Event Ordering & Clocks in Distributed Systems - CS533 Concepts

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

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 CS533 - Concepts of Operating Systems

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

4. Space-time Diagram 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<a> : define clock Ci to process Pi for event a • System of clock represented by: C<b> = Cj<b> CS533 - Concepts of Operating Systems

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

7. Clock Condition • Clock Condition (CC): For events a,b: if a  b then C<a>  C<b> • Converse condition will not hold => concurrent events happen at the same time • CC is satisfied by: • C1: if a & b are events by Pi, a comes before b, then Ci<a> Ci<b> • C2: if a sends message m by Pi, b is a receipt of m by Pj, then Ci<a> Cj<b> 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) • A. if a is sending message m by Pi then m contains timestamp Tm = Ci<a> • B. upon receiving m, Pj sets Cj  its present value and  Tm • IR1 and 2 imply that CC is satisfied 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<a>  Cj<b> or • Ci<a> = Cj<b> and Pi < Pj • a  b means Ci<a>  Cj<b> •  extends  CS533 - Concepts of Operating Systems

10. Total Ordering of Events • Algorithm for solving mutex problem: • Process which granted the resource must release before granting resource to another Process • Different requirements for resource must be granted in order they’re made • 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 CS533 - Concepts of Operating Systems

11. Scheduling Issue • Cannot be solved by Central Scheduling Process • Ex: P1 requests P0, P1 sends message P2, P2 requests P0 If P2 is granted first, violate II (granted in the order they make) CS533 - Concepts of Operating Systems

12. Algorithm Rules • Resource Request by Pi • Pi sends message, M: “Tm: Pi request resource” to every Processes • Pi puts message M to its request Queue • When Message Received by Pj • Pj places M on request Queue • Sends acknowledgement message to Pi • Releasing Resource • Pi removes any M from request Queue • Pi sends message, M3: “Tm3: Pi releases resource” to every Processes CS533 - Concepts of Operating Systems

13. Algorithm Rules Cont. • When Pj received Pi release resource • Removes any M: “Tm: Pi requests resource” from request Queue • Pi is granted the resource • M in request Queue ordered before any other requests defined by  • Pi has received M2 from every other process time stamped Tm2 (where Tm2 Tm) 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<a>  C<b> • : events in all systems •  uses physical clocks to eliminate anomalous behavior 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)| <  CS533 - Concepts of Operating Systems

16. Physical Clocks Cont. • a b Cj<a> = t, Cj<b> = 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)  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’ • If Pi sends message M at physical time t, then M contains Tm = Ci(t) • Upon receiving M at time t’ Pj sets Cj(t’) = max ( Cj(t’ – 0), Tm + m ) 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  t0 • PC1 holds •  constant  and  such that every  seconds a message sent over every arch (m ) PC2 is satisfied by:  d (2k  + ) t ≳ t0 + d Assumption:  +  ≪  CS533 - Concepts of Operating Systems