Synchronizationin

Distributed Systems

Chapter 6

Guide to Synchronization Lectures

• Synchronization in shared memory systems• Event ordering in distributed systems

– Logical time, logical clocks, time stamps,

• Mutual exclusion in distributed systems– Centralized, decentralized, etc.– Election algorithms

• Data race detection in multithreaded programs

Background

• Synchronization: coordination of actions between processes.

• Processes are usually asynchronous, (operate independent of events in other processes)

• Sometimes need to cooperate/synchronize– For mutual exclusion– For event ordering (was message x from process P

sent before or after message y from process Q?)

Introduction

• Synchronization in centralized systems is primarily accomplished through shared memory– Event ordering is clear because all events are

timed by the same clock

• Synchronization in distributed systems is harder– No shared memory– No common clock

Clock Synchronization

• Some applications rely on event ordering to be successful– See page 232 for some examples– Event ordering is easier if you can accurately

time-stamp events, but in a distributed system the clocks may not always be synchronized

• Is it possible to synchronize clocks in a distributed system?

Physical Clocks - pages 233-238• Physical clock example: counter + holding

register + oscillating quartz crystal– The counter is decremented at each oscillation– Counter interrupts when it reaches zero – Reloads from the holding register– Interrupt = clock tick (often 60 times/second)

• Software clock: counts interrupts– This value represents number of seconds since some

predetermined time (Jan 1, 1970 for UNIX systems; beginning of the Gregorian calendar for Microsoft)

– Can be converted to normal clock times

Clock Skew

• In a distributed system each computer has its own clock

• Each crystal will oscillate at slightly different rate.

• Over time, the software clock values on the different computers are no longer the same.

Clock Skew

• Clock skew(offset): the difference between the times on two different clocks

• Clock drift : the difference between a clock and actual time

• Ordinary quartz clocks drift by ~ 1sec in 11-12 days. (10-6 secs/sec)

• High precision quartz clocks drift rate is somewhat better

Various Ways of Measuring Time*• The sun

– Mean solar second – gradually getting longer as earth’s rotation slows.

• International Atomic Time (TAI)– Atomic clocks are based on transitions of the cesium

atom

– Atomic second = value of solar second at some fixed time (no longer accurate)

• Universal Coordinated Time (UTC)– Based on TAI seconds, but more accurately reflects

sun time (inserts leap seconds to synchronize atomic second with solar second)

Getting the Correct (UTC) Time*

• WWV radio station or similar stations in other countries (accurate to +/- 10 msec)

• UTC services provided by earth satellites (accurate to .5 msec)

• GPS (Global Positioning System) (accurate to 20-35 nanoseconds)

Clock Synchronization Algorithms*

• In a distributed system one machine may have a WWV receiver and some technique is used to keep all the other machines in synch with this value.

• Or, no machine has access to an external time source and some technique is used to keep all machines synchronized with each other, if not with “real” time.

Clock Synchronization Algorithms

• Network Time Protocol (NTP):– Objective: to keep all clocks in a system synchronized to

UTC time (1-50 msec accuracy) – not so good in WAN– Uses a hierarchy of passive time servers

• The Berkeley Algorithm:– Objective: to keep all clocks in a system synchronized to

each other (internal synchronization)– Uses active time servers that poll machines periodically

• Reference broadcast synchronization (RBS)– Objective: to keep all clocks in a wireless system

synchronized to each other

Three Philosophies of Clock Synchronization

• Try to keep all clocks synchronized to “real” time as closely as possible

• Try to keep all clocks synchronized to each other, even if they vary somewhat from UTC time

• Try to synchronize enough so that interacting processes can agree upon an event order.– Refer to these “clocks” as logical clocks

6.2 Logical Clocks

• Observation: if two processes (running on separate processors) do not interact, it doesn’t matter if their clocks are not synchronized.

• Observation: When processes do interact, they are usually interested in event order, instead of exact event time.

• Conclusion: Logical clocks are sufficient for many applications

Formalization

• The distributed system consists of n processes, p1, p2, …pn (e.g, a MPI group)

• Each pi executes on a separate processor

• No shared memory

• Each pi has a state si

• Process execution: a sequence of events– Changes to the local state – Message Send or Receive

Two Versions

• Lamport’s logical clocks: synchronizes logical clocks– Can be used to determine an absolute

ordering among a set of events although the order doesn’t necessarily reflect causal relations between events.

• Vector clocks: can capture the causal relationships between events.

Lamport’s Logical Time

• Lamport defined a “happens-before” relation between events in a process.

• "Events" are defined by the application. The granularity may be as coarse as a procedure or as fine-grained as a single instruction.

Happened Before Relation (a b)

• a b: (page 244-245)– in the same [sequential] process, – send, receive in different processes,

(messages)– transitivity: if a b and b c, then a c

• If a b, then a and b are causally related; i.e., event a potentially has a causal effect on event b.

Concurrent Events

• Happens-before defines a partial order of events in a distributed system.

• Some events can’t be placed in the order

• a and b are concurrent (a || b) if !(a b) and !(b a).

• If a and b aren’t connected by the happened-before relation, there’s no way one could affect the other.

Logical Clocks

• Needed: method to assign a “timestamp” to event a (call it C(a)), even in the absence of a global clock

• The method must guarantee that the clocks have certain properties, in order to reflect the definition of happens-before.

• Define a clock (event counter), Ci, at each process (processor) Pi.

• When an event a occurs, its timestamp ts(a) = C(a), the local clock value at the time the event takes place.

Correctness Conditions

• If a and b are in the same process, anda b then C (a) < C (b)

• If a is the event of sending a message from Pi, and b is the event of receiving the message by Pj, then Ci (a) < Cj (b).

• The value of C must be increasing (time doesn’t go backward).– Corollary: any clock corrections must be

made by adding a positive number to a time.

Implementation Rules

• Between any two successive events a & b in Pi, increment the local clock (Ci = Ci + 1)

– thus Ci(b) = Ci(a) + 1

• When a message m is sent from Pi, set its time-stamp tsm to Ci, the time of the send event after following previous step.

• When the message is received at Pj the local time must be greater than tsm . The rule is (Cj = max{Cj, tsm} + 1).

Lamport’s Logical Clocks (2)

Figure 6-9. (a) Three processes, each with its own clock. The clocks “run” at different rates.

Event a: P1 sends m1 to P2 at t = 6, Event b: P2 receives m1 at t = 16.If C(a) is the time m1 was sent, and C(b) is the time m1 is received, do C(a) and C(b) satisfy the correctness conditions ?

Lamport’s Logical Clocks (3)

Figure 6-9. (b) Lamport’s algorithm corrects the clocks.

Event c: P3 sends m3 to P2 at t = 60Event d: P2 receives m3 at t = 56Do C(c) and C(d) satisfy the conditions?

Application Layer

Application sends message mi

Adjust local clock,Timestamp mi

Middleware sendsmessage

Network Layer

Message mi is received

Adjust local clock

Deliver mi to application

Middleware layer

Figure 6-10. The positioning of Lamport’s logical clocks in distributed systemsHandling clock management as a middleware operation

Figure 5.3 (Advanced Operating Systems,Singhal and Shivaratri) How Lamport’s logical clocks advance

e11 e12 e13 e14 e15 e16 e17

e21 e22 e23 e24 e25

P1

P2

Which events are causally related?Which events are concurrent?

eij represents event j on processor i

A Total Ordering Rule(does not guarantee causality)

• A total ordering of events can be obtained if we ensure that no two events happen at the same time (have the same timestamp).

• Why? So all processors can agree on an unambiguous order.

• How? Attach process number to low-order end of time, separated by decimal point; e.g., event at time 40 at process P1 is 40.1,event at time 40 at process P2 is 40.2

Figure 5.3 - Singhal and Shivaratri

e11 e12 e13 e14 e15 e16 e17

e21 e22 e23 e24 e25

P1

P2

What is the total ordering of the events in these two processes?

Example: Total Order Multicast

• Consider a banking database, replicated across several sites.

• Queries are processed at the geographically closest replica

• We need to be able to guarantee that DB updates are seen in the same order everywhere

Totally Ordered Multicast

Update 1: Process 1 at Site A adds $100 to an account, (initial value = $1000)Update 2: Process 2 at Site B increments the account by 1%Without synchronization,it’s possible thatreplica 1 = $1111,replica 2 = $1110

• Message 1: add $100.00Message 2: increment account by 1%

• The replica that sees the messages in the order m1, m2 will have a final balance of $1111

• The replica that sees the messages in the order m2, m1 will have a final balance of $1110

The Problem

• Site 1 has final account balance of $1,111 after both transactions complete and Site 2 has final balance of $1,100.

• Which is “right”? Either, from the standpoint of consistency.

• Problem: lack of consistency.– Both values should be the same

• Solution: make sure both sites see/process all messages in the same order.

Implementing Total Order

• Assumptions: – Updates are multicast to all sites, including

(conceptually) the sender– All messages from a single sender arrive in

the order in which they were sent – No messages are lost– Messages are time-stamped with Lamport

clock values.

Implementation

• When a process receives a message, put it in a local message queue, ordered by timestamp.

• Multicast an acknowledgement to all sites• Each ack has a timestamp larger than the

timestamp on the message it acknowledges

• The message queue at each site will eventually be in the same order

Implementation

• Deliver a message to the application only when the following conditions are true:– The message is at the head of the queue– The message has been acknowledged by all other

receivers. This guarantees that no update messages with earlier timestamps are still in transit.

• Acknowledgements are deleted when the message they acknowledge is processed.

• Since all queues have the same order, all sites process the messages in the same order.

Causality

• Causally related events: – Event a may causally affect event b if a b – Events a and b are causally related if either

a b or b a. – If neither of the above relations hold, then

there is no causal relation between a & b. We say that a || b (a and b are concurrent)

Vector Clock Rationale

• Lamport clocks limitation: – If (ab) then C(a) < C(b) but – If C(a) < C(b) then we only know that either

(ab) or (a || b), i.e., b a

• In other words, you cannot look at the clock values of events on two different processors and decide which one “happens before”.

• Lamport clocks do not capture causality

Lamport’s Logical Clocks (3)

Figure 6-12.

Suppose we add a message to the scenario in Fig. 6.12(b).

• Tsnd(m1) < Tsnd(m3’). (6) < (32) • Does this mean send(m1) send(m3’)? But …• Tsnd(m1) < Tsnd(m2’). (6) < (20) • Does this mean send(m1) send(m2)?

m2’

m3’

Figure 5.4Time

P1

P2

P3

e11.

e21

e12

e22

e31 e32 e33

(1) (2)

(1) (3)

(1) (2) (3)

C(e11) < C(e22) and C(e11) < C(e32) but while e11 e22, we cannot say e11 e32 since there is no causal path connecting them. So, with Lamport clocks we can guarantee that if C(a) < C(b) then b a , but by looking at the clock values alone we cannot say whether or not the events are causally related.

Space

Vector Clocks – How They Work

• Each processor keeps a vector of values, instead of a single value.

• VCi is the clock at process i; it has a component for each process in the system.– VCi[i] corresponds to Pi‘s local “time”.– VCi[j] represents Pi‘s knowledge of the “time”

at Pj (the # of events that Pi knows have occurred at Pj

• Each processor knows its own “time” exactly, and updates the values of other processors’ clocks based on timestamps received in messages.

Implementation Rules

• IR1: Increment VCi[i] before each new event.• IR2: When process i sends a message m it sets

m’s (vector) timestamp to VCi (after incrementing VCi[i])

• IR3: When a process receives a message it does a component-by-component comparison of the message timestamp to its local time and picks the maximum of the two corresponding components. Adjust local components accordingly.

• Then deliver the message to the application.

Review• Physical clocks: hard to keep synchronized• Logical clocks: can provide some notion of

relative event occurrence• Lamport’s logical time

– happened-before relation defines causal relations– logical clocks – don’t capture causality– total ordering relation– use in establishing totally ordered multicast

• Vector clocks– Unlike Lamport clocks, vector clocks capture causality– Have a component for each process in the system

Figure 5.5. Singhal and Shivaratri

(1, 0 , 0) (2, 0, 0) (4, 5, 2)

e11 e12 e14

(0, 1, 0) (2, 2, 0) (2, 3, 1) (2, 5, 2)

(0, 0, 1) (0, 0, 2)

e21 e22 e23 e24

e31 e32

P1

P2

P3

(2,4,2)

e25

Vector clock values. In a 3- process system, VC(Pi) = vc1, vc2, vc3

e13

(3, 0, 0)

e33

(0, 0, 3)

Establishing Causal Order

• When Pi sends a message m to Pj, Pj knows– How many events occurred at Pi before m was sent– How many relevant events occurred at other sites before

m was sent (relevant = “happened-before”)

• In Figure 5.5, VC(e24) = (2, 4, 2). Two events in P1 and two events in P3 “happened before” e24. – Even though P1 and P3 may have executed other events,

they don’t have a causal effect on e24.

Happened Before/Causally Related Events - Vector Clock Definition

• a → b iff ts(a) < ts(b)

(a happens before b iff the timestamp of a is less than the timestamp of b)

• Events a and b are causally related if– ts(a) < ts(b) or– ts(b) < ts(a)

• Otherwise, we say the events are concurrent.• Any pair of events that satisfy the vector clock

definition of happens-before will also satisfy the Lamport definition, and vice-versa.

Comparing Vector Timestamps• Less than: ts(a) < ts(b) iff at least one

component of ts(a) is strictly less than the corresponding component of ts(b) and all other components of ts(a) are either less than or equal to the corresponding component in ts(b).

• (3,3,5) ≤ (3,4,5), (3, 3, 3) ═ (3, 3, 3), (3,3,5) ≥ (3,2,4), (3, 3 ,5) | | (4,2,5).

Figure 5.4Time

P1

P2

P3

e21

e12

e22

e31 e32 e33

(1, 0, 0) (2, 0, 0)

(0, 1, 0) (2, 2, 0)

(0, 0,1) (0, 0, 2) (0, 0, 3)

ts(e11) = (1, 0, 0) and ts(e32) = (0, 0, 2), which shows that the two events are concurrent.ts(e11) = (1, 0, 0) and ts(e22) = (2, 2, 0), which shows that e11 e22

e11

Causal Ordering of Messages An Application of Vector Clocks

• Premise: Deliver a message only if messages that causally precede it have already been received– i.e., if send(m1) send(m2), then it should be

true that receive(m1) receive(m2) at each site.

– If messages are not related (send(m1) || send(m2)), delivery order is not of interest.

Compare to Total Order

• Totally ordered multicast (TOM) is stronger (more inclusive) than causal ordering (COM).– TOM orders all messages, not just those that

are causally related.– “Weaker” COM is often what is needed.

Enforcing Causal Communication

• Clocks are adjusted only when sending or receiving messages; i.e, these are the only events of interest.

• Send m: Pi increments VCi[i] by 1 and applies timestamp, ts(m).

• Receive m: Pi compares VCi to ts(m); set VCi[k] to max{VCi[k] , ts(m)[k]} for each k, k ≠ i.

Message Delivery Conditions

• Suppose: PJ receives message m from Pi

• Middleware delivers m to the application iff– ts(m)[i] = VCj[i] + 1

• all previous messages from Pi have been delivered

– ts(m)[k] ≤ VCi[k] for all k ≠ i

• PJ has received all messages that Pi had seen before it sent message m.

• In other words, if a message m is received from Pi, you should also have received every message that Pi received before it sent m; e.g., – if m is sent by P1 and ts(m) is (3, 4, 0) and you

are P3, you should already have received exactly 2 messages from P1 and at least 4 from P2

– if m is sent by P2 and ts(m) is (4, 5, 1, 3) and if you are P3 and VC3 is (3, 3, 4, 3) then you need to wait for a fourth message from P2 and at least one more message from P1.

P0

P1

P2

(1, 0, 0)

P1 received message m from P0 before sending message m* to P2; P2 must wait for delivery of m before receiving m*

(Increment own clock only on message send)

Before sending or receiving any messages, one’s own clock is (0, 0, …0)

VC2(1, 0, 0) (1, 1, 0)

(1, 1, 0)VC1

m

m*

VC0

VC2

Figure 6-13. Enforcing Causal Communication

VC0

(1, 1, 0)

(0, 0, 0)VC2

History

• ISIS and Horus were middleware systems that supported the building of distributed environments through virtually synchronous process groups

• Provided both totally ordered and causally ordered message delivery.– “Lightweight Causal and Atomic Group Multicast”– Birman, K., Schiper, A., Stephenson, P, ACM Transactions on

Computer Systems, Vol 9, No. 3, August 1991, pp 272-314.

Location of Message Delivery

• Problems if located in middleware:– Message ordering captures only potential causality;

no way to know if two messages from the same source are actually dependent.

– Causality from other sources is not captured.

• End-to-end argument: the application is better equipped to know which messages are causally related.

• But … developers are now forced to do more work; re-inventing the wheel.