5_DSS_Global State.ppt

8/14/2019 5_DSS_Global State.ppt

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Global State Collection


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Introduction

In a distributed system, each process executes actions on thebasis of local information that consists of its own state, and thestates of its neighbors, or messages through the incomingchannels.

Many applications need to find out the global state of thesystem by collecting the local states of the componentprocesses like :

Computation of the network topology

Counting the number of processes in a distributed system Detecting termination Detecting deadlock Detecting loss of coordination


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Global State collection

The algorithms for global state collection have beenclassified into various types:

Probe-echo algorithm,

Wave algorithm,

Heartbeat algorithm


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Wave Algorithms

A wave algorithm is a distributed algorithm that satisfies thefollowing three requirements:

Termination:Each computation is finite

Decision:Each computation contains at least one decide

event

Dependence: In each computation each decide event iscausally preceded by an event in each process


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Traversal Algorithms

A traversal algorithm is an algorithm with thefollowing three properties:

In each computation there is one initiator, which

starts the algorithm by sending out exactly onemessage.

A process, upon receipt of a message, either sends

out one message or decides.

The algorithm terminates in the initiator and when thishappens, each process has sent a message at leastonce.


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Waveform Algorithm

One or more initiators start a computation.

The computation in a non-initiator node is triggeredby the computation in an adjacent node.

Each node reaches local termination when a

predefined local goal is reached.

The system-wide computation terminates in abounded number of steps after it has been initiated.


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AN ELEMENTARY ALGORITHMFOR BROADCASTING

Each process i has a stable value s(i) associated withit.

The goal is to devise an algorithm by which everyprocess i can broadcast its value s(i) to every otherprocess in this system.

At the end, each process i will have a setV.i = {forall k : 0 k N 1 : s(k)}.

InitiallyV.i = {s(i)}.


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Continued..

Every process i will periodically (i) send itscurrentV.i along each of its outgoing channels

Receive values along the incoming channels to

updateV.i.

The operation resembles the pumping of bloodin the heart, so

Heartbeat algorithms!


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Two important issues need attention:

The termination of the algorithmThe message complexity

To save unnecessary work, it makes little sense to sendV.i, if it has not changed since the last operation.

Furthermore, even ifV.i has changed since the last

send operation, it suffices to send the incrementalchange onlythis will keep the message size small.


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program broadcast (for process i}

defineV.i, W.i: set of values;

initiallyV.i = {s(i)}, W.i = {and every channel isempty}

1. doV.i W.isend (V.i \ W.i) to every outgoingchannel;

W.i := V.i

2. empty (k, i) receive X from channel (k, i);V.i := V.i U X


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empty(i.k) => W.i V.k.

Induction step. Between two consecutive executions ofstatement 1, statement 2 must be executed at least once.

Assume W.i V.k holds after process i executes the firststatement r times, and (i, k) is empty.

We will show that W.i V.k holds after process i executes thefirst statement (r + 1) times, and (i, k) is empty.


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Algorithm broadcast terminates when everyprocess has received the value of s(j) from

every process j = i.

Proof.When all guards are false, the conditionV.i =W.i holds for each i, and the channels are empty.

From Lemma 9.1, empty (i. k)=>W.i V.k.Therefore,V.i V.k.

Now consider a directed cycle, If for every pair ofprocesses i and k across a channel (i, k) the conditionV.i V.k holds, then for i,j :V.i = V.j.


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Continued..

In a strongly connected graph every pair of processes(i,j) are contained in a directed cycle, therefore theconditionV.i = V.j must hold for every pair ofprocesses in the system.

Also, since s(i)V.i, and no element is removed froma set, eachV must contain all the s-values.


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Message Complexity

A process i broadcasts only whenV.i changes. Starting from the initial value s(i),V.i can

change at most (N 1) times.

Also, since each node can have at most (N 1) neighbors, each broadcast may consist of atmost N 1 messages.

Thus a typical process can send at most (N 1)2messages.


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TERMINATION DETECTION ALGORITHM

One possible mechanism of distributing thecomputation to the various processes is as follows:

The task is initially assigned to an initiator node.

The initiator delegates various parts of this task to itsneighbors, which delegate parts of their work to theirneighbors, and so on.

As the computation makes progress, these nodesexchange messages among themselves.


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States of a node

Active and Passive

A process is active, when it has some enabled guards.

If a process is in a passive state, then it does notnecessarily mean that the process will always remainpassivea message sent by an active neighbor maywake up the process.

An active process on the other hand eventuallyswitches to a passive state, when it has executed allits local actions.


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Active & Passive Processes


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Termination of a process

Termination corresponds to the following three criteria:

(a) every process is in a passive state

(b) all channels are empty

(c) the global state of the system satisfies the desiredpostcondition.

To see why termination detection is important, remember that

many computations in distributed systems runs in phases. Eachphase of a computation runs over the entire system, and tolaunch phase (i+1), the initiator has to ascertain that phase ihas terminated.


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THE DIJKSTRASCHOLTEN ALGORITHM

The computation initiated by a single initiator and spreading

over to several other nodes in the network is called a diffusingComputation.

Termination is reported to the initiator as a single event.

There are two kinds of messages in the network:1. signals propagate along the direction of the Edges.

2. Acknowledgments propagate in the opposite direction.

The initiator is a special node (called the environment node)that has no edge directed toward it.

Every other node is called an internal node, and is reachable

from the environment node via the edges of the directed path.


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Global State Collection


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INV2. (C > 0) (D = 0)


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TERMINATION DETECTION ON A

UNIDIRECTIONAL RING

The algorithm works on a unidirectional ring that is embeddedon the topology of the given networkthe order of theprocesses in the ring is used to decide the order in which thetoken traverses the network.

The ring topology has no connection with the sending andreceiving of messages by the underlying algorithmso amessage can be sent by one process to another as long as apath exists, even if they are not neighbors in the ring.

All communication channels are assumed to be FIFO.


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Active & Passive Processes

Assume that process 0 is the initiator of termination detection .

The initiator initiates the algorithm by sending out a tokenittraverses the network and eventually returns to the initiator.

A process k accepting the token will not forward it to

k1 until it becomes passive.

When the initiator receives the token back, it detects termination.


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Limitations

What if the token is with process k, but a processm(n 1 > m > k) that was passive, now becomesactive by receiving a message from some process l(k> l > 0)?

This could lead to a false detection, since theactivation of process m will go unnoticed!

To prevent this, refine the scheme by assigning the

colors white and black to processes and the token.


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Rules: ForUNIDIRECTIONAL RING

Initially, all processes are white, and the initiatorsends a white token to process (n 1).

Rule 1. When a non-initiator process sends amessage to a higher numbered process, it turns black.

Rule 2. When a black process sends a token, thetoken turns black. If a white process forwardsa token, then it retains the color of the token.

Rule 3.When a black process sends a token to itssuccessor, it turns white.

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5_DSS_Global State.ppt