Lecture 1: Logical, Physical & Casual Time (Part 2) Anish Arora CSE 763.

Lecture 1: Logical, Physical & Casual Time (Part 2)

Anish Arora

CSE 763

Physical Clocks

• Assume each process i has a physical clock, Ci(t), that is a continuous, differentiable function except where the clock is reset

• Necessary conditions for a system of physical clocks to be correct:

1. Each clock must run at the approximately correct rate

2. The clocks must be synchronized|

Physical Clock Synchronization

Physical Clock Synchronization

• Assume that message transmission time has two components: a minimum delay and an unpredictable delay

Algorithm

• When sending a message, a process timestamps it with the current value of its physical clock

• Upon receiving a message, a process sets its physical clock to the maximum of

1. its current value and

2. the timestamp plus the minimum message delay

Importance of Clock Synchronization

Synchronized clocks are fundamental to the correct functioning of a distributed system

• ordering events (e.g., FCFS scheduling)• consistent updates of replicated data• expiration of privileges• prearranged synchronization• ordering multi-version objects• interpreting data that is a function of

time

The Problem

A distributed system having synchronized clocks should have the following properties:

• At any instant the values of the clocks at any two sites in the distributed should differ by no more than a known quantity

• At any instant the value of a clock at a site should differ from universal time (i. e., “real” time) by at most /2

• The values assumed by any clock should be monotonically increasing

The first property cannot be achieved absolutely, but only with some very high probability

Difficulty of Clock Synchronization

The following factors conspire to prevent perfectly synchronized clocks:

• Clocks cannot be engineered to run at precisely the correct rate

• Sites in a distributed system cannot communicate infinitely often

• There are always unpredictable delays in message delivery

• Faulty or malicious sites may provide incorrect or inconsistent time values to other sites

Standard Time Dissemination

To coordinate time throughout the world, national administrations maintain and disseminate standard time (such as International Atomic Time, TAl, and Coordinated Universal Time, UTC)

U.S. National Institute of Standards and Technology

• WWV, Fort Collins, CO• WWVH, Kauai, HI• WWBV, Boulder, CO• Geosynchronous Orbiting Environmental Satellite

(GOES)• LORAN-C• Global Positioning System (GPS)

Distributed Time Services

There are two widely-used technologies for time service:

OSF DCE's Distributed Time Service• based on Digital’s DECdts

• developed during 1986-90

• a mature commercial product

• described in reference 2

NTP - Network Time Protocol• specified in 1985

• adopted as an Internet Standard Recommended Protocol

• Transarc’s implementation proposed to OSF

DCE Distributed Time Service

A clock is a device that provides a measure of UTC

Real clocks always exhibit some deviation from universal time, or error. The error can never be known exactly, but it can be bounded

So, a clock reports a range of values, anyone of which could be the universal time

DCE DTS Architecture

Obtaining a Time Value from a Server

Unsolicited time information is of minimal value

A request/response protocol gives more information

Obtaining a Time Value from a Server

When a clerk requests a time value from a server it doesn't know exactly when the server read its clock

Obtaining a Time Value from a Server

A interval containing the server's time at the “synchronization instant” can be computed

If lower bounds exist on the times required for intervening activities, the interval can be narrowed

Computing a Correct Time

Time values are obtained from several servers, in case some of them are faulty

If all servers are correct, then the narrowest correct time is simply the intersection of the intervals

Computing a Correct Time

Assume at most one server is faulty

Computing a Correct Time

Assume at most two servers are faulty

Marzullo's Algorithm

1. Arrange the endpoints of the intervals into a list

2. Mark each endpoint as a minimum or maximum

3. Sort the list. (If two endpoints have the same value, the minimums must precede the maximums)

4. Set the initial estimate of the number of faulty servers, f

5. Scan the list in increasing order to find the first endpoint that is in at least M - f intervals, where M is the number of servers

6. Scan the list in decreasing order to find the first endpoint in at least M - f intervals

7. If no such points are found, then there are more than f faulty servers. Increment f and go to step 5

8. The two points found delimit a correct time interval

Adjusting a Clock

Depending on the difference between the local clock and the computed time, one of two methods is used to update the local clock

Abrupt adjustment immediately sets the local clock to the computed time. This is done only if the difference is greater than 10 minutes

Gradual adjustment changes the amount by which the clock is incremented at each tick. It preserves the property that time is a monotonically increasing, continuous function

Adjusting a Clock

For gradual adjustment, a fast clock must be slowed down so that UTC catches up; a slow clock must be speeded up so it catches up to UTC

If the clock is usually incremented by , then during adjustment it is incremented by +

( > 0 clock gains time; < 0 clock loses time)

To achieve the necessary adjustment, the tick increment is adjusted for

ticks

Adjusting a Clock

Example

normal clock increment, =1

additional adjustment, =0.5

clock reading = 100

correct time =102

number of adjustments =(102-100) / 0.5 = 4

Determining the Inaccuracy

Whenever a clock is read, its inaccuracy must be calculated

This inaccuracy has four components:

1. The base inaccuracy at the synchronization point

2. The drift increase

3. The decrease due to the adjustment in the clock

4. The clock resolution

Clerk Synchronization

A clerk synchronizes when its local clock exceeds a specified inaccuracy

1.Obtain time values from a specified number of servers

2.Read the local clock to determine the synchronization instant

3.Translate each server’s time to the synchronization instant

4.Compute best correct time from servers’ time values

5.Compare the local time with best correct time. Report faulty clock or initiate clock adjustment

6.Schedule the next synchronization

Server Synchronization

If the server has a time provider, it periodically synchronizes with its time provider

1.Obtain time value(s) from time provider2.Read the local clock to determine the synchronization instant3.Translate the time provider's time(s) to the synchronization instant4.Compute best correct time from time provider's time(s) and own clock value5.Compare the local time with best correct time. Report faulty clock or initiate clock adjustment6.Schedule the next synchronization

Server Synchronization

If a server has no local time provider, it periodically synchronizes with other servers.

1. Obtain time values from all local servers

2. Read the local clock to determine the synchronization instant

3. Translate the server’s times to the synchronization instant

4. Compute best correct time from time server’s times and own clock value

5. Compare the local time with best correct time. Report faulty clock or initiate clock adjustment

6. Schedule the next synchronization