algorithm ... On delivering the message: Merge V_M (in message) with V_P2 as follows. If (P,t) is not there in V_P2, merge. If (P,t) is present in V_P2, t is updated with max(t in Vm, t in V_P2). Message cannot be delivered until t in V_M is greater than t in V_P2 Update site P2�s local, logical clock. Check buffered messages after local, logical clock update.

29. 29 SES Example What does the condition t > Tp2 imply? t is message vector time stamp. t > Tp2 -> For all j, t[j] > Tp2[j] This implies some events occurred without P2�s knowledge in other processes. So P2 decides to buffer the message. When t < Tp2, message is delivered & Tp2 is updated with the help of V_P2 (after the merge operation).

30. 30 Global State

31. 31 Recording Global State Send(Mij): message M sent from Si to Sj rec(Mij): message M received by Sj, from Si time(x): Time of event x LSi: local state at Si send(Mij) is in LSi iff (if and only if) time(send(Mij)) < time(LSi) rec(Mij) is in LSj iff time(rec(Mij)) < time(LSj) transit(LSi, LSj) : set of messages sent/recorded at LSi and NOT received/recorded at LSj

32. 32 Recording Global State � inconsistent(LSi,LSj): set of messages NOT sent/recorded at LSi and received/recorded at LSj Global State, GS: {LS1, LS2,�., LSn} Consistent Global State, GS = {LS1, ..LSn} AND for all i in n, inconsistent(LSi,LSj) is null. Transitless global state, GS = {LS1,�,LSn} AND for all I in n, transit(LSi,LSj) is null.

33. 33 Recording Global State ..

34. 34 Recording Global State... Strongly consistent global state: consistent and transitless, i.e., all send and the corresponding receive events are recorded in all LSi.

35. 35 Chandy-Lamport Algorithm Distributed algorithm to capture a consistent global state. Communication channels assumed to be FIFO. Uses a marker to initiate the algorithm. Marker sort of dummy message, with no effect on the functions of processes. Sending Marker by P: P records its state. For each outgoing channel C, P sends a marker on C with the state info. Receiving Marker by Q: If Q has NOT recorded its state: a. Record the state as an empty sequence, SEND marker (use above rule). Else (Q has recorded state before): Record the state of C as sequence of messages received along C, after Q�s state was recorded and before Q received the marker.

36. 36 Chandy-Lamport Algorithm Initiation of marker can be done by any process, with its own unique marker: <process id, sequence number>. Several processes can initiate state recording by sending markers. Concurrent sending of markers allowed. One possible way to collect global state: all processes send the recorded state information to the initiator of marker. Initiator process can sum up the global state.

37. 37 Chandy-Lamport Algorithm ... Example:

38. 38 Cuts Cuts: graphical representation of a global state. Cut C = {c1, c2, .., cn}; ci: cut event at Si. Consistent Cut: If every message received by a Si before a cut event, was sent before the cut event at Sender. One can prove: A cut is a consistent cut iff no two cut events are causally related, i.e., !(ci -> cj) and !(cj -> ci).

39. 39 Time of a Cut C = {c1, c2, .., cn} with vector time stamp VTci. Vector time of the cut, VTc = sup(VTc1, VTc2, .., VTcn). sup is a component-wise maximum, i.e., VTci = max(VTc1[I], VTc2[I], .., VTcn[I]). Now, a cut is consistent iff VTc = (VTc1[1], VTc2[2], .., VTcn[n]).

40. 40 Termination Detection Termination: completion of the sequence of algorithm. (e.g.,) leader election, deadlock detection, deadlock resolution. Use a controlling agent or a monitor process. Initially, all processes are idle. Weight of controlling agent is 1 (0 for others). Start of computation: message from controller to a process. Weight: split into half (0.5 each). Repeat this: any time a process send a computation message to another process, split the weights between the two processes (e.g., 0.25 each for the third time). End of computation: process sends its weight to the controller. Add this weight to that of controller�s. Rule: Sum of W always 1. Termination: When weight of controller becomes 1 again.

41. 41 Huang�s Algorithm B(DW): computation message, DW is the weight. C(DW): control/end of computation message; Rule 1: Before sending B, compute W1, W2 (such that W1 + W2 is W of the process). Send B(W2) to Pi, W = W1. Rule 2: Receiving B(DW) -> W = W + DW, process becomes active. Rule 3: Active to Idle -> send C(DW), W = 0. Rule 4: Receiving C(DW) by controlling agent -> W = W + DW, If W == 1, computation has terminated.

42. 42 Lamport�s Clocks: Limitations Clearly if an event a � b, then C(a) < C(b) What�s known if C(a) < C(b)? Only that b didn�t happen before a Can concurrent events be identified? Answer: NO What�s the case if C(a) >= C(b) ??? Correctly identifying all causal relationships will require more horsepower, but Lamport�s clocks are useful when you need to know about relationships, but can live with �false� causality reporting One example: some mutual exclusion algorithms

43. 43 Lamport�s Clocks: Total Order � defines a partial order rather than a total order How to impose a total order? Use process ID�s to break ties Important: Total order is �artificial�--it has nothing to do with the clock on the wall!

44. 44 Vector Time Vector time correctly captures the causality relationship between distributed events (captures the transitive closure of the � relation) Each process i maintains a vector of state numbers TSi TSi[i] contains the current state number for process i; TSi[n], n � i, contains the most recent state number of process n upon which i currently depends

45. 45 Vector Time: Updates TSi is updated as follows: TSi[i] is incremented between successive events at i When i sends a message m, TSi is attached to the message When i receives a message m, TSi[k] := max(TSi[k], m.TS[k])

46. 46 Vector Time: Comparison Vector timestamps are compared in the following manner: TSi < TSj iff " k, TSi[k] � TSj[k] and TSi <> TSj. An event e causally depends�on an event e' iff e'.TS < e.TS Two events e and e' are concurrent if neither e'.TS < e.TS nor e.TS < e'.TS

47. 47 Vector Time: The Picture

48. 48 More Efficient Vector Time Protocols The bad news Bernadette Charron-Bost�s theorem The good news �Never send the receiver�s value� �Plausible Clocks� Singhal/Kshemkalyani VT (static) Richard VT (dynamic)

49. 49 Singhal/Kshemkalyani Transmit only portions of vector timestamps that have changed Don�t have to send element for receiver Instead of a vector attachment for messages, now use set data structure: { (PID, clock), � , (PID, clock) } Why? Larger memory footprint is traded for reduced message size

50. 50 Singhal, Cont. Data structures: TS Vector Timestamp O(n) LS �Last Sent� O(n) LU �Last Updated� O(n) LR �Last Received� O(n2) All except the latter is a vector (LR is a vector of vectors) Need LR to be able to reconstitute complete vector timestamps for message reception events

51. 51 Vector Time: The Picture

52. 52 Optimized Vector Time: The Picture

53. 53 Singhal: Rules For process i: When updating any element at index k of TS: LU[k] = TS[i] When sending a message from j: Attach all (pk, TS[k]) such that LU[k] > LS[k] LS[k] = TS[i] When receiving a message m from j: Update TS as usual For all x, LR[j][x] = max(LR[j][x], m.TS[x]) If logging, can then attach LR[j] to message to represent complete vector timestamp

54. 54 Singhal: Simple Analysis Good if communication is highly localized N = # of processes, b = # of bits in one vector clock element Beneficial only if: