# Lamport Clocks, Vector Clocks

## Lamport Clocks

• In a distributed system, there is no global time and no global state $$\implies$$ the clock of different nodes in a distributed system can have different values.
• Happened-before Relationship:

• Some events in a distributed system happened before other events and others are concurrent
• Happened-before is a partial ordering on events in a distributed system:

Given events $$E1, E2, E3$$ and $$E1$$ happens before $$E2$$ and $$E1$$ happens before $$E3$$, we have $$E2$$ and $$E3$$ are concurrent and $$E1 < E3$$ and $$E1 < E3$$.

• $$\rightarrow$$ relation satisfies the following conditions:

1) If $$a$$ and $$b$$ are events in the same process, and $$a$$ comes before $$b$$, then $$a \rightarrow b$$

2) If $$a$$ is the sending of a message by one process and $$b$$ is the receipt of the same message by another process, then $$a \rightarrow b$$

3) If $$a \rightarrow b$$ and $$b \rightarrow c$$, then $$a \rightarrow c$$

• Two distinct events $$a$$ and $$b$$ are said to be concurrent if $$a \not\rightarrow b$$ and $$b \not\rightarrow a$$

• Logical Clocks:

• Assigns a monotonically increasing number $$C(x)$$ for each event $$x$$ in a process
• If event $$x$$ happens before event $$y$$, $$C(x) < C(y)$$ (Note, $$C(x) < C(y) \not\implies x < y$$)
• If $$x$$ and $$y$$ are in the same process, and $$x < y$$, then $$C(x) < C(y)$$
• If $$x$$ is sending of message, and $$y$$ receipt of the message, then $$x < y$$ and $$C(x) < C(y)$$
• Implementing Logical Clocks:

• Within a process $$X$$, increment $$C(x)$$ every time an event happens
• When process $$X$$ receives a message with timestamp $$T$$, $$C(x) = \max(T, C(x)) + 1$$
• How do we break the tie of the concurrent events and achive total ordering of the events in the sytem:

• If $$x$$ and $$y$$ in same process, and $$x < y$$, $$C(x) < C(y)$$
• If $$x$$ and $$y$$ are concurrent ($$x = y$$), then $$P(x) < P(y) \implies C(x) < C(y)$$ ($$P(\cdot)$$ means process ID)

## Vector Clocks

• Limitation of Lamport Clocks:

• If $$C(x) < C(y)$$, we cannot tell whether $$x < y$$
• We can only say if $$x < y$$, then $$C(x) < C(y)$$
• Goal: to enable each process to have an approximation of global time at all processes (Every message propagates info about state of whole system)

• Each process has a vector of clocks:

• Clock $$C_i$$ is time for process $$i$$ as seen by the owner of the vector
• $$C_i$$ in two different vectors may not be the same
• Implementing Vector Clocks:

• Each process $$P_i$$ updates its component $$C_i$$ in its vector clock (This update happens for each internal event (e.g. on receiving a message))
• Each message has a vector clock time stamp
• On getting the message, for each field $$x$$ in the vector: $$C[x] = \max(C[x], message\_time\_stamp[x])$$
• Comparing Vector Timestamps:

• Timestamp $$X \le Y$$ if all components of $$X \le$$ corresponding components in $$Y$$
• Timestamp $$X < Y$$ if at least one component is strictly lesser, with all others being equal
• Otherwise, $$X$$ and $$Y$$ are concurrent