Lecture 14 Synchronization (cont)

1. Lecture 14Synchronization (cont)

2. Logistics • Project • P01 deadline on Wednesday November 3rd. • Non-blocking IO lecture: Nov 4th. • P02 deadline on Wednesday November 15th. • Next quiz • Tuesday 16th.

3. Roadmap • Clocks can not be perfectly synchronized. • What can I do in these conditions? • Figure out how large is the drift • Example: GPS systems • Design the system to take drift into account • Example: server design to provide at-most-once semantics • Do not use physical clocks! • Consider only event order • (1) Logical clocks (Lamport) • But this does not account for causality! • (2) Vector clocks! • Mutual exclusion; leader election

4. Last time: “Happens-before” relation The happened-before relation on the set of events in a distributed system: • if a and b in the same process, and a occurs before b, thena → b • if a is an event of sending a message by a process, and b receiving same message by another process thena → b Two events are concurrent if nothing can be said about the order in which they happened (partial order)

5. Lamport’s logical clocks • Each process Pimaintains a local counter Ciand adjusts this counter according to the following rules: • For any two successive events that take place within process Pi, the counter Ci is incremented by 1. • Each time a message m is sent by process Pi the message receives a timestamp ts(m) = Ci • Whenever a message m is received by a process Pj, Pjadjusts its local counter Cjto max{Cj, ts(m)}; then executes step 1 before passing m to the application.

6. Updating Lamport’s logical timestamps Physical Time 1 2 p 1 8 0 7 1 8 3 p 2 0 2 2 3 6 p 3 4 0 10 9 3 5 4 7 p 4 0 5 6 7 Clock Value n timestamp Message

7. Problem with Lamport logical clocks Notation: timestamp(a) is the Lamport logical clock associated with event a By definition if a  b=> timestamp(a) < timestamp(b) (if a happens before b, then Lamport_timestamp(a) < Lamport_timestamp(b)) Q: is the converse true? That is: if timestamp(a) < timestamp(b) => a  b (If Lamport_timestamp(a) < Lamport_timestamp(b), it does NOT imply that a happens before b

8. Example logically concurrent events Physical Time 1 2 p 1 8 0 7 1 8 3 p 2 0 2 2 3 6 p 3 4 0 10 9 3 5 4 7 p 4 0 5 6 7 Clock Value n timestamp Message Note: Lamport Timestamps: 3 < 7, but event with timestamp 3 is concurrent to event with timestamp 7, i.e., events are not in ‘happen-before’ relation.

9. Causality • Timestamps don’t capture causality • Example: news postings have multiple independent threads of messages • To model causality – use Lamport’s vector timestamps • Intuition: each item in vector logical clock for one causality thread.

10. Vector Timestamps

11. Vector clocks • Each process Pihas an array VCi[1..n] of clocks (all initialized at 0) • VCi[j] denotes the number of events that process Piknows have taken place at process Pj. • Piincrements VCi[i]: when an event occurs or when sending • Vector value is the timestamp of the event • When sending • Messages sent by VCiinclude a vector timestamp vt(m). • Result: upon arrival, recipient knows Pi’s timestamp. • When Pjreceives a message sent by Piwith vector timestamp ts(m): • for k ≠ j: updates each VCj[k] to max{VCj[k], ts(m)[k]} • for k = j: VCj[k] = VCj[k] + 1 Note: vector timestamps require a static notion of system membership Question: What does VCi[j] = k mean in terms of messages sent and received?

12. Example: Vector Logical Time 1,0,0,0 2,0,0,0 4,0,2,2 3,0,2,2 (1,0,0,0) (4,0,2,2) 1,2,0,0 1,1,0,0 (2,0,0,0) (1,2,0,0) (2,0,2,2) 2,0,2,0 4,2,5,3 4,2,4,2 2,0,1,0 2,2,3,0 (2,0,2,0) (2,0,2,3) 2,0,2,2 2,0,2,3 2,0,2,1 Physical Time p 1 0,0,0,0 p 2 0,0,0,0 p 3 0,0,0,0 p 4 0,0,0,0 Vector logical clock n,m,p,q (vector timestamp) Message

13. Comparing vector timestamps VT1 = VT2, (identical) iff VT1[i] = VT2[i], for all i = 1, … , n VT1 ≤ VT2, iff VT1[i] ≤ VT2[i], for all i = 1, … , n VT1 < VT2, (happens before relationship) iff VT1 ≤ VT2 and  j (1 ≤ j ≤ n) such that VT1[j] < VT2 [j] VT1 is concurrent with VT2 iff (not VT1 ≤ VT2 AND not VT2 ≤ VT1)

14. Quiz like problem Show: a  b if and only if vectorTS(a) < vectorTS(b)

15. Message delivery for group communication • ASSUMPTIONS • messages are multicast to named process groups • reliable and fifo channels (from a given source to a given destination) • processes don’t crash (failure and restart not considered) • processes behave as specified e.g., send the same values to all processes (i.e., we are not considering Byzantine behaviour) application process may specify delivery order to message service e.g. total order,FIFO order, causal order (last time total order) Messaging middleware may reorder delivery to application by buffering messages assume FIFO from each source (done at lower levels) OS comms. interface

16. [Last time] Totally Ordered Multicast • Process Pisends timestamped message msgito all others. The message itself is put in a local queue queuei. • Any incoming message at Pkis queued in queuek, according to its timestamp, and acknowledged to every other process. • Pkpasses a message msgito its application if: • msgiis at the head of queuek • for each process Px, there is a message msgxin queuekwith a larger timestamp. Note: We are assuming that communication is reliable and FIFO ordered. Guarantee: all multicasted messages in the same order at all destination. • Nothing is guaranteed about the actual order!

17. FIFO multicast • Fifoor sender orderedmulticast: Messages are delivered in the order they were sent (by any single sender) a e P1 P2 P3 P4

18. FIFO multicast • Fifoor sender orderedmulticast: Messages are delivered in the order they were sent (by any single sender) a e P1 P2 P3 P4 b c d delivery of c to P1 is delayed until after b is delivered

19. Implementing FIFO multicast • Basic reliable multicast algorithm has this property • Without failures all we need is to run it on FIFO channels (like TCP) • [Later: dealing with node failures]

20. Causal multicast • Causalor happens-beforeordering • If send(a)  send(b) then deliver(a) occurs before deliver(b) at common destinations a P1 P2 P3 P4 b

21. Ordering properties: Causal • Causalor happens-beforeordering • If send(a)  send(b) then deliver(a) occurs before deliver(b) at common destinations a P1 P2 P3 P4 b c delivery of c to P1 is delayed until after b is delivered

22. Ordering properties: Causal • Causalor happens-beforeordering • If send(a)  send(b) then deliver(a) occurs before deliver(b) at common destinations a e P1 P2 P3 P4 b c d e is sent (causally) after b and c e is sent concurrently with d

23. Ordering properties: Causal • Causalor happens-beforeordering • If send(a)  send(b) then deliver(a) occurs before deliver(b) at common destinations a e P1 P2 P3 P4 b c d delivery of c to P1 is delayed until after b is delivered delivery of e to P3 is delayed until after b&c are delivered delivery of e and d to P2 and P3 in any relative order (concurrent)

24. Causally ordered multicast VC0=(2,2,0) VC1=(1,2,0) VC1=(1,1,0) VC2=(1,2,2) VC2=(1,0,1)

25. Implementing causal order • Start with a FIFO multicast • We can strengthen this into a causal multicast by adding vector time • No additional messages needed! • Advantage: FIFO and causal multicast are asynchronous: • Sender doesn’t get blocked and can deliver a copy to itself without “stopping” to learn a safe delivery order

26. So far … • Physical clocks • Two applications • Provide at-most-once semantics • Global Positioning Systems • ‘Logical clocks’ • Where only ordering of events matters • Other coordination primitives • Mutual exclusion • Leader election

27. Mutual exclusion algorithms Problem: A number of processes in a distributed system want exclusive access to some resource. Basic solutions: • Via a centralized server. • Completely decentralized • Completely distributed, with no roles imposed. • Completely distributed along a (logical) ring. Additional objective: Fairness

28. Mutual Exclusion: A Centralized Algorithm • Process 1 asks the coordinator for permission to enter a critical region. Permission is granted • Process 2 then asks permission to enter the same critical region. The coordinator does not reply. • When process 1 exits the critical region, it tells the coordinator, when then replies to 2

29. Decentralized Mutual Exclusion Principle: Assume the resource is replicated n times, with each replica having its own coordinator • Access requires a majority vote from m > n/2 coordinators. • A coordinator always responds immediately to a request. Assumption: When a coordinator crashes, it will recover quickly, but will have forgotten about permissions it had granted. Correctness: probabilistic! Issue: How robust is this system?

30. Decentralized Mutual Exclusion (cont) Principle: Assume every resource is replicated n times, with each replica having its own coordinator • Access requires a majority vote from m > n/2 coordinators. • A coordinator always responds immediately to a request. Issue: How robust is this system? • p the probability that a coordinator resets (crashes and recovers) in an interval Δt • p = Δt /T, where T is the an average peer lifetime Quiz—like question: what’s the probability to violate mutual exclusion?

31. Decentralized Mutual Exclusion (cont) Principle: Assume every resource is replicated n times, with each replica having its own coordinator • Access requires a majority vote from m > n/2 coordinators. • A coordinator always responds immediately to a request. Issue: How robust is this system? • p the probability that a coordinator resets (crashes and recovers) in an interval Δt • p = Δt /T, where T is the an average peer lifetime • The probability that k out m coordinators reset during Δt P[k]=C(k,m)pk(1-p)m-k: • Violation when at least 2m-n coordinators reset

33. Mutual Exclusion: A Distributed Algorithm (Ricart & Agrawala) Idea: Similar to Lamport ordered group communication except that acknowledgments aren’t sent. Instead, replies (i.e. grants) are sent only when: • The receiving process has no interest in the shared resource; or • The receiving process is waiting for the resource, but has lower priority (known through comparison of timestamps). • In all other cases, reply is deferred • (results in some more local administration)

34. Mutual Exclusion: A Distributed Algorithm (II) • Two processes (0 and 2) want to enter the same critical region at the same moment. • Process 0 has the lowest timestamp, so it wins. • When process 0 is done, it sends an OK also, so 2 can now enter the critical region. Question: Is a fully distributed solution, i.e. one without a coordinator, always more robust than any centralized coordinated solution?

35. Mutual Exclusion: A Token Ring Algorithm Principle:Organize processes in a logical ring, and let a token be passed between them. The one that holds the token is allowed to enter the critical region (if it wants to)

36. Logistics • Project • P01 deadline tomorrow. • Project/Non-blocking IO lecture: Thursday • P02 deadline on Wednesday November 15th. • Next quiz • Tuesday 16th.

37. So far … • Physical clocks • Two applications • Provide at-most-once semantics • Global Positioning Systems • ‘Logical clocks’ • Where only ordering of events matters • Lamport clocks • Vector clocks • Other coordination primitives • Mutual exclusion • Leader election: How do I choose a coordinator?

38. [Last time] Mutual exclusion algorithms Problem: A number of processes in a distributed system want exclusive access to some resource. Basic solutions: • Via a centralized server. • Completely decentralized (voting based) • Completely distributed, with no roles imposed. • Completely distributed along a (logical) ring. Additional objectives: Fairness; no starvation

39. Mutual Exclusion: Algorithm Comparison

40. Mutual Exclusion: Algorithm Comparison

41. Mutual Exclusion: Algorithm Comparison

42. So far … • Physical clocks • Two applications • Provide at-most-once semantics • Global Positioning Systems • ‘Logical clocks’ • Where only ordering of events matters • Other coordination primitives • Mutual exclusion • Leader election: How do I choose a coordinator?

43. Leader election algorithms Context: An algorithm requires that some process acts as a coordinator. Question: how to select this special process dynamically. Note: In many systems the coordinator is chosen by hand (e.g. file servers). This leads to centralized solutions single point of failure.

44. Leader election algorithms Context:Each process has an associated priority (weight). The process with the highest priority needs to be elected as the coordinator. Issue: How do we find the ‘heaviest’ process? Two important assumptions: • Processes are uniquely identifiable • All processes know the identity of all participating processes Traditional algorithm examples • The bully algorithm • Ring based algorithm

45. Election by Bullying • Any process can just start an election by sending an election message to all other (heavier) processes • If a process Pheavy receives an election message from a lighter process Plight, it sends a take-over message to Plight. Plight is out of the race. • If a process doesn’t get a take-over message back, it wins, and sends a victory message to all other processes.

46. The Bully Algorithm • Process 4 detects 7 has failed and holds an election • Process 5 and 6 respond, telling 4 to stop • Now 5 and 6 each hold an election (also send message to 7 as they have not detected 7 failure)

47. The Bully Algorithm (2) • Process 6 tells 5 to stop • Process 6 wins and announces itself everyone

48. Election in a Ring Principle: Organize processes into a (logical) ring. Process with the highest priority should be elected as coordinator. • Any process can start an election by sending an election message to its successor. If a successor is down, the message is passed on to the next successor. • If a message is passed on, the sender adds itself to the list. • The initiator sends a coordinator message around the ring containing a list of all living processes. The one with the highest priority is elected as coordinator.

49. The Ring Algorithm • Question: What happens if two processes initiate an election at the same time? Does it matter? • Question: What happens if a process crashes during the election?

50. Summary so far … A distributed system is: • a collection of independent computers that appears to its users as a single coherent system Components need to: • Communicate • Point to point: sockets, RPC/RMI • Point to multipoint: multicast, epidemic • Cooperate • Naming to enable some resource sharing • Naming systems for flat (unstructured) namespaces: consistent hashing, DHTs • Naming systems for structured namespaces: EECE456 for DNS • Synchronization: physical clocks, logical clocks, mutual exclusion, leader election