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Distribution Seminar

Distribution Seminar. Chien-Liang Fok liang@cse.wustl.edu. Topic One. Clocks, Order, and Mutual Exclusion in a Distributed System Leslie Lamport, "Time, Clocks, and the Ordering of Events in a Distributed System", Communications of the ACM, 21(7), pp. 558-565, July 1978. Process. Process.

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Distribution Seminar

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  1. Distribution Seminar Chien-Liang Fok liang@cse.wustl.edu

  2. Topic One • Clocks, Order, and Mutual Exclusion in a Distributed System • Leslie Lamport, "Time, Clocks, and the Ordering of Events in a Distributed System", Communications of the ACM, 21(7), pp. 558-565, July 1978. CS 687 SP03 Chien-Liang Fok

  3. Process Process Process Process Process What is a Distributed System? • A collection of processes communicating through message passing. CS 687 SP03 Chien-Liang Fok

  4. E1 E1 E1 E2 E2 E2 E3 E3 E3 … … … En En En Representation of a Process • A process is a sequence of events • It may not be possible to tell which of two events in different processes occurred first. • “Ex occurs before Ey” is only a partial order P1: P2: Pm: CS 687 SP03 Chien-Liang Fok

  5. The ab relation • “ab” denotes “a occurs before b” • We want to develop an algorithm that uses this relation to determine a total ordering of events in our system • Real clocks are not easily synchronized • Must define truth of ab w/o using physical clocks CS 687 SP03 Chien-Liang Fok

  6. … … P0: A … B … Truth of A  B • AB is true when: • A occurs before B in the same process • A and B in different processes; A sends message while B receives it • AC and CB … A … … … P1: … … … B … P2: CS 687 SP03 Chien-Liang Fok

  7. Concurrency • Events a and b are concurrentiff: • This implies that a cannot causally affect b and vice versa • Note that for any event, e, (ee) is true • is an irreflexive partial ordering on the set of all events in the system (AB)  (BA) CS 687 SP03 Chien-Liang Fok

  8. Concurrency (Continued) • Given the space time diagram on right: • P1P2, Q1Q3 • P1Q1, Q3  P3 • (P2Q2)  (Q2P2) • P2 and Q2 are concurrent! P3 Q3 Q2 P2 Q1 P1 Time Process P Process Q Event Sent Message CS 687 SP03 Chien-Liang Fok

  9. Logical Clocks • Assign a number to each event such that if ab then C(a) < C(b)where C(x) denotes the number assigned to event x. • This is known as the clock condition • Note: the converse is not true CS 687 SP03 Chien-Liang Fok

  10. Clock “tick” • Occurs between events on a process • Let a and b be two events such that c(a)=4 and c(b)=7 • Ticks 5, 6, and 7 occur between a and b • A tick lineconnects like-times between two or more processes • Must be between any two events on a process • Every message line must cross a tick line CS 687 SP03 Chien-Liang Fok

  11. P3 P3 Q3 Q3 Q2 P2 P2 Q2 = Q1 Q1 Time P1 Time P1 Process P Process Q Process P Process Q Tick Lines: Visually Rep. Event Sent Message Tick Line CS 687 SP03 Chien-Liang Fok

  12. Clock Implementation • How to implement a clock that satisfies the clock condition?? • Add a register to each process • Increment it after each event • Augment each message with a timestamp Tm • When received message, increase the clock register’s value to be greater than both its current value and Tm CS 687 SP03 Chien-Liang Fok

  13. Obtaining Total Order • Using system of clocks, total ordering of all events in the system is easy • Order events by the time they occur • Break ties by using an arbitrary ordering of processes • Let ab be true if c(a)<c(b) or c(a)=c(b) and a’s process is preferred over b’s • The  relation is NOT unique! CS 687 SP03 Chien-Liang Fok

  14. Process Resource Process Process Using Total Order to Solve theMutual Exclusion Problem • Only one process can be granted the resource at a time • Processes must be granted the resource in the order they requested for it • Every process that is granted the resource will eventually release it CS 687 SP03 Chien-Liang Fok

  15. Mutual Exclusion Algorithm (1/4) • Implement the system of clocks • Each process has a clock register • Augment each process with a request queue rq • Initialize all rq’s to contain message t0:p0 • t0 is smaller than all clock registers • p0 is the process initially granted the resource CS 687 SP03 Chien-Liang Fok

  16. Process Resource Process Process Mutual Exclusion Algorithm (2/4) • pi requests resource by sending tm:pi to every other process and putting tm:pi in rqi • When pj receives tm:pi, add to rqj and send acknowledgement to pi pi Acknowledge Request CS 687 SP03 Chien-Liang Fok

  17. Process Resource Process Process Mutual Exclusion Algorithm (3/4) • pi releases resource by sending a request to everyone and removing tm:pi from rqi • When pj receives the request, it removes tm:pi from rqj pi Request CS 687 SP03 Chien-Liang Fok

  18. Mutual Exclusion Algorithm (4/4) • pi is granted the resource when both: • tm:pi {all other requests in rqi} • pireceived a message from everyone else with time stamp greater than tm • Note: this can be determined locally CS 687 SP03 Chien-Liang Fok

  19. Vulnerabilities • Two vulnerabilities: • If just one process deadlocks, the whole system dies • Anomalous behavior if system model does not match real-life model CS 687 SP03 Chien-Liang Fok

  20. Resource Anomalous Behavior • User b’s message may have a lower time stamp than a Hay!! Request it! User B User A CS 687 SP03 Chien-Liang Fok

  21. Addressing Anomalous Behavior • Introduce strong clock condition, ab • For any two events a and b in the system, if ab then c(a)<c(b) • This is not supported by our clock system! CS 687 SP03 Chien-Liang Fok

  22. Solution to Anomalous Behavior • Use real clocks, let • Ci(t) = reading of clock i at time t •  = maximum clock error rate, # sec off/sec •  = maximum error between clocks, sec •  = maximum message transmission delay • To prevent anomalous behavior, ensure: Ci(t + ) - Cj(t) > 0 • For the above to be true, /(1-)   • See end of paper for derivation/proof. CS 687 SP03 Chien-Liang Fok

  23. Topic 2 • Vector Clocks • Friedemann Mattern, Virtual Time and Global States of Distributed Systems. • Cosnard M. et al. (Eds): Proc. Workshop on Parallel and Distributed Algorithms, North-Holland / Elsevier, pp. 215-226, 1989 • Reprinted in: Z. Yang, T.A. Marsland (Eds.), "Global States and Time in Distributed Systems", IEEE, 1994, pp. 123-133.) CS 687 SP03 Chien-Liang Fok

  24. Motivation • Previously, partially ordered events were mapped into a total order • Two simultaneous events are treated as if one occurred first • Useful information is lost • Linear ordering of events is sometimes not good enough CS 687 SP03 Chien-Liang Fok

  25. The Nature of Time • Time has the following properties • Transitivity • Irreflexivity • Linearity • Eternity • goes on forever • Density • can be divided into infinitesimally small units CS 687 SP03 Chien-Liang Fok

  26. The BIG Question • Can we develop a virtual clock system that preserves more of the system’s timing properties? • Lamport’s algorithm does not preserve causal independence CS 687 SP03 Chien-Liang Fok

  27. Time Vector time • Suppose a deity can observe all clocks and store their values in a vector Process P Process Q Process R 0 0 1 0 1 1 1 1 1 1 2 1 1 2 2 1 3 2 2 3 2 CS 687 SP03 Chien-Liang Fok

  28. Goal • Create algorithm so each process gets an optimal approximation of this vector CS 687 SP03 Chien-Liang Fok

  29. Technique • Replace the register in each process with a vector. • Size of vector = number of processes • Update value in vector of own time like usual • When receive message, update estimated time of other process based on • current time • timestamp vector within message CS 687 SP03 Chien-Liang Fok

  30. Time Using our Technique 1 0 0 2 0 0 Process P 0 1 1 0 2 1 1 3 1 Process Q 0 2 2 0 0 1 Process R 0 0 1 0 1 1 1 1 1 1 2 1 1 2 2 1 3 2 2 3 2 Ideal CS 687 SP03 Chien-Liang Fok

  31. Things to Note • Each process has perfect local information • Given two time vectors u, v • u≤ v iff i : u[ i ] ≤ v[ i ] • u < v iff (u ≤ v)  (u ≠ v) • u || v iff (u < v) (v < u) • u≤ v and u < v are partial orders • u || v is the concurrent relation • It is NOT transitive!! CS 687 SP03 Chien-Liang Fok

  32. Time Cuts • A timing diagrams with consistent cuts can be modified so the cuts are straight lines. Process P Process Q Process R Consistent Cut Inconsistent Cut Event Sent Message Cut Event Cut Line CS 687 SP03 Chien-Liang Fok

  33. Time Time at a Cut • The time vector of a consistent cut is the time of each individual process at the cut Process P Process Q Process R Cut 1 Cut 2 Event Sent Message Cut Event Cut Line CS 687 SP03 Chien-Liang Fok

  34. Key Point • For any set of events: {the lattice of consistent cuts} = {the lattice of possible time vectors} • Thus, two events e and e’ are causally related iff TimeVector(e) < TimeVector(e’) CS 687 SP03 Chien-Liang Fok

  35. Applications • When do we care which event in a set of concurrent events occurred first?? • Distributed debugging • Must consider causal relationship between events in the system • Performance analysis • Vector clocks allows one to calculate potential concurrency CS 687 SP03 Chien-Liang Fok

  36. Topic 3 • Global Snapshot • K. Mani Chandy and Leslie Lamport, "Distributed Snapshots: Determining Global States of Distributed Systems", ACM Transactions on Computer Systems, 3(1), pp. 63-75, February 1985. CS 687 SP03 Chien-Liang Fok

  37. Motivation • Knowing the global state of the system is useful CS 687 SP03 Chien-Liang Fok

  38. Restriction • Cannot pause the system • Cannot prevent system from performing regular processing CS 687 SP03 Chien-Liang Fok

  39. Problem • Given the restrictions, it is impossible to obtain global state • Cannot halt system • System is constantly changing • What can we do? CS 687 SP03 Chien-Liang Fok

  40. Goal • Find a possible global state • Can determine value of stable system properties • deadlock • Termination • By definition if a possible global state satisfies a stable property, the system will forever satisfy this property. CS 687 SP03 Chien-Liang Fok

  41. Process Process Process Process Process The Model Channel • Processes send and receive messages through channels CS 687 SP03 Chien-Liang Fok

  42. Global State • Consists of: • Process states • What’s the state of the process? • Channel states • What messages are being sent through it? CS 687 SP03 Chien-Liang Fok

  43. The Algorithm • Sender process p: • Record state • Send marker on all outgoing channels • Receiver process q: • If q has not recorded state • record state • record channel state as empty • If q has recorded state • record channel state as all messaged received after recording, but before receiving marker CS 687 SP03 Chien-Liang Fok

  44. The Algorithm (2/2) • Assuming strongly connected graph, all process will have recorded • Process state • Channel state for each incoming channel • Consolidate these records to form global snapshot • The paper proves this snapshot is a reachable from one that actually existed. • Enough to prove stable properties of system CS 687 SP03 Chien-Liang Fok

  45. Conclusions • Virtual clocks are necessary since physical clocks are not easily synchronized • Vector clocks improve upon Lamport’s virtual clock since it preserves causal independence • Global snapshots of possible states is useful to determine stable properties of the system CS 687 SP03 Chien-Liang Fok

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