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author | Julian T <julian@jtle.dk> | 2022-01-19 14:40:23 +0100 |
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committer | Julian T <julian@jtle.dk> | 2022-01-19 14:40:53 +0100 |
commit | 1adb9c6114975fe9b25cfb1b18868464d031b061 (patch) | |
tree | eba7b8810818bd25a22251c762bb64d74c42e0b1 /sem7/dist/eksamnen.md | |
parent | 2b780bf79aa3b5d835442687b76ad3c42b2ce44a (diff) |
Add incomplete notes for distributed systems
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diff --git a/sem7/dist/eksamnen.md b/sem7/dist/eksamnen.md new file mode 100644 index 0000000..f10a861 --- /dev/null +++ b/sem7/dist/eksamnen.md @@ -0,0 +1,631 @@ + +# TODO + + - Lav FIFO opgave i exercise5 + - Læs mere om gossip architecture. + - Read about transactions 17(LOW) + +# Distributed Mutual Exclusion + +## Notes + +**Mutual exclusion** is an algorithm that ensures that one and only one process can access a resource at a given time. +Some examples include: + + - Storage + - Printing + - Coffee machines + - Wireless or wired communication + +### System Model + +A computer system is a tuple with a set of states, an initial state, a set of messages, and a transition function. +We will count time as the number of messages/events, as use this as a measure of performance. + +Messages can be sent in two different ways. +**Asynchronous** where messages arrive with arbitrary delays, and where processing time is unknown. +**Synchronous** hard or known limit on delays and a known drift. + +### Mutex Algorithm + +We can set up some requirements for the mutex algorithm + + - **Safety** is when at most one process is given access. + - **Liveness** dictates that requests for access are eventually granted. + - **Ordering/fairness** requires that the ordering of requests should be the order in which they are granted. + +And some properties + + - **Fault tolerance**, what happens when a process chrashes or a message is lost. Does that take the whole system with it. + - **Performance** + - **Message Complexity** is how many messages are required to lock/unlock mutex. + - **Client Delay** time from a request to the grant. + - **Synchronization Delay** time from release of lock to next grant. + +### Central Server Method + +Request for at grant are sent to a central server, which then grants according to a queue. +This is a save and liveness method, however because of the travel time it is not ordered. + +This fails if either a mutex holder or the server fails. + +### Token Ring Method + +Grants are sent in a ring, where each process knowns its next neighbour. +To lock the mutex, we just wait by forwarding the message. + +This is a save and liveness method, however does not uphold the ordering of "requests". +It also fails if just one processor fails. +It also takes up a constant amount of network traffic. + +### Ricart and Agrawala's Algorithm + +Ordering of events is ensured with a lamport clock. + +It works by having processes send requests to all other processes. +Everyone not holding the lock will then grant it access, but a locked process will wait giving access til it is done. + +This does achieve ordering, however it will fail if just one of the processes fails. + +### Meakawas Algorithm + +We do not need everyone to say yes, just some subset. +However we must ensure that all subsets have some overlapping processes. +Therefore processes end up voting for each other. + +However it can deadlock. + +### Detection with Heartbeats + +Assume a transmission or beat every T seconds. +Therefore a process can be assumed dead if not observed in the last `T + D` seconds, where `D` is the transmission delay. + +### Election + +Often we need to chose a process for a central role. +Such as the server in mutual exclusion. +This is done with election, where a process *calls the election*. + +Each process has a chosen elected value, which when undefined is this wierd grounding symbol. + +We have some requirements for election: + + - **Safety**: a participating process has chosen a `undefined` process or a non-crashed process `P`. + Here `P` must have the largest identifier. Here `P` must be the same for all `p_i`'s. + - **Liveness**: all processes must either crash or select some process. + +An *identifier* is just some general value for each progress, which must give some total ordering. + +#### Ring Based Election + +Again we have processes in a ring. +If assuming that no failures occur, we can start the election. +At first no proccess is marked as participating, but a process can call for election by adding ifself as a pariticipant and sendings it's id in an election message. +When receiving a process will just forward if the message identifier is larger than itself. + +Because this works by sequentially sending messages (requiring at most `3*N-1` messages), this is not very fast. +It is also very prone to failure. + +#### Bully Algorithm + +This is different in that each process knowns all other processes with higher id's, and can talk to such processes. + +Processes that know they are the highest can send a `coordinator` message to all lower processes. +If it knows higher processes it can send a `election` message, and wait for an answer. +If no answer comes it will consider itself a coordinator and send `coordinator` message to all lower processes. +It it receives an answer, it will wait for a `coordinator` message. + +This does not work if we replace crashed processes with new processes that have the same id. +Then we can end up with processes electing themselves as coordinator. + +Also in the worst case, where the lowest process detects a failure, the algorithm requires `O(N^2)` messages. + +# Multicast + +Here we assume static and closed groups of processes. + +In the tcp/ip stack we have dedicated ip address ranges for multicasting. +However it may be the case that hardware does not support multicast, and we actually need to each receiver manually. +UDP also has the problem that messages are not ordered and retransmission are not done. + +We can setup some properties for reliable multicast algorithms. + + - **Integrity**: requires that all messages are unique and are only delivered once. + - **Validity**: if a process multicasts message `m`, it will eventually also deliver `m`. + - **Agreement**: if one process delivers message `m`, then all other processes also deliver `m`. + - **Uniform agreement**: if a process, whether it is correct or not, delivers a message `m`, then all correct processes will eventually deliver `m`. + +## Basic Multicast + +Each sender just sends the message to all other participating devices, including itself. + +This has the problem that the sender might fail and send message to a subset of other devices. +Also if using a reliable send mechanism, there will be an ACK explosion. + +## Reliable Multicast + +We introduce a store where we can lookup messages. +Then when we multicast a message, we `b-multicast` to multicast to other devices. +If they receive and they have not seen the message before they multicast the message to everyone else, and delivers to the application. + +This works, however is very expensive. + +## Reliable Multicast over IP + +Here we piggyback acknowledgements in the messages itself, instead of sending acks. +Then when we detect that we miss packets, we use `NACK`. + +This is achieved by each process maintaning a sequence number for each other process (including ifself). +This is then sent along with every message. + +Then each process knows about the next expected message from each device, and can NACK then this skips. + + +## Orderings for Multicast + + - **FIFO ordered**: all messages from `p_n` are received by `p_k` in the order they are sent by `p_n`. + - **Total ordered**: all messages are received in the same order on each process. + - **Causally ordered**: if `p_n` received `m_1` before `m_2`, then `m_1` happened before `m_2`. + +We know that casual order implies FIFO order. +These two are only partial order. + +Total ordering does not imply FIFO og casual, as the order in which everyone agrees can be anything. +We can therefore also have hybrid, such as *FIFO-total*. + +## Implementing Total Ordering + +We can implement total ordering with *sequencer*, as follows. +A single central server is chosen as the sequencer. +Then multicasted messages are held in a buffer at each process until they are instructed to deliver this message by the sequencer. + +This means that the sequencer has complete control over the ordering of messages, enforcing at total order. + +If messages are sent to the sequencer as FIFO, the ordering can be said to be casual. + +Alternatively each process can try to aggree on a sequence number without a central process. +This can be done by letting each receiver propose sequence numbers to the sender. +The sender can then choose the largest, and return this to everyone. + +## Implementing Causal Ordering + +Here we utilize a vector clock to give message order. +We add one to our time each time we send a message, and include our vector in each of our messages. +That way if `a` receives a message `m` from `b`, we will save that message until we have seen all messages from `b` before `m`, and any message `b` has received before sending `m`. + +# Consensus + +We have looked at specific cases of agreeing. +Such as election, ordering, mutual exclusion. +Consensus is a generalization of this. + +Here we consider the case that there may exist *byzentine* processes that try to screw with the consensus. +Here message signing can limit the harm done by such processes. +However, it is assumed that messages are not signed. + +In the consensus problem we have some processes that each draw a value `v_i`. +Then after exchanging some message, they will each decide on a value `d_i`. +We have some requirements for this: + + - **Termination**: Each correct process will decide on a value. + - **Agreement**: All correct processes decide on the same value. + - **Integrity**: If all correct processes propose the same value, that value is also decided by all correct processes. + +## With no Failures + +When failures are impossible, we can just let each process send their `v_i` to everyone else, and then use a majority function to find the most common value. +Here Agreement and Integrity are ensured because of the same majority function on each process. +Termination is also guarantied by the multicast algorithm. + +## Byzentine Generals + +Three or more generals must decide whether to attack or retreat. +But one or more of the generals can be treacharous. + +This differs from normal consensus, in that only one process chooses a value, that the others must agree or disagree with. + +## Interactive Consistency + +Here processes must agree on a vector off values, where each place in the vector represents the decided value of a process. +This is not covered by the slides, and is probably not that important. + +## Consensus in a Synchronous System + +We can get consensus in a synchronous system by using multiple rounds. +Here we let `f` be the maximal number of faulty (not Byzentine) processes. +Then we can reach consensus in `f+1` rounds. + +In each round all processes send values not already sent, and accumulate received values. +In the end a decision is made from the accumulated values. + +Given that this is synchronous we know that it will terminate. +Proof of correctness and thereby agreement and integrity: + +> Assume, to the contrary, that two processes differ in their final set of values. +> Without loss of generality, some correct process p i possesses a value v that another +> correct process p j ( i ≠ j ) does not possess. The only explanation for p i possessing a +> proposed value v at the end that p j does not possess is that any third process, p k , say, +> that managed to send v to p i crashed before v could be delivered to p j . In turn, any +> process sending v in the previous round must have crashed, to explain why p k possesses +> v in that round but p j did not receive it. Proceeding in this way, we have to posit at least +> one crash in each of the preceding rounds. But we have assumed that at most f crashes +> can occur, and there are f + 1 rounds. We have arrived at a contradiction. + +## Byzentine Generals in a Synchronous System + +Here any process may decide to do random stuff, such as sending messages at the wrong time, sending from data, or just not sending anything. +It can be shown that this cannot be solved for `N = 3` or `N \leq 3 * f`. + +The **Byzentine Integrity** requirement requires that if all non-failty processes start with a value, they all decide on that value. + +If there is only one byzentine general, then we can just use majority vote to find a value. +However it there are ties, we find no solution. + +There is also the king algorithm for cases where `N > 4 * f`. +Here each process takes turn at choosing the value for a round. + +## Paxos + +In a async setting we cannot guarantee that there is a solution. + +In paxos once a majority agree on something there is consensus, which will eventually be known by everyone. +Here faulty communication is taken into account. + +In paxos there are 3 roles for processes: + + - **Proposers**: propose values, to reach consensus on. + - **Accepters**: contribute to reaching concensus. + - **Learners**: who learn the agreed on value. + +Nodes can have multiple nodes, or even all of them. +However they can not change these roles. + +1. First a proposer proposes a certian value with a prepare message to all accepters. + These are sent with an ID, such as the timestamp is milliseconds. +2. Then accepters will accept this if they have not promised to ignore this is. + If they accept they promise to ignore any id lover than this. + This is done with a promise message containing that id. +3. If a proposer gets a majority of promise messages it will send accept-request with id and value to all or a majority of acceptors. +4. If a accepter gets an accept-request with an ignored id, it will do nothing. + Otherwise it will send an accept message with the value to all learners. + +There are 3 milestones in this process. + + - A majority of accepters promise that no id over that some id can make it through. + - A majority of accepters accept some id and value. + - A majority of learners and proposers gets majority of accepts on some id. They then know that consensus is on the value. + +There is some extra logic for when a value has already been accepted by a accepter. +Here the promise with also include the last accepted value and id. +The proposer must then create an accept-request with the value with the highest id. + +# Replication + +Employing replication can have some different advantages over just a single device. + + - **Performance**: Instead of everyone pulling from a single server, multiple servers can be employed to serve the same content. + This can give major performance improvements. + - **Availability**: A service should be available for close to 100% of the time. + By using replication multiple services can together give a very high availability of a service. + A second case where networks are split appart (such as a laptop on a train), replication can be used to keep a subset of the service available. + - **Fault tolerance**: Data that is highly available is not always correct. + Fault tolerance guarantees correct behavior up to some number of failing processes. + +A basic model for a replicated system is one where multiple clients talk to a number of frontends. +These frontends can then talk to the service, via a set of replica managers. +This communication is all request response. + +These replica managers are represented as state machines, meaning their state only depends on the operations that have been applied, such as write or read. +In general there are 5 stages in a single operation on replicated objests. + +1. **Request**: A frontend issues a request to one or more replica managers. + This can happen either by sending to a single replica manager which will communicate with the other replicas, or with multicast. +2. **Coordination**: Here replica managers must coordinate how to execute this request consistently, and whether it should be applied. + They will also decide on the ordering of the request in regards to other requests. This comes back to the orderings from before. + Most systems use FIFO ordering. +3. **Execution**: The managers execute the request. This can be done *tentatively* such that they can undo the effects later. +4. **Agreement**: The managers reach consensus on the effects of the request to be committed.. +5. **Response**: One or more managers send a response to the frontend. This can use majority voting to combat Byzentine failures. + +## Consistency + +We want to make sure that our whole system functions like it would if there was only a single server. +For example if client 1 writes to `x = 1` and `y = 2`, then it makes no sense if another client first reads `y = 2` and then `x = 0`. +This is because `x` is written before `y`, so given that `y` is read correctly `x` should also be. + +Here we introduce the property that the system is *linearizable*. +A replicated shared object service is then linearizable if there is some interleaving of operations issued by all clients, such that + - we arrive at a (single) correct copy of the object, + - and the order is consistent with real time. + +However this is very hard because the real-time requirement requires accurate synchonized clocks. +Therefore the weaker *sequential consistency* captures some of the same order requirements without using a real-time clock. +It requires that + - we arrive at a (single) correct copy of the object, + - and the order in the interleaving is consistent with the order in which the induvidual clients executed operations in. + +This means that operations can be shuffled around as much as we, as long as we respect the ordering of the induvidual clients. + +## Passive Replication + +Here we choose a single manager which talks to all frontends. +After executing the request, it will push the update to all other managers. + +If the primary crashes then operation will happen on a backup. + +Does not handle Byzentine very well. + +## Active Replication + +Here the frontend sends the request to all managers with total ordered reliable multicast. +After executing and updating, each manager will respond with the result. +Because of majority voting we can handle up to `(n/2) - 1` Byzentine failures. + +Here the frontend waits on the response before sending the next request. +Therefore FIFO ordering is ensured in regards to the frontends. + +If clients can talk together we would need to use a casually totally ordered multicast. + +## Gossip Framework + +Here data is replicated between managers periodically. +Therefore we only need to read or write to a single manager. + +Here we can guarantee some relaxes consistency in that + - operations are eventually applied with some specific order, + - and clients can receive outdated data but newer older than the clients current data. + +Here reads are causually ordered while writes can be causal order, total-causal order, or immediate order. +Immediate order updates are applied consistenly in order to any other update. +Here causal order is the cheapest to implement. + +Vector clocks are used to ensure this, with each replica tracking the number of unique updates + +# Distributed Storage + +## GFS + +Has a single *GFS master* which contains the file namespace, pointing filenames to chunks. +Will return the chunk handle and location to the client. + +The client can then request the clunk from one of the many *chunk servers*. + +Because filenamespace are kept on master, mutations of this is atomic. +The master also handles replica management, allocating new chunks, or reallocating when there is not enough replication. +Also handles garbage collection and balancing of chunks. + +Log and state of master is also replicated in stable storage, such that it is fast and easy to recover. +There are also *shadow masters*, providing read only access. +External services can start new master if it detects failure in main master. + +Writes are done by having the master select a primary replica, which will determine the order things are applied in. +This works like passive replication only that data is written to the all the replicas by the client, but the operation is only given to the primary. +One should note that multiple writes at the same location can not be applied together, as appends can. + +## Chubby + +For very small files such as locks etc. +Can be used for stuff like master election, where processes write to file, and the one is written is the master. +Because files are small, there is whole file read and write, instead of chunks. + +Communication with clients happen through a master, which then forwards onto replicas. +Clients can find the master using DNS, or with other non-masters refering to master. +Clients will keep using a master until a negative answer. + +Reads are handled by master, while writes are done like paxos. + +*Sessions* are mentained between a master and client, with keep alive(eg. 12 seconds). +If session is lost server releases handles held by client. +If a client does not get a renew on lease, session is *in jeopardy*. +Here cache is cleared, and a grace period is done before trying again. + +Clients cache content of files, to reduce traffic. +Invalidation is then piggybacked on the keep-alive. Flush of cache is ack'ed in lease reneval. + +Master relection is done with paxos, and updated in DNS by new master. + +## BigTable + +DIstributed storage of table. +Works kind of like a map: + +```haskell +(String, String, Int64) -> String -- (row, column, time) -> content +``` + +In google it is used to store + + - Analytics, where each row is a user. + - Earth, where each row is a location and column in a source. + - Personlized serach, where row is user and column is action type. + + +A *tablets* is a set of rows, with a size of around 200Mb. +These can be merged of split depending on their size. +Each tables is stored by a *Tables server*, similar to a gfs chunkserver. +Storage is done with the *Sorted String tables* file format from GFS. +Provides atomic row access. + +Like GFS also uses a single master, and a set of servers. +Master and server use chubby for lock files etc, and GFS for storage of table data and logs. + +Searching is done with B+tree index. +Clients search this index and caches tablet locations. + +# Big Data Analytics + +The 4 v's + + - **Volume**: the large scale of data collected and processes. + - **Velocity**: the timeliness?? of data and analysis. + - **Variety**: different types of data, semi-structured or unstructured (such as text). + - **Value**: a lot of data, but with low density. + +Often when data is collected we need to do a large amount of processing to make it usefull. +With the massive volumes of data this is not practical on a single computer. + +Therefore we develop new methods for storing (GFS, NoSQL), and programming/processing (Map reduce and Pregel). + +Sawzall is a bit like map reduce, only in that there are many filter tasks, and then a single aggregator. + +## Map Reduce + +Inspired by the two functions from functional programming. +Here we as a programmer must introduce two functions: + + - **Map**: takes input data and produces `(key, value)` pairs. + - **Reduce**: takes all values with the same key and produces a result. + +In between the map and reduce we have a *shuffle phase* which collects the results up so tuples with the same key are together. +This shuffle phase involves the network. + +For the execution we introduce a *master* which assigns the function applications to workers. +When a map is done the result is written to disk, and the location is returned to the master. + +The master must take into consideration the + + - **Locality** of the data in regards to the worker. + - **Granularity** in that the number of map and reduce tasks should be much higher than the number of workers. + - **Stragglers** in that large systems always has workers that are slower, and the master should schedule around this. + - **Pipelining** can we start reducing while still mapping other data? + - **Failures** when a worker fails, the job should be done by somebody else. + +When the master fails there is not much to do, so we terminate the whole job. + +## Spark + +Lets programmers write parallel computations easily with high level operations, without having to handle work distribution and fault tolerance. +However does not make it easy to handle memory, and is therefore hard to reuse results (as in graph algorithms, pagerank, regression). + +Here we can use RDD or Resilient Distributed Datasets. +Here datasets are saved in immutable partitioned collections of records. +This is then used to store intermediary results. +Also provides operators like map, filter and join. + +RDD have dependencies, where rows depend on other rows. +With map, union and joins give *narrow dependencies* where each row in the operands is used by at most one row in the result. +*Wide dependencies* is when this is not true, and happens for `groupByKey`. + +## Pregel + +Like spark/RDD but tailored to graph computations. +Also has a in memory store to keep intermediary results. + +The computational model is *vertex-centric* where program are a sequence of iterations, where in each a vertex can change state or send messages to other vertices. +The algorithm halts when all vertices want to halt. +Here it's beneficial to also have the number of vertices be much larger than the number of processes. + +Vertices start out in a active state, and can deactivate by voting to halt. +They can be reactivated when they get a message. + +Page rank is a graph algorithm. + +Also uses a single master many workers thing. + +# Blockchains + +**Merkle trees** are trees build on hashes. +So leaves are hashes of the content, and internal nodes are hashes of children. +Used by git for example. + +For a binary merkle tree, calculating the root takes `2N` hashes. + +**Blockchain** works like this tamper proof linked list. +Given that it is distrubuted, it has some nice properties: + + - **Consistency**: Information is held of shared distributed database. + - **Robustness**: No centralized version that can be hacked. + - **Availability**: Data is stored by millions of computers and can be verified by everyone. + +All nodes contain a full copy of the blockchain, and validate and relay data. + +We can prevent double spending by disallowing forks and checking if there is anough money. +How do we choose the newest head, we can't use paxos because hacker can just create 1000 new identities. +Creating identities is cheap, we need something expensive (like hashing (spoiler (triple parenteser, nice))). + +(*Nakamoto Consensus*) Blockchain has the rule that the longest blockchain has consensus. +Therefore we can ignore all chains that are shorter than my own. +By making it hard to add blocks, we trust blocks that are burried. + +By making it hard to add blocks, hackers have a hard to make a competing fork as they have to work against all other miners. +To make it hard we use a nonce on each block. +Then the hash of the block must start with x amount of 0's. + +A bitcoin user is someone who can transfer money, and has a wallet or identity. +This identity is just a key pair. + +A transaction has multiple inputs and outputs (with distribution) and then signatures of inputs. +More generally they use scripts which often contain signatures, but can also be a small non-turing complete program. +These transactions are then stored in a merkle tree, with the root being in the block. + +Each transaction has a small difference in the ingoing and outgoing money. +This is the fee to the miner who finds the nonce. +Also miners get some bitcoin for each nonce they find. + +## Smart Contracts + +Bassicly an extension of the challenge scripts in the bitcoin transactions. +Extended in ethereum. + +Here it is turing complete, but the script runs on gas, which can run out. + +# Peer-to-peer networks + +**Overlay network** is a set of nodes and links built on top of a existing network. +This overlay network can add features that are not present in the underlying network, such as extra service, routing, multicast or enhanced security. + +Here are some types of overlay networks + + - **Distributed hash tables** (application needs): offers a service where one can map keys to values. + - **Peer to peer file sharing** (application needs): offers easier addressing and routing to support downloading of files etc. + - **Content delivery networks** (application needs): provides replication, caching and placement strategies for delivering content. + - **Wireless and adhoc networks** (Network style) + - **Multicast** (extra features) + +The classic client server architecture has some limitations in terms of scalability and reliability. +Here one possible solution is peer to peer. +Peer to peer solves many problems but is often more complicated. +Because networks are often public it is hard to stop some people from exploiting the rest (*free-riding*). + +Peer to peer networks can be descibed as a set of automonous entities (peers) that are able to auto-organize and share some distributed resources. +Most peer to peer networks can be put in 3 categories: + + - **Distributed computing** + - **File sharing** + - **Collaborative applications** + +With filesharing there is a very common set of primitives: join, publish, search and fetch. + +## Napster and Centralized Peer to Peer + +Napster allows users to download free music over the internet. +Because it is impossible for the napster server to contain all the content on one machine, napster employs a peer to peer system to store music files. + +However for simplicity napster has a centralized index server, where users can find which peer has which files. +This has the advantage of allowing easier and nicer search and indexing, at the cost of robustness and scalability. + +## Unstructured Peer to Peer + +Used by the gnutella file sharing program. +Works which query flooding, where a client ask other known clients about a file and they ask their known clients and so on. +When the file is found, the client can directly contact the file holder and download the file (via HTTP). +Here known clients are established from a bootstrap node. + +HTTP has the advantage of being allowed by many firewalls, and can do partial file transfer. + +Gnutella has the advantage of being totally decentralized, and thus very robust. +However its flooding nature does not make it very scalable. +And free-loading can download but no answer queries. + +A newer protocol, *fasttrack*, tries to solve some of these issues. +Here some peers are designated as *supernode* (or *ultrapeers*). + +In fasttrack when joining the client contract a supernode. +It can use this node to publish files. +Then when querying, the client only asks the supernode which will flood the request to all other supernodes (not normal peers). +Peers with enough reputation can themselves become supernodes. + +## Structured Peer to Peer + +# Iot and Routing in IoT + |