1. CS533 Concepts of Operating Systems Class 8 Time, Clocks, and the Ordering of Events in a Distributed System By Constantia Tryman

2. CS533 - Concepts of Operating Systems 2 What will be covered  Concept of events ordering in distributed system  Synchronization of logical clocks to order events totally  Specialized synchronization using physical clocks  Bound on how far synchrony clocks can drift apart

3. CS533 - Concepts of Operating Systems 3 Partial Ordering   : “happened before”  Definition: o If a and b are events from Pi, a comes before b then a  b (same process) o If a is sending message m by Pi and b is receiving m by Pj then a  b (b/t 2 processes) o If a  b and b  c, then a  c (1 or more processes)  “space-time” diagram o Horizontal: space o Vertical: time o Wavy lines: message

4. CS533 - Concepts of Operating Systems 4 Space-time Diagram

5. CS533 - Concepts of Operating Systems 5 Logical Clocks  Clock: a way of assigning number to an event  Logical Clock: order in which events occur  Ci : define clock Ci to process Pi for event a  System of clock represented by: C = Cj

6. CS533 - Concepts of Operating Systems 6 Space-Time diagram

7. CS533 - Concepts of Operating Systems 7 Clock Condition  Clock Condition (CC): For events a,b: if a  b then C  C  Converse condition will not hold => concurrent events happen at the same time  CC is satisfied by: o C1: if a & b are events by Pi, a comes before b, then Ci  Ci o C2: if a sends message m by Pi, b is a receipt of m by Pj, then Ci  Cj

8. CS533 - Concepts of Operating Systems 8 Implementation Rule  To guarantee that system of clocks satisfies CC  IR1: Each process Pi increments Ci between any two successive events (tick is occurring between P’s events)  IR2: (each message contains Tm = time msg sent) o A. if a is sending message m by Pi then m contains timestamp Tm = Ci o B. upon receiving m, Pj sets Cj  its present value and  Tm  IR1 and 2 imply that CC is satisfied

9. CS533 - Concepts of Operating Systems 9 Ordering Events Totally  Define  :  If event a in Pi and b in Pj then a  b if either Ci  Cj or Ci = Cj and Pi < Pj  a  b means Ci  Cj   extends 

10. CS533 - Concepts of Operating Systems 10 Total Ordering of Events  Algorithm for solving mutex problem: I. Process which granted the resource must release before granting resource to another Process II. Different requirements for resource must be granted in order they’re made III. Every Process granted with resource will eventually release it so every request is eventually granted  Issue: doesn’t tell which Process granted if request resource concurrently with another Process

11. CS533 - Concepts of Operating Systems 11 Scheduling Issue  Cannot be solved by Central Scheduling Process  Ex: P 1 requests P 0, P 1 sends message P 2, P 2 requests P 0 If P 2 is granted first, violate II (granted in the order they make)

12. CS533 - Concepts of Operating Systems 12 Algorithm Rules 1) Resource Request by Pi o Pi sends message, M: “Tm: Pi request resource” to every Processes o Pi puts message M to its request Queue 2) When Message Received by Pj o Pj places M on request Queue o Sends acknowledgement message to Pi 3) Releasing Resource o Pi removes any M from request Queue o Pi sends message, M 3 : “Tm 3 : Pi releases resource” to every Processes

13. CS533 - Concepts of Operating Systems 13 Algorithm Rules Cont. 4) When Pj received Pi release resource o Removes any M: “Tm: Pi requests resource” from request Queue 5) Pi is granted the resource i.  M in request Queue ordered before any other requests defined by  ii. Pi has received M 2 from every other process time stamped Tm 2 (where Tm 2  Tm)

14. CS533 - Concepts of Operating Systems 14 Anomalous Behavior  Resource scheduling algorithm ordered request by  total ordering will result in Anomalous Behavior  Strong Clock Condition:  event a,b in  : if a  b then C  C   : events in all systems   uses physical clocks to eliminate anomalous behavior

15. CS533 - Concepts of Operating Systems 15 Physical Clocks  Ci(t): reading of clock Ci at physical time t  dCi(t)/dt = rate of clock is running  1  PC1:  a constant K << 1 such that  i: | dCi(t)/dt - 1 | < k, where k  10 -6  PC2:  i,j: |Ci(t) – Cj(t)| < 

16. CS533 - Concepts of Operating Systems 16 Physical Clocks Cont.  a  b Cj = t, Cj = t +     shortest transmission time for interprocess messages   i,j,t Cj (t+  ) – Ci (t) > 0  By PC1 Ci (t+  ) – Ci (t) > (1 - k)   By PC2 Ci (t+  ) – Cj (t) > 0 if  / (1-k)  

17. CS533 - Concepts of Operating Systems 17 Implementation Rules  IR1’:  i if Pi doesn’t receive a message at physical time t then Ci is differentiable at t and dCi(t)/dt  0  IR2’ a. If Pi sends message M at physical time t, then M contains Tm = Ci(t) b. Upon receiving M at time t’ Pj sets Cj(t’) = max ( Cj(t’ – 0), Tm +  m )

18. CS533 - Concepts of Operating Systems 18 Theorem Theorem: Assume strongly connected graph of Processes with diameter d obeying IR1’ and IR2’ Assume  m,  m   for constant  and  t  t 0 a) PC1 holds b)  constant  and  such that every  seconds a message sent over every arch (  m   ) PC2 is satisfied by:   d (2k  +  )  t ≳ t 0 +  d Assumption:  +  ≪ 