1. Models and Clocks

2. Characteristics of a Distributed System Absence of a shared clock Absence of shared memory Absence of failure detection

3. Model of a Distributed System Asynchronous Message Passing

4. A Simple Distributed Program Each process is defined as a set of states

5. Model of a Distributed Computation Interleaving model A global sequence of events eg. P1 sends “what is my checking balance” to P2 P1 sends “what is my savings balance to P2” P2 receives “what is my checking balance” from P1 P1 sets total to 0 P2 receives “what is my savings balance” from P1 P2 sends “checking balance = 40” to P1 P1 receives “checking balance = 40” from P2...

6. Model of a Distributed Computation Happened before model Happened before relation If e occurred before f in the same process, then e --> f If e is the send event of a message and f is the receive event of the same message, then e --> f If there exists an event g such that e --> g and g --> f, then e --> f

7. A run in the happened-before model

8. Logical Clocks A logical clock C is a map from the set of events E to N (the set of natural numbers) with the following constraint:

9. Lamport's logical clock algorithm public class LamportClock { int c; public LamportClock() { c = 1; } public int getValue() { return c; } public void tick() { // on internal actions c = c + 1; } public void sendAction() { // include c in message c = c + 1; } public void receiveAction(int src, int sentValue) { c = Util.max(c, sentValue) + 1; }

10. Vector Clocks Map from the set of states to vectors of natural numbers with the constraint: For all s, t: s--> t iff s.v < t.v...... where s.v is the vector assigned to the state s. Given vectors x,y : x < y All elements of x are less than or equal to the corresponding elements of y At least one element of x is strictly less than the corresponding element of y

11. A Vector clock algorithm public class VectorClock { public int[] v; int myId; int N; public VectorClock(int numProc, int id) { myId = id; N = numProc; v = new int[numProc]; for (int i = 0; i < N; i++) v[i] = 0; v[myId] = 1; } public void tick() { v[myId]++; } public void sendAction() { //include the vector in the message v[myId]++; } public void receiveAction(int[] sentValue) { for (int i = 0; i < N; i++) v[i] = Util.max(v[i], sentValue[i]); v[myId]++; }

12. An execution of the vector clock algorithm

13. Direct-Dependency Clocks Weaker version of the vector clock Maintain a vector clock locally Process sends only its local component of the clock Directly precedes relation: only one message in the happened-before diagram of the computation Direct-dependency clocks satisfy

14. A Direct-dependency clock algorithm public class DirectClock { public int[] clock; int myId; public DirectClock(int numProc, int id) { myId = id; clock = new int[numProc]; for (int i = 0; i < numProc; i++) clock[i] = 0; clock[myId] = 1; } public int getValue(int i) { return clock[i]; } public void tick() { clock[myId]++; } public void sendAction() { // sentValue = clock[myId]; tick(); } public void receiveAction(int sender, int sentValue) { clock[sender] = Util.max(clock[sender], sentValue); clock[myId] = Util.max(clock[myId], sentValue) + 1; }

15. Matrix Clocks N x N matrix Gives processes additional knowledge

16. The matrix clock algorithm public class MatrixClock { int[][] M; int myId; int N; public MatrixClock(int numProc, int id) { myId = id; N = numProc; M = new int[N][N]; for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) M[i][j] = 0; M[myId][myId] = 1; } public void tick() { M[myId][myId]++; } public void sendAction() { //include the matrix in the message M[myId][myId]++; } public void receiveAction(int[][] W, int srcId) { // component-wise maximum of matrices for (int i = 0; i < N; i++) if (i != myId) { for (int j = 0; j < N; j++) M[i][j] = Util.max(M[i][j], W[i][j]); }