Time

1. Time This powerpoint presentation has been adapted from: www.cse.buffalo.edu/~bina/cse486/.../TimeGlobalStatesApr20.ppt

2. Contents • Introduction • Clocks, events and process states • Synchronizing physical clocks • Logical time & logical clocks

3. Contents • Introduction • Clocks, events and process states • Synchronizing physical clocks • Logical time & logical clocks

4. Time • Introduction • Why time is important in distributed systems? • A quantity that needs to be measured accurately • to know at what time of day a particular event occurred at a particular computer • is important for auditing purposes • to maintain the consistency of distributed data

5. Contents • Introduction • Clocks, events and process states • Synchronizing physical clocks • Logical time & logical clocks

6. Time • Clocks, events and process states • How to timestamp events in terms of their execution? • Consider the following notations • ϸ • A collection of N processes pi, i = 1,2, .. N (p executes on a single processor) • si • The state of pi (each p has a state, the state changed when it is executed) • Actions of pi • Operations that transform pi’s state (p executes with a series of actions. • Send or receive message between pi

7. Time • Clocks, events and process states • e • Event: occurrence of a single action • Relation between the events(i) • The series of events for a single process p • e.g., eie` : e occurs before e` at pi • history(pi ) = hi= <ei0, ei1, ei2, …> • The series of event e in process pi

8. Time • Clocks, events and process states • How to timestamp the events (e)? • Clock in computer: • Each computer has its own physical clock • Is a device that counts oscillations occurring in a crystal at a definite frequency • The OS reads the node’s hardware time: Hi(t) • The counts of oscillation since an original point • Then, scale it and add offset to produce software clock, Ci(t) = Hi(t)+ • To timestamp of an event

9. Time • Clocks, events and process states • Computer clocks tend not to be in a perfect agreement. • Clock drift • Clocks count time at different rates • Clock skew • The instantaneous (direct) difference between the readings of any two clocks • Why? Oscillators are subject to physical variations • Frequency, temperature

10. Time • Clocks, events and process states • How to synchronize computer clocks? • Use external source that provide highly accurate time • Use atomic oscillator • Used by International Atomic Time

11. Time • Clocks, events and process states • What is the international standard for time keeping? • Coordinated Universal Time (UTC) • Based on atomic time • Time is coordinated with astronomical time • UTC signal is broadcasted from land-based radio station to satellites covering many parts of the world

12. Contents • Introduction • Clocks, events and process states • Synchronizing physical clocks • Logical time & logical clocks

13. Time • Synchronizing physical clocks • How to know at what time of the day an event occurs? • Two types of synchronization: • External • Internal • Notations: • Ci: pi’s clock • I : an interval of real time

14. Time • Synchronizing physical clocks • External synchronization • For a synchronization bound D > 0, and for a source S of UTC time, |S(t)-Ci(t)| < D, for i= 1, 2, … N and for all real times t in I • Clocks Ci are accurate to within the bound D • Internal synchronization • For a synchronization bound D > 0, |Ci(t)-Cj(t)| < D for i, j =1,2, … N, and for all real times t in I • Clocks Ciagree within the bound D • Clocks that are internally synchronized are not necessarily externally synchronized • If the system ϸ is externally synchronized with a bound D, then the same system is internally synchronized with a bound of 2D.

15. t t + min t +Ttrans t+max Time • Synchronizing physical clocks • Synchronization in a synchronous system • there will be a minimum time of transmission where no other processes executed at the same time and no other network traffic existed. • Maximum time of transmission in synchronous mode is always set (i.e., time out is applied) • Protocol • Sender: send M(t) • Receiver: set time to t + Ttrans • Bounds are known in synchronous system • min < Ttrans < max (constant) • Optimum transmission time, • Ttrans = (min+max) / 2 • Receiver’s clock = t + (min+max) / 2

16. Time • Synchronizing physical clocks • The common practice in distributed system is asynchronous; • The factors lead to message delay are not bounded (no upper bound max) • The Internet is asynchronous • Ttrans = min + x, where x ≥ 0, the value of x is not known • Methods for synchronizing clock in asynchronous distributed systems: • Cristian’s method • The Berkeley algorithms • The Network Time Protocol

17. m r m t p Time server,S Time • Synchronizing physical clocks • Cristian’s method of synchronizing clocks • Use time server • Protocol • mr– process p requests the time from server • mt – process receives the time (t is inserted in the message) • Tround - process p records the round-trip (send request-get reply) • Estimated time: t + Tround/2

18. t + min t +Tround-min t t +Tround/2 t +Tround Time • Synchronizing physical clocks • Cristian’s method of synchronizing clocks • Accuracy analysis • If the minimum delay of a message transmission is min, then accuracy: (Tround/2 – min)

19. Time and Global State • Synchronizing physical clocks • The Berkeley algorithms • Internal synchronization using a coordinator computer (master). Other computers that their clocks need to be synchronized is known as slaves • The master polls the slaves’ clocks • The master estimates the slaves’ clocks by round-trip time • The master averages the slaves’ clock values • The master sends back to the slaves the amount that the slaves’ clocks should adjust • Slave adjust its clock

20. Time • Synchronizing physical clocks • The Network Time Protocol (NTP) • An architecture for a time service and a protocol to distribute time information over the Internet • Aims: • External synchronization • Enable clients across the Internet to be synchronized accurately to UTC • Reliability • Can survive lengthy losses of connectivity • Redundant server & redundant path between servers • Scalability • Enable clients to resynchronize sufficiently frequently to offset the rates of drift found in most computers • Security • Protect against interference with the time service

21. Time • Synchronizing physical clocks • NTP service is provided by servers located across the Internet • Primary servers are connected directly to a time source, e.g. radio clock receiving UTC • Secondary servers are synchronized to primary servers

22. 1 2 2 3 3 3 Note: Arrows denote synchronization control, numbers denote strata. Time • Synchronizing physical clocks • Network Time Protocol Architecture

23. Source: Wikipedia

24. Time • Synchronizing physical clocks • 3 modes of NTP synchronization: • Multicast mode • Intended for use on a high speed LAN • One or more servers multicast the time to other servers in the LAN • Low accuracy but sufficient • Procedure-call mode • Similar to Christian’s • Higher accuracy than multicast • Symmetric mode • Use by the servers that supply time information in LANs • The highest accuracy

25. Contents • Introduction • Clocks, events and process states • Synchronizing physical clocks • Logical time & logical clocks

26. Time • Logical time and logical clocks • Events in a single process is ordered uniquely by times shown in the local clock • Clock is unable to be synchronized perfectly. Hence physical time is not accurate to determine the occurrence of events

27. Time • Logical time and logical clocks • Happened-before relation • It is also sometimes known as the relation of causal ordering or potential causal ordering.

28. Time • Logical time and logical clocks • Logical clocks- a simple mechanism to capture HB order numerically. Known as Lamport timestamps algorithm (it is a software counter). • LC1 • Li is incremented before each event is issued at process pi : Li :=Li+1 • LC2: (a) When a process pi sends a message m, it adjoin the value t = Li on m (b) On receiving (m,t), a process Pj computes Lj := max(Lj, t) and then applies LC1 before timestamping the event receive(m)

29. Time • Logical time and logical clocks • Totally ordered logical clocks algorithm Assumption Ti: local timestamp of e that is an event occurring at pi Tj: local timestamp of e` that is an event occurring at pj The timestamps of two events eand e` are (Ti, i), (Tj, j) When (Ti, i) < (Tj, j), if and only if Ti< Tj, or Ti = Tjand i < j

30. Time • Logical time and logical clocks • Vector Clocks algorithm • Each process pi keeps a vector clock Vi VC1: Initially, Vi[j]=0, for i, j = 1,2…, N VC2: Just before pi timestamps an event, it sets Vi[i] := Vi[i] +1 VC3: pi includes the value t= Vi in every message it sends VC4: When pi receives a timestamp t in a message, it sets Vi[j] :=max(Vi[j], t[j]), for j=1,2…,N

31. End of the Chapter…