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Chapter 5 Synchronization

- Clocks and Synchronization Algorithms
- Lamport Timestamps and Vector Clocks
- Distributed Snapshots
- Termination Detection
- Election Algorithms
- Distributed Mutual Exclusion
- Transactions concurrency control

What Do We Mean By Time?

- Monotonic increasing
- Useful when everyone agrees on it
- UTC is Universal Coordinated Time.
- NIST operates on a short wave radio frequency WWV

and transmits UTC from Colorado.

Clock Synchronization

- When each machine has its own clock, an event

that occurred after another event may

nevertheless be assigned an earlier time.

Time

- Time is complicated in a distributed system.
- Physical clocks run at slightly different rates

so they can drift apart. - Clock makers specify a maximum drift rate ?

(rho). - By definition
- 1-? lt dC/dt lt 1? where C(t) is the

clocks time as a function of the real time.

Clock Synchronization

- The relation between clock time and UTC when

clocks tick at different rates.

Clock Synchronization

- 1-? lt dC/dt lt 1?
- A perfect clock has dC/dt 1
- Assuming 2 clocks have the same max drift rate ?.

To keep them synchronized to within a time

interval delta, ?, they must re-sync every ?/2?

seconds.

Cristians Algorithm

- One of the nodes (or processors) in the

distributed system is a time server TS

(presumably with access to UTC). How can the

other nodes be synced? - Periodically, at least every ?/2? seconds, each

machine sends a message to the TS asking for the

current time and the TS responds.

Cristian's Algorithm

- Getting the current time from a time server.

Cristians Algorithm

- Should the client node simply force his clock to

the value in the message?? - Potential problem if clients clock was fast,

new time may be less than his current time, and

just setting the clock to the new time might make

time appear to run backwards on that node. - TIME MUST NEVER RUN BACKWARDS. There are many

applications that depend on the fact that time is

always increasing. So new time must be worked in

gradually.

Cristians Algorithm

- Can we compensate for the delay from when TS

sends the response to T1 (when it is received)? - Add (T1 T0)/2. If no outside info is

available. - Estimate or ask server how long it takes to

process time request, say R. Then add (T1 T0

R)/2. - Take several measurements and taking the smallest

or an average after throwing out the large values.

The Berkeley Algorithm

- The server actively tries to sync the clocks of a

DS. This algorithm is appropriate if no one has

UTC and all must agree on the time. - Server polls each machine by sending his

current time and asking for the difference

between his and theirs. Each site responds with

the difference. - Server computes average with some compensation

for transmission time. - Server computes how each machine would need to

adjust his clock and sends each machine

instructions.

The Berkeley Algorithm

- The time daemon asks all the other machines for

their clock values - The machines answer
- The time daemon tells everyone how to adjust

their clock

Analysis of Sync Algorithms

- Cristians algorithm N clients send and receive

a message every ?/2? seconds. - Berkeley algorithm 3N messages every ?/2?

seconds. - Both assume a central time server or coordinator.

More distributed algorithms exist in which each

processor broadcasts its time at an agreed upon

time interval and processors go through an

agreement protocol to average the value and agree

on it.

Analysis of Sync Algorithms

- In general, algorithms with no coordinator have

greater message complexity (more messages for the

same number of nodes). Thats the price you pay

for equality and no-single-point-of-failure. - With modern hardware, we can achieve loosely

synchronized clocks. This forms the basis for

many distributed algorithms in which logical

clocks are used with physical clock timestamps to

disambiguate when logical clocks roll over or

servers crash and sequence numbers start over

(which is inevitable in real implementations).

Logical Clocks

- What do we really need in a clock? For many

applications, it is not necessary for nodes of a

DS to agree on the real time, only that they

agree on some value that has the attributes of

time. - Attributes of time X(t) has the sense or

attributes of time if it is strictly increasing. - A real or integer counter can be used. A real

number would be closer to reality, however, an

integer counter is easier for algorithms and

programmers. Thus, for convenience, we use an

integer which is incremented anytime an event of

possible interest occurs.

Logical Clocks in a DS

- What is important is usually not when things

happened but in what order they happened so the

integer counter works well in a centralized

system. - However, in a DS, each system has its own logical

clock, and you can run into problems if one

clock gets ahead of others. (like with

physical clocks) - We need a rule to synchronize the logical clocks.

Lamport Clocks

- Lamport defined the happens-before relation for

DS. - A ? B means A happens before B.
- If A and B are events in the same process and A

occurs before B then A ? B is true. - If A is the event of a message being sent by one

process-node and B is the event of that message

being received by another process, then then A ?

B is true. (A message must be sent before it is

received). - Happens-before is the transitive closure of 1 and

2. That is, if A?B and B?C, then A?C. - Any other events are said to be concurrent.

Lamport Clocks

P

Q

R

q1

p1

q2

p2

r1

q3

r2

p3

- p1?q2 and q1?p2 and q1?q2 but p1 and q1 are

incomparable. p1?q3 and p1?r2 Does p1 ? r1?

Lamport Clocks

- Desired properties
- (1) anytime A? B , C(A) lt C(B), that is the

logical clock value of the earlier event is less - (2) the clock value C is increasing (never runs

backwards)

Lamport Clocks Rules

- An event is an internal event or a message send

or receive. - The local clock is increased by one for each

message sent and the message carries that

timestamp with it. - The local clock is increased for an internal

event. - When a message is received, the current local

clock value, C, is compared to the message

timestamp, T. If the message timestamp, T C,

then set the local clock value to C1. If T gt C,

set the clock to T1. If TltC, set the clock to

C1.

Lamport Clocks

P

Q

R

2

5

3

6

4

6

7

8

7

- Anytime A? B , C(A) lt C(B)
- However, C(E) lt C(F) doesnt mean E? F
- (ex event 6 on P may not proceed event 7 on Q)

Lamport Timestamps

- If you need a total ordering, (distinguish

between event 6 on P and event 6 on Q) use

Lamport timestamps. - Lamport timestamp of event A at node i is (C(A),

i) - For any 2 timestamps T1(C(A),I) and T2(C(B),J)
- If C(A) gt C(B) then T1 gt T2.
- If C(A) lt C(B) then T1 lt T2.
- If C(A) C(B) then consider node numbers. If

IgtJ then T1 gt T2. If IltJ then T1 lt T2. If IJ

then the two events occurred at the same node, so

since their clock C is the same, they must be the

same event.

Lamport Timestamps

P1

P2

P3

(2,2)

(5,1)

(3,3)

(6,2)

(4,3)

(6,1)

(7,2)

(8,3)

(7,1)

- (6,1) ? (6,2) and (4,3) ? (6,2)

Lamport Timestamps

- Three processes, each with its own clock. The

clocks run at different rates. - Lamport's algorithm corrects the clocks.

Exercise Lamport Clocks and Timestamps

1 2 3 4

5 6

7

A B C

- Assuming the only events are message send and

receive, what are the clocks at 1-7

Why Vector Timestamps

- Lamport timestamps gives us the property if A ? B

then C(A) lt C(B). But it doesnt give us the

property if C(A) lt C(B) then A?B. (if C(A) lt

C(B), A and B may be concurrent or incomparable,

but never B?A).

1,1 2,1

1,2

2,2

A1 B2 C3

Lamport timestamp of 1,1 lt 2,2 but the events are

unrelated

1,3 2,3

Why Vector Timestamps

- Also, Lamport timestamps do not detect causality

violations. Causality violations are caused by

long communications delays in one channel that

are not present in other channels or a non-FIFO

channel.

A B C

Causality Violation

- Causality violation example A gets a message

from B that was broadcast to all nodes. A

responds by broadcasting an answer to all nodes.

C gets As answer to B before it receives Bs

original message. - How can B tell that this message is out of order?

A B C

Causality Solution

- The solution is vector timestamps Each node

maintains an array of counters. - If there are N nodes, the array has N integers

V(N). V(I) C, the local clock, if I is the

designation of the local node. - In general, V(X) is the latest info the node has

on what Xs local clock is. - Gives us the property e ? f iff ts(e) lt ts(f)

Vector Timestamps

- Each site has a local clock incremented at

each event (not according to Lamport clocks) The

vector clock timestamp is piggybacked on each

message sent. RULES - Local clock is incremented for a local event and

for a send event. The message carries the vector

time stamp. - When a message is received, the local clock is

incremented by one. Each other component of the

vector is increased to the received vector

timestamp component if the current value is less.

That is, the maximum of the two vector components

is the new value.

Vector Timestamps and Causal Violations

- C receives message (2,1,0) then (0,1,0)
- The later message causally precedes the first

message if we define how to compare timestamps

right

A B C

Vector Clock Comparison

- VC1 gt VC2 if for each component j, VC1j gt

VC2j, and for some component k, VC1k gt VC2k - VC1 VC2 if for each j, VC1j VC2j
- Otherwise, VC1 and VC2 are incomparable and the

events they represent are concurrent

1 2 3 4

Clock at point 1 (2,1,0) 2 (2,2,0) 3

(2,1,1) 4 (2,1,2)

A B C

Vector Clock Exercise

- Assuming the only events are send and receive
- What is the vector clock at events 1-6?
- Which events are concurrent?

6

1 2 5 3 4

A B C

Matrix Timestamps

- Matrix timestamps can be used to give each node

more information about the state of the other

nodes. - Each site keeps a 2 dimensional time table
- If Tij,k v then site i knows that site j

is aware of all events at site k up to v - Row x is the view of the vector clock at site x

As TT A B C A 3 2

3 B 1 2 0 C 2 2 3

A B C

Global State

- Matrix timestamps is one way of getting

information about the distributed system.

Another way is to sample the global state. - The Global state is the combination of the states

of all the processors and channels at some time

which could have occurred. - Because there is no way of recording states at

the exact same time at every node, we will have

to be careful how we define this.

Global State

- There are many reasons for wanting to sample the

global state take a snapshot. - deadlock detection
- finding lost token
- termination of a distributed computation
- garbage collection
- We must define what is meant by the state of a

node or a channel.

Defining Global State

- There are N processes P1Pn. The state of the

process Pi is defined by the system and

application being used. - Between each pair of processors, Pi and Pj, there

is a one-way communications channel Ci,j.

Channels are reliable and FIFO, ie, the messages

arrive in the order sent. The contents of Ci,j

is an ordered list of messages Li,j (m1, m2,

m3). The state of the channel is the messages in

the channel and their order. - Li,j (m1, m2, ) is the channel from Pi to Pj

and m1 (head or front) is the next message to be

delivered.

Defining Global State

- It is not necessary for all processors to be

interconnected, but each processor must have at

least one incoming channel and one outgoing

channel and it must be possible to reach each

processor from any other processor (graph is

strongly connected).

2

1

4

3

Defining Global State

- The Global state is the combination of the states

of all the processors and channels. - The state of all the channels, L, is the set of

messages sent but not yet received. - Defining the state was easy, getting the state is

more difficult. - Intuitively, we say that a consistent global

state is a snapshot of the DS that looks to the

processes as if it were taken at the same instant

everywhere.

Defining Global State

- For a global state to be meaningful, it must be

one that could have occurred. - Suppose we observe processor Pi (getting state

Si) and it has just received a message m from

processor Pk. When we observe processor Pk to

get Sk, it should have sent m to Pi in order for

us to have a consistent global state. In other

words, if we get Pks state before it sent

message m and then get Pis state after it

received m, we have an inconsistent global state.

Pi Pk

Pi Pk

Consistent Cut

- So we say that the global state must represent a

consistent cut. - One way of defining a consistent cut is that the

observations resulting in the states Si should

all occur concurrently (as defined using vector

clocks). - Also, a consistent cut is one where all the

events before the cut happen-before the ones

after the cut or are unrelated (uses

happens-before relation).

Global State (1)

- A consistent cut
- An inconsistent cut

Algorithm for Distributed Snapshot

- Well known algorithm by Chandy and Lamport
- When instructed, each processor will stop other

processing and record its state Pi, send out

marker messages and record the sequence of

messages arriving on each incoming channel until

a marker comes in (this will enable us to get the

channel state Ci,j). - At end of algorithm, initiator or other

coordinator collects local states and compiles

global state.

Chandy Lamport Snapshot

- Organization of a process and channels for a

distributed snapshot

Chandy Lamport Snapshot

- One processor starts the snapshot by recording

his own local state and immediately sends a

marker message M on each of its outgoing

channels. (This indicates the causal boundary

between before the local state was recorded and

after). It begins to record all the messages

arriving on all incoming channels. When it has

received markers from all incoming channels, it

is done. - When a processor who was not the initiator

receives the marker for the first time, it

immediately records its local state, sends out

markers on all outgoing channels. It begins

recording the received message sequence on all

incoming channels other than the one it just

received the marker on. When a marker has been

received on each incoming channel, the processor

is done with its part of the snapshot.

Chandy Lamport Snapshot

- Process Q receives a marker for the first time

and records its local state - Q records all incoming message
- Q receives a marker for its incoming channel and

finishes recording the state of the incoming

channel

Snapshot

M

Recorded

a

M

State S2

2

2

1

4

b

3

c

- Node 2 initiates snapshot

Snapshot

Recorded

M

State S2

2

2

M

1

4

b

3

c

- Node 2 initiates snapshot

Snapshot

Recorded

State S2

2

2

M

State S1

1

1

b

4

4

4

State S4

M

M

d

3

- Node 2 initiates snapshot

Snapshot

Recorded

State S2

2

2

M

State S1

1

1

M

d

4

4

4

State S4

L3,2 b

3

M

Snapshot

Recorded

State S2

2

2

State S1

1

1

d

4

4

4

State S4

L3,2 b

3

L1,2 empty

M

L4,2 empty

Snapshot

Recorded

State S2

2

2

State S1

1

1

4

4

4

State S4

M

L3,2 b

M

3

3

3

L1,2 empty

L4,2 empty

State S3

L3,1 d

Snapshot

Recorded

State S2

2

2

State S1

1

1

M

M

4

4

4

State S4

L3,2 b

3

3

3

L1,2 empty

L4,2 empty

State S3

L3,1 d

Snapshot

Recorded

State S2

2

2

2

State S1

1

1

1

4

4

4

State S4

L3,2 b

3

3

3

L1,2 empty

L4,2 empty

State S3

L3,1 d

Chandy Lamport Snapshot

2

2

2

1

1

1

4

4

4

3

3

3

- Uses O(E) messages where E is the number of

edges. Time bound is dependent on the topology

of the graph.

Next Termination detection