MC0085 solved assignment

Master of Computer Application (MCA) – Semester 5

MC0085 – Advanced Operating Systems

(Distributed Systems) – 4 Credits

(Book ID: B0967)

Assignment Set – 1 (60 Marks)

1. What is a message passing system? Discuss the desirable features of a message passing system.

Ans.

Message passing is the paradigm of communication where messages are sent from a sender to one or more recipients. Forms of messages include (remote) method invocation, signals, and data packets. When designing a message passing system several choices are made:

Whether messages are transferred reliably

Whether messages are guaranteed to be delivered in order

Whether messages are passed one-to-one, one-to-many (multi-casting or broadcasting), or many-to-one (client–server).

Whether communication is synchronous or asynchronous.

Prominent theoretical foundations of concurrent computation, such as the Actor model and the process calculi are based on message passing. Implementations of concurrent systems that use message passing can either have message passing as an integral part of the language, or as a series of library calls from the language. Examples of the former include many distributed object systems. Examples of the latter include Micro-kernel operating systems pass messages between one kernel and one or more server blocks, and the Message Passing Interface used in high-performance computing.

Message passing systems and models

Distributed object and remote method invocation systems like ONC RPC, Corba, Java RMI, DCOM, SOAP, .NET Remoting, CTOS, QNX Neutrino RTOS, OpenBinder, D-Bus and similar are message passing systems.

Message passing systems have been called "shared nothing" systems because the message passing abstraction hides underlying state changes that may be used in the implementation of sending messages.

Message passing model based programming languages typically define messaging as the (usually asynchronous) sending (usually by copy) of a data item to a communication endpoint (Actor, process, thread, socket, etc.). Such messaging is used in Web Services by SOAP. This concept is the higher-level version of a datagram except that messages can be larger than a packet and can optionally be made reliable, durable, secure, and/or transacted.

Messages are also commonly used in the same sense as a means of interprocess communication; the other common technique being streams or pipes, in which data are sent as a sequence of elementary data items instead (the higher-level version of a virtual circuit).

Examples of message passing style

#Actor model implementation

#Amorphous computing

#Flow-based programming

#SOAP (protocol)

Synchronous versus asynchronous message passing

Synchronous message passing systems require the sender and receiver to wait for each other to transfer the message. That is, the sender will not continue until the receiver has received the message.

Synchronous communication has two advantages. The first advantage is that reasoning about the program can be simplified

in that there is a synchronization point between sender and receiver on message transfer. The second advantage is that no buffering is required. The message can always be stored on the receiving side, because the sender will not continue until the receiver is ready.

Asynchronous message passing systems deliver a message from sender to receiver, without waiting for the receiver to be ready. The advantage of asynchronous communication is that the sender and receiver can overlap their computation because they do not wait for each other.

Synchronous communication can be built on top of asynchronous communication by ensuring that the sender always wait for an acknowledgement message from the receiver before continuing.

The buffer required in asynchronous communication can cause problems when it is full. A decision has to be made whether to block the sender or whether to discard future messages. If the sender is blocked, it may lead to an unexpected deadlock. If messages are dropped, then communication is no longer reliable.

2. Discuss the implementation of RPC Mechanism in detail.

Ans.

In computer science, a remote procedure call (RPC) is an inter-process communication that allows a computer program to cause a subroutine or procedure to execute in another address space (commonly on another computer on a shared network) without the programmer explicitly coding the details for this remote interaction. That is, the programmer writes essentially the same code whether the subroutine is local to the executing program, or remote. When the software in question uses object-oriented principles, RPC is called remote invocation or remote method invocation.

Note that there are many different (often incompatible) technologies commonly used to accomplish this.

Message passing

An RPC is initiated by the client, which sends a request message to a known remote server to execute a specified procedure with supplied parameters. The remote server sends a response to the client, and the application continues its process. There are many variations and subtleties in various implementations, resulting in a variety of different (incompatible) RPC protocols. While the server is processing the call, the client is blocked (it waits until the server has finished processing before resuming execution).

An important difference between remote procedure calls and local calls is that remote calls can fail because of unpredictable network problems. Also, callers generally must deal with such failures without knowing whether the remote procedure was actually invoked. Idempotent procedures (those that have no additional effects if called more than once) are easily handled, but enough difficulties remain that code to call remote procedures is often confined to carefully written low-level subsystems.

Sequence of events during a RPC

The client calls the Client stub. The call is a local procedure call, with parameters pushed on to the stack in the normal way.

The client stub packs the parameters into a message and makes a system call to send the message. Packing the parameters is called marshalling.

The kernel sends the message from the client machine to the server machine.

The kernel passes the incoming packets to the server stub.

Finally, the server stub calls the server procedure. The reply traces the same steps in the reverse direction.

3. Discuss the following with respect to Distributed Shared Memory:

a. Memory Coherence (Consistency) Models

b. Memory Consistency models

c. Implementing Sequential Consistency

d. Centralized – Server Algorithm

Ans.

a) Memory Coherence (Consistency) Models

Memory Consistency Model is:

A set of rules that the applications must obey if they want the DSM system toprovide the degree of consistency guaranteed by the consistency model.

• Weaker the consistency model, better the concurrency.• Researchers try to invent new consistency models which are weaker than theexisting ones in such a way that a set of applications will function correctly underthe new consistency model.

•Note that an application written for a DSM that implements a strongerconsistency model may not work correctly under a DSM that implements aweaker consistency model

b) Memory Consistency models

i) Strict consistency:

Each read operation returns the most recently written value. This is possible to implement only in systems with the notion of global time. So,this model is impossible to implement. Hence, DSM systems based on underlying distributed systems have to use weaker consistency models.

ii)Sequential consistency:

Proposed by Lamport (1979). All processes in the system observe the same order of all memory access operations on the shared memory. i.e. , if three operations read(r1), write(w1) and read(r2) are performed on a memory address in that order, then any of the six orderings (r1,w1, r2), (r2,w1,r1), (w1, r2, r1).... is acceptable provided all processes see the same ordering. It can be implemented by serializing all requests on a central server node. This model is weaker than the strict consistency model. This model provides one-copy/single-copy semantics because all processes sharing a memory location always see exactly the same contents stored in it. Sequential consistency is the most intuitively expected semantics for memory coherence. So, sequential consistency is acceptable for most applications.

iii) Causal consistency model:

Proposed by Hutto and Ahamad (1990).In this model, all write operations that are potentially causally related are seen by all processes in the same (correct) order. For example, if a process did a read operation and then performed a write operation, then the value written may have depended in some way on the value read. A write operation performed by one process P1 is not causally related to the write operation performed by another process P2 if P1 has read neither the value written by P2 or any memory variable that was directly or indirectly derived from the value written by P2 and vice versa. For implementing DSMs that support causal consistency one has to keep track of which memory operation is dependent on which other operation. This model is weaker than Sequential consistency model

iii)Pipelined Random

Access Memory (PRAM) consistency model. This model was proposed by Lipton and Sandberg (1988). In this model, all write operations performed by a single process are seen by all other processes in the order in which they were performed. This model can be implemented easily by sequencing the write operations performed by each node independently. This model is weaker than all the above consistency models.

v)Processor Consistency Model:

Proposed by Goodman (1989). In addition to PRAM consistency, for any memory location, all processes agree on the same order of all write operations to that location.

vi) Weak Consistency Model:

Proposed by Dubois et al. (1988). This model distinguishes between ordinary accesses and synchronization accesses. It requires that memory become consistent only on synchronization accesses. ADSM that supports weak consistency model uses a special variable, called synchronization variable. The operations on it are used to synchronize memory. For supporting weak consistency, the following should be satisfied:

All accesses to synchronization variables must obey sequential consistency semantics.

vii) Release Consistency Model:

In the weak consistency model, the entire shared memory is synchronized when a synchronization variable is accessed by a process i.e.

• All changes made to the memory are propagated to other nodes.• All changes made to the memory by other processes are propagated from other nodes to the process’s node.

This is not really necessary because the first operation needs to be performed only when a process exits from critical section and the second operation needs to be performed only when the process enters critical section. So, instead of one synchronization variable, two synchronization variables, called acquire and release have been proposed.

Acquire is used by a process to tell the system that it is about to enter a critical section.

Release is used to tell the system that it had exited critical section. If processes use appropriate synchronization accesses properly, a release consistency DSM system will produce the same results for an application as that if the application was executed on a sequentially consistent DSM system.

viii) Lazy Release consistency model:

It is a variation of release consistency model. In this approach, when a process does a release access, the contents of all the modifications are not immediately sent to other nodes but they are sent only on demand. i.e. When a process does an acquire access, all modifications of other nodes are acquired by the process’s node. It minimizes network traffic.

c) Implementing Sequential Consistency

Sequential consistency supports the intuitively expected semantics. So, this is the most preferred choice for designers of DSM system. The replication and migration strategies for DSM design include:

1. Non-replicated, non-migrating blocks (NRNMBs)
2. Non-replicated, migrating blocks (NRMBs)
3. Replicated, migrating blocks (RMBs)
4. Replicated, non-migrating blocks (RNMBs).

i) Implementing under NRNMBs strategy:

Under this strategy, only one copy of each block of the shared memory is in the system and its location is fixed. All requests for a block are sent to the owner node of the block. Upon receiving a request from a client node, the memory management unit (MMU) and the operating system of the owner node perform the access request and return the result. Sequential consistency can be trivially enforced, because the owner node needs to only process all requests on a block in the order it receives.

Disadvantage:

• Parallelism is not possible in this strategy
• Mapping between blocks and nodes need to be maintained at each node.

ii) Implementing under NRMBs strategy

Under this strategy, only the processes executing on one node can read or write a given data item at any time, so sequential consistency is ensured.

The advantages of this strategy include:

–No communication cost for local data access.

–Allows applications to take advantage of data access locality

The disadvantages of this strategy include:

–Prone to thrashing

–Parallelism cannot be achieved in this method also

–Locating a block in the NRMB strategy.

d) Centralized-Server Algorithm

A central server maintains a block table containing owner-node and copy-set information for each block. When a read/write fault for a block occurs at node N, the fault handler at node N sends a read/write request to the central server. Upon receiving the request, the central-server does the following:

• If it is a read request:
• adds N to the copy-set field and
• sends the owner node information to node N
• upon receiving this information, N sends a request for the block to the owner node.
• upon receiving this request, the owner returns a copy of the block to N.

If it is a write request:

• It sends the copy-set and owner information of the block to node N and initializes copy-set to {N}
• Node N sends a request for the block to the owner node and an invalidation message to all blocks in the copy-set.
• Upon receiving this request, the owner sends the block to node N

4.Describe the following:

A) Task assignment Approach B) Load – Balancing Approach

C) Load – Sharing Approach

Ans:

A) Task assignment Approach

Each process is viewed as a collection of tasks. These tasks are scheduled to suitable processor to improve performance. This is not a widely used approach because:

• It requires characteristics of all the processes to be known in advance.
• This approach does not take into consideration the dynamically changing state of the system.

In this approach, a process is considered to be composed of multiple tasks and the goal is to find an optimal assignment policy for the tasks of an individual process. The following are typical assumptions for the task assignment approach:

• Minimize IPC cost (this problem can be modeled using network flow model)
• Efficient resource utilization
• Quick turnaround time
• A high degree of parallelism

B) Load – Balancing Approach

In this, the processes are distributed among nodes to equalize the load among all nodes. The scheduling algorithms that use this approach are known as Load Balancing or Load Leveling Algorithms. These algorithms are based on the intuition that for better resource utilization, it is desirable for the load in a distributed system to be balanced evenly. This a load balancing algorithm tries to balance the total system load by transparently transferring the workload from heavily loaded nodes to lightly loaded nodes in an attempt to ensure good overall performance relative to some specific metric of system performance.

We can have the following categories of load balancing algorithms:

• Static: Ignore the current state of the system. E.g. if a node is heavily loaded, it picks up a task randomly and transfers it to a random node. These algorithms are simpler to implement but performance may not be good.

• Dynamic: Use the current state information for load balancing. There is an overhead involved in collecting state information periodically; they perform better than static algorithms.
• Deterministic: Algorithms in this class use the processor and process characteristics to allocate processes to nodes.
• Probabilistic: Algorithms in this class use information regarding static attributes of the system such as number of nodes, processing capability, etc.
• Centralized: System state information is collected by a single node. This node makes all scheduling decisions.
• Distributed: Most desired approach. Each node is equally responsible for making scheduling decisions based on the local state and the state information received from other sites.
• Cooperative: A distributed dynamic scheduling algorithm. In these algorithms, the distributed entities cooperate with each other to make scheduling decisions. Therefore they are more complex and involve larger overhead than non-cooperative ones. But the stability of a cooperative algorithm is better than of a non-cooperative one.
• Non-Cooperative: A distributed dynamic scheduling algorithm. In these algorithms, individual entities act as autonomous entities and make scheduling decisions independently of the action of other entities.

C) Load – Sharing Approach

Several researchers believe that load balancing, with its implication of attempting to equalize workload on all the nodes of the system, is not an appropriate objective. This is because the overhead involved in gathering the state information to achieve this objective is normally very large, especially in distributed systems having a large number of nodes. In fact, for the proper utilization of resources of a distributed system, it is not required to balance the load on all the nodes. It is necessary and sufficient to prevent the nodes from being idle while some other nodes have more than two processes. This rectification is called the Dynamic Load Sharing instead of Dynamic Load Balancing.

The design of a load sharing algorithms require that proper decisions be made regarding load estimation policy, process transfer policy, state information exchange policy, priority assignment policy, and migration limiting policy. It is simpler to decide about most of these policies in case of load sharing, because load sharing algorithms do not attempt to balance the average workload of all the nodes of the system. Rather, they only attempt to ensure that no node is idle when a node is heavily loaded. The priority assignments policies and the migration limiting policies for load-sharing algorithms are the same as that of load-balancing algorithms.

5. Explain the following with respect to Distributed File Systems:

a. The Key Challenges of Distributed Systems

b. Client’s Perspective: File Services

c. File Access Semantics

d. Server’s Perspective Implementation

e. Stateful Versus Stateless Servers

Ans:

a) The Key Challenges of Distributed Systems

i) Transparency

Location: a client cannot tell where a file is located

Migration: a file can transparently move to another server

Replication: multiple copies of a file may exist

Concurrency: multiple clients access the same file

ii) Flexibility

In a flexible DFS it must be possible to add or replace file servers. Also, a DFS should support multiple underlying file system types (e.g., various Unix file systems, various Windows file systems, etc.)

iii) Reliability

In a good distributed file system, the probability of loss of stored data should be minimized as far as possible. i.e. users should not feel compelled to make backup copies of their files because of the unreliability of the system. Rather, the file system should automatically generate backup copies of critical files that can be used in the event of loss of the original ones. Stable storage is a popular technique used by several file systems for higher reliability.

iv) Consistency:

Employing replication and allowing concurrent access to files may introduce consistency problems.

v) Security:

Clients must authenticate themselves and servers must determine whether clients are authorized to perform requested operation. Furthermore communication between clients and the file server must be secured.

vi) Fault tolerance:

Clients should be able to continue working if a file server crashes. Likewise, data must not be lost and a restarted file server must be able to recover to a valid state.

vii) Performance:

In order for a DFS to offer good performance it may be necessary to distribute requests across multiple servers. Multiple servers may also be required if the amount of data stored by a file system is very large.

viii) Scalability:

A scalable DFS will avoid centralized components such as a centralized naming service, a centralized locking facility, and a centralized file store. A scalable DFS must be able to handle an increasing number of files and users. It must also be able to

handle growth over a geographic area (e.g., clients that are widely spread over the world), as well as clients from different administrative domains.

b) Client’s Perspective: File Services

The File service interface represents files as an uninterpreted sequence of bytes that are associated with a set of attributes (owner, size, creation date, permissions, etc.) including information regarding protection (i.e., access control lists or capabilities of clients). Moreover, there is a choice between the upload/download model and there mote access model. In the first model, files are downloaded from the server to the client. Modifications are performed directly at the client after which the file is uploaded back to the server. In the second model all operations are performed at the server itself,with clients simply sending commands to the server. There are benefits and drawbacks to both models. The first model, for example, can avoid generating traffic every time it performs operations on a file. Also, a client can potentially use a file even if it cannot access the file server. A drawback of performing operations locally and then sending an updated file back to the server is that concurrent modification of a file by different clients can cause problems. The second approach makes it possible for the file server to order all operations and therefore allow concurrent modifications to the files. A drawback is that the client can only use files if it has contact with the file server. If the file server goes down, or the network connection is broken, then the client loses access to the files.

c) File Access Semantics

Ideally, the client would perceive remote files just like local ones. Unfortunately,the distributed nature of a DFS makes this goal hard to achieve. In the following discussion, we present the various file access semantics available, and discuss how appropriate they are to a DFS.

The first type of access semantics that we consider are called Unix semantics and they imply the following:

 A read after a write returns the value just written.

 When two writes follow in quick succession, the second persists.

In the case of a DFS, it is possible to achieve such semantics if there is only a single file server and no client-side caching is used. In practice, such a system is unrealistic because caches are needed for performance and write-through caches (which would make Unix semantics possible to combine with caching) are expensive. Furthermore deploying only a single file server is bad for scalability. Because of this it is impossible to achieve Unix semantics with distributed file systems.

Alternative semantic models that are better suited for a distributed implementation include:

1. Session Semantics:

In the case of session semantics, changes to an open file are only locally visible. Only after a file is closed, are changes propagated to the server (and other clients). This raises the issue of what happens if two clients modify the same file simultaneously. It is generally up to the server to resolve conflicts and merge the changes. Another problem with session semantics is that parent and child processes cannot share file pointers if they are running on different machines.

2. Immutable Files:

Immutable files cannot be altered after they have been closed. In order to change a file,instead of overwriting the contents of the existing file a new file must be created. This file may then replace the old one as a whole. This approach to modifying files does require that directories (unlike files) be updatable. Problems with this approach include a race condition when two clients try to replace the same file as well as the question of what to do with processes that are reading a file at the same time as it is being replaced by another process.

3. Atomic Transactions:

In the transaction model, a sequence of file manipulations can be executed indivisibly,which implies that two transactions can never interfere. This is the standard model for databases, but it is expensive to implement.

d) Server’s Perspective Implementation

Observation about the expected use of a file system can be used to guide the design of a DFS. For example, a study by Satyanarayanan found the following usage patterns for Unix systems at a university:

Most files are small

–less than 10k

Reading is much more common than writing

Usually access is sequential; random access is rare

Most files have a short lifetime

File sharing is unusual

Most processes use only a few files

Distinct files classes with different properties exist.

These usage patterns (small files, sequential access, high read-write ratio) would suggest that an update/download model for a DFS would be appropriate. Note, however, that different usage patterns may be observed at different kinds of institutions. In situations where the files are large, and are updated more often it may make more sense to use aDFS that implements a remote access model.

Besides the usage characteristics, implementation tradeoffs may depend on the requirements of a DFS. These include supporting a large file system, supporting many users, the need for high performance, and the need for fault tolerance. Thus, for example, a fault tolerant DFS may sacrifice some performance for better reliability guarantees, while a high performance DFS may sacrifice security and wide-area scalability in order to achieve extra performance.

e) Stateful Versus Stateless Servers

The file servers that implement a distributed file service can be stateless or Stateful. Stateless file servers do not store any session state. This means that every client request is treated independently, and not as a part of a new or existing session. Stateful servers, on the other hand, do store session state. They may, therefore, keep track of which clients have opened which files, current read and write pointers for files, which files have been locked by which clients, etc.

The main advantage of stateless servers is that they can easily recover from failure. Because there is no state that must be restored, a failed server can simply restart after a crash and immediately provide services to clients as though nothing happened. Furthermore, if clients crash the server is not stuck with abandoned opened or locked files. Another benefit is that the server implementation remains simple because it does not have to implement the state accounting associated with opening, closing, and locking of files.

The main advantage of Stateful servers, on the other hand, is that they can provide better performance for clients. Because clients do not have to provide full file information every time they perform an operation, the size of messages to and from the server can be significantly decreased. Likewise the server can make use of knowledge of access patterns to perform read-ahead and do other optimizations. Stateful servers can also offer clients extra services such as file locking, and remember read and write positions.

6. Describe the Clock Synchronization Algorithms and Distributed Algorithms in the context of Synchronization.

Ans:

Clock Synchronization Algorithms

Clock synchronization algorithms may be broadly classified as Centralized and Distributed:

Centralized Algorithms

In centralized clock synchronization algorithms one node has a real-time receiver. This node, called the time server node whose clock time is regarded as correct and used as the reference time. The goal of these algorithms is to keep the clocks of all other nodes synchronized with the clock time of the time server node. Depending on the role of the time server node, centralized clock synchronization algorithms are again of two types – Passive Time Sever and Active Time Server.

1. Passive Time Server Centralized Algorithm: In this method each node periodically sends a message to the time server. When the time server receives the message, it quickly responds with a message (“time = T”), where T is the current time in the clock of the time server node. Assume that when the client node sends the “time = ?” message, its clock time is T0, and when it receives the “time = T” message, its clock time is T1. Since T0 and T1 are measured using the same clock, in the absence of any other information, the best estimate of the time required for the propagation of the message “time = T” from the time server node to the client’s node is (T1-T0)/2. Therefore, when the reply is received at the client’s node, its clock is readjusted to T + (T1-T0)/2. 2. Active Time Server Centralized Algorithm: In this approach, the time server periodically broadcasts its clock time (“time = T”). The other nodes receive the broadcast message and use the clock time in the message for correcting their own clocks. Each node has a priori knowledge of the approximate time (Ta) required for the propagation of the message “time = T” from the time server node to its own node, Therefore, when a broadcast message is received at a node, the node’s clock is readjusted to the time T+Ta. A major drawback of this method is that it is not fault tolerant. If the broadcast message reaches too late at a node due to some communication fault, the clock of that node will be readjusted to an incorrect value. Another disadvantage of this approach is that it requires broadcast facility to be supported by the network.
2. Another active time server algorithm that overcomes the drawbacks of the above algorithm is the Berkeley algorithm proposed by Gusella and Zatti for internal synchronization of clocks of a group of computers running the Berkeley UNIX. In this algorithm, the time server periodically sends a message (“time = ?”) to all the computers in the group. On receiving this message, each computer sends back its clock value to the time server. The time server has a priori knowledge of the approximate time required for the propagation of a message from each node to its own node. Based on this knowledge, it first readjusts the clock values of the reply messages, It then takes a fault-tolerant average of the clock values of all the computers (including its own). To take the fault tolerant average, the time server chooses a subset of all clock values that do not differ from one another by more than a specified amount, and the average is taken only for the clock values in this subset. This approach eliminates readings from unreliable clocks whose clock values could have a significant adverse effect if an ordinary average was taken. The calculated average is the current time to which all the clocks should be readjusted, The time server readjusts its own clock to this value, Instead of sending the calculated current time back to other computers, the time server sends the amount by which each individual computer’s clock requires adjustment, This can be a positive or negative value and is calculated based on the knowledge the time server has about the approximate time required for the propagation of a message from each node to its own node.

Centralized clock synchronization algorithms suffer from two major drawbacks:

1. They are subject to single – point failure. If the time server node fails, the clock synchronization operation cannot be performed. This makes the system unreliable. Ideally, a distributed system, should be more reliable than its individual nodes. If one goes down, the rest should continue to function correctly.
2. From a scalability point of view it is generally not acceptable to get all the time requests serviced by a single time server. In a large system, such a solution puts a heavy burden on that one process.

Distributed Algorithms

We know that externally synchronized clocks are also internally synchronized. That is, if each node’s clock is independently synchronized with real time, all the clocks of the system remain mutually synchronized. Therefore, a simple method for clock synchronization may be to equip each node of the system with a real time receiver so that each node’s clock can be independently synchronized with real time. Multiple real time clocks (one for each node) are normally used for this purpose. Theoretically, internal synchronization of clocks is not required in this approach. However, in practice, due to inherent inaccuracy of real-time clocks, different real time clocks produce different time. Therefore, internal synchronization is normally performed for better accuracy. One of the following two approaches is used for internal synchronization in this case.

1. Global Averaging Distributed Algorithms: In this approach, the clock process at each node broadcasts its local clock time in the form of a special “resync” message when its local time equals T0+iR for some integer I, where T0 is a fixed time in the past agreed upon by all nodes and R is a system parameter that depends on such factors as the total number of nodes in the system, the maximum allowable drift rate, and so on. i.e. a resync message is broadcast from each node at the beginning of every fixed length resynchronization interval. However, since the clocks of different nodes run slightly different rates, these broadcasts will not happen simultaneously from all nodes. After broadcasting the clock value, the clock process of a node waits for time T, where T is a parameter to be determined by the algorithm. During this waiting period, the clock process records the time, according to its own clock, when the message was received. At the end of the waiting period, the clock process estimates the skew of its clock with respect to each of the other nodes on the basis of the times at which it received resync messages. It then computes a fault-tolerant average of the next resynchronization interval.
2. The global averaging algorithms differ mainly in the manner in which the fault-tolerant average of the estimated skews is calculated. Two commonly used algorithms are: 1. The simplest algorithm is to take the average of the estimated skews and use it as the correction for the local clock. However, to limit the impact of faulty clocks on the average value, the estimated skew with respect to each node is compared against a threshold, and skews greater than the threshold are set to zero before computing the average of the estimated skews. 2. In another algorithm, each node limits the impact of faulty clocks by first discarding the m highest and m lowest estimated skews and then calculating the average of the remaining skews, which is then used as the correction for the local clock. The value of m is usually decided based on the total number of clocks (nodes).

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