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The System Design Primer


Motivation

Learn how to design large scale systems.

Prep for the system design interview.

Learn how to design large scale systems

Learning how to design scalable systems will help you become a better engineer.

System design is a broad topic. There is a vast amount of resources scattered throughout the web on system design principles.

This repo is an organized collection of resources to help you learn how to build systems at scale.

Learn from the open source community

This is an early draft of a continually updated, open source project.

Contributions are welcome!

Prep for the system design interview

In addition to coding interviews, system design is a required component of the technical interview process at many tech companies.

Practice common system design interview questions and compare your results with sample solutions: discussions, code, and diagrams.

Additional topics for interview prep:

Anki flashcards


The provided Anki flashcard decks use spaced repetition to help you retain key system design concepts.

Great for use while on-the-go.

Contributing

Learn from the community.

Feel free to submit pull requests to help:

  • Fix errors
  • Improve sections
  • Add new sections

Content that needs some polishing is placed under development.

Review the Contributing Guidelines.

Translations

Interested in translating? Please see the following ticket.

Index of system design topics

Summaries of various system design topics, including pros and cons. Everything is a trade-off.

Each section contains links to more in-depth resources.


Study guide

Suggested topics to review based on your interview timeline (short, medium, long).

Imgur

Q: For interviews, do I need to know everything here?

A: No, you don't need to know everything here to prepare for the interview.

What you are asked in an interview depends on variables such as:

  • How much experience you have
  • What your technical background is
  • What positions you are interviewing for
  • Which companies you are interviewing with
  • Luck

More experienced candidates are generally expected to know more about system design. Architects or team leads might be expected to know more than individual contributors. Top tech companies are likely to have one or more design interview rounds.

Start broad and go deeper in a few areas. It helps to know a little about various key system design topics. Adjust the following guide based on your timeline, experience, what positions you are interviewing for, and which companies you are interviewing with.

  • Short timeline - Aim for breadth with system design topics. Practice by solving some interview questions.
  • Medium timeline - Aim for breadth and some depth with system design topics. Practice by solving many interview questions.
  • Long timeline - Aim for breadth and more depth with system design topics. Practice by solving most interview questions.
Short Medium Long
Read through the System design topics to get a broad understanding of how systems work 👍 👍 👍
Read through a few articles in the Company engineering blogs for the companies you are interviewing with 👍 👍 👍
Read through a few Real world architectures 👍 👍 👍
Review How to approach a system design interview question 👍 👍 👍
Work through System design interview questions with solutions Some Many Most
Work through Object-oriented design interview questions with solutions Some Many Most
Review Additional system design interview questions Some Many Most

How to approach a system design interview question

How to tackle a system design interview question.

The system design interview is an open-ended conversation. You are expected to lead it.

You can use the following steps to guide the discussion. To help solidify this process, work through the System design interview questions with solutions section using the following steps.

Step 1: Outline use cases, constraints, and assumptions

Gather requirements and scope the problem. Ask questions to clarify use cases and constraints. Discuss assumptions.

  • Who is going to use it?
  • How are they going to use it?
  • How many users are there?
  • What does the system do?
  • What are the inputs and outputs of the system?
  • How much data do we expect to handle?
  • How many requests per second do we expect?
  • What is the expected read to write ratio?

Step 2: Create a high level design

Outline a high level design with all important components.

  • Sketch the main components and connections
  • Justify your ideas

Step 3: Design core components

Dive into details for each core component. For example, if you were asked to design a url shortening service, discuss:

  • Generating and storing a hash of the full url
    • MD5 and Base62
    • Hash collisions
    • SQL or NoSQL
    • Database schema
  • Translating a hashed url to the full url
    • Database lookup
  • API and object-oriented design

Step 4: Scale the design

Identify and address bottlenecks, given the constraints. For example, do you need the following to address scalability issues?

  • Load balancer
  • Horizontal scaling
  • Caching
  • Database sharding

Discuss potential solutions and trade-offs. Everything is a trade-off. Address bottlenecks using principles of scalable system design.

Back-of-the-envelope calculations

You might be asked to do some estimates by hand. Refer to the Appendix for the following resources:

Source(s) and further reading

Check out the following links to get a better idea of what to expect:

System design interview questions with solutions

Common system design interview questions with sample discussions, code, and diagrams.

Solutions linked to content in the solutions/ folder.

Question
Design Pastebin.com (or Bit.ly) Solution
Design the Twitter timeline (or Facebook feed)
Design Twitter search (or Facebook search)
Solution
Design a web crawler Solution
Design Mint.com Solution
Design the data structures for a social network Solution
Design a key-value store for a search engine Solution
Design Amazon's sales ranking by category feature Solution
Design a system that scales to millions of users on AWS Solution
Add a system design question Contribute

Design Pastebin.com (or Bit.ly)

View exercise and solution

Imgur

View exercise and solution

Imgur

Design a web crawler

View exercise and solution

Imgur

Design Mint.com

View exercise and solution

Imgur

Design the data structures for a social network

View exercise and solution

Imgur

Design a key-value store for a search engine

View exercise and solution

Imgur

Design Amazon's sales ranking by category feature

View exercise and solution

Imgur

Design a system that scales to millions of users on AWS

View exercise and solution

Imgur

Object-oriented design interview questions with solutions

Common object-oriented design interview questions with sample discussions, code, and diagrams.

Solutions linked to content in the solutions/ folder.

Note: This section is under development

Question
Design a hash map Solution
Design a least recently used cache Solution
Design a call center Solution
Design a deck of cards Solution
Design a parking lot Solution
Design a chat server Solution
Design a circular array Contribute
Add an object-oriented design question Contribute

System design topics: start here

New to system design?

First, you'll need a basic understanding of common principles, learning about what they are, how they are used, and their pros and cons.

Step 1: Review the scalability video lecture

Scalability Lecture at Harvard

  • Topics covered:
    • Vertical scaling
    • Horizontal scaling
    • Caching
    • Load balancing
    • Database replication
    • Database partitioning

Step 2: Review the scalability article

Scalability

Next steps

Next, we'll look at high-level trade-offs:

  • Performance vs scalability
  • Latency vs throughput
  • Availability vs consistency

Keep in mind that everything is a trade-off.

Then we'll dive into more specific topics such as DNS, CDNs, and load balancers.

Performance vs scalability

A service is scalable if it results in increased performance in a manner proportional to resources added. Generally, increasing performance means serving more units of work, but it can also be to handle larger units of work, such as when datasets grow.1

Another way to look at performance vs scalability:

  • If you have a performance problem, your system is slow for a single user.
  • If you have a scalability problem, your system is fast for a single user but slow under heavy load.

Source(s) and further reading

Latency vs throughput

Latency is the time to perform some action or to produce some result.

Throughput is the number of such actions or results per unit of time.

Generally, you should aim for maximal throughput with acceptable latency.

Source(s) and further reading

Availability vs consistency

CAP theorem


Source: CAP theorem revisited

In a distributed computer system, you can only support two of the following guarantees:

  • Consistency - Every read receives the most recent write or an error
  • Availability - Every request receives a response, without guarantee that it contains the most recent version of the information
  • Partition Tolerance - The system continues to operate despite arbitrary partitioning due to network failures

Networks aren't reliable, so you'll need to support partition tolerance. You'll need to make a software tradeoff between consistency and availability.

CP - consistency and partition tolerance

Waiting for a response from the partitioned node might result in a timeout error. CP is a good choice if your business needs require atomic reads and writes.

AP - availability and partition tolerance

Responses return the most recent version of the data, which might not be the latest. Writes might take some time to propagate when the partition is resolved.

AP is a good choice if the business needs allow for eventual consistency or when the system needs to continue working despite external errors.

Source(s) and further reading

Consistency patterns

With multiple copies of the same data, we are faced with options on how to synchronize them so clients have a consistent view of the data. Recall the definition of consistency from the CAP theorem - Every read receives the most recent write or an error.

Weak consistency

After a write, reads may or may not see it. A best effort approach is taken.

This approach is seen in systems such as memcached. Weak consistency works well in real time use cases such as VoIP, video chat, and realtime multiplayer games. For example, if you are on a phone call and lose reception for a few seconds, when you regain connection you do not hear what was spoken during connection loss.

Eventual consistency

After a write, reads will eventually see it (typically within milliseconds). Data is replicated asynchronously.

This approach is seen in systems such as DNS and email. Eventual consistency works well in highly available systems.

Strong consistency

After a write, reads will see it. Data is replicated synchronously.

This approach is seen in file systems and RDBMSes. Strong consistency works well in systems that need transactions.

Source(s) and further reading

Availability patterns

There are two main patterns to support high availability: fail-over and replication.

Fail-over

Active-passive

With active-passive fail-over, heartbeats are sent between the active and the passive server on standby. If the heartbeat is interrupted, the passive server takes over the active's IP address and resumes service.

The length of downtime is determined by whether the passive server is already running in 'hot' standby or whether it needs to start up from 'cold' standby. Only the active server handles traffic.

Active-passive failover can also be referred to as master-slave failover.

Active-active

In active-active, both servers are managing traffic, spreading the load between them.

If the servers are public-facing, the DNS would need to know about the public IPs of both servers. If the servers are internal-facing, application logic would need to know about both servers.

Active-active failover can also be referred to as master-master failover.

Disadvantage(s): failover

  • Fail-over adds more hardware and additional complexity.
  • There is a potential for loss of data if the active system fails before any newly written data can be replicated to the passive.

Replication

Master-slave and master-master

This topic is further discussed in the Database section:

Domain name system


Source: DNS security presentation

A Domain Name System (DNS) translates a domain name such as www.example.com to an IP address.

DNS is hierarchical, with a few authoritative servers at the top level. Your router or ISP provides information about which DNS server(s) to contact when doing a lookup. Lower level DNS servers cache mappings, which could become stale due to DNS propagation delays. DNS results can also be cached by your browser or OS for a certain period of time, determined by the time to live (TTL).

  • NS record (name server) - Specifies the DNS servers for your domain/subdomain.
  • MX record (mail exchange) - Specifies the mail servers for accepting messages.
  • A record (address) - Points a name to an IP address.
  • CNAME (canonical) - Points a name to another name or CNAME (example.com to www.example.com) or to an A record.

Services such as CloudFlare and Route 53 provide managed DNS services. Some DNS services can route traffic through various methods:

  • Weighted round robin
    • Prevent traffic from going to servers under maintenance
    • Balance between varying cluster sizes
    • A/B testing
  • Latency-based
  • Geolocation-based

Disadvantage(s): DNS

  • Accessing a DNS server introduces a slight delay, although mitigated by caching described above.
  • DNS server management could be complex, although they are generally managed by governments, ISPs, and large companies.
  • DNS services have recently come under DDoS attack, preventing users from accessing websites such as Twitter without knowing Twitter's IP address(es).

Source(s) and further reading

Content delivery network


Source: Why use a CDN

A content delivery network (CDN) is a globally distributed network of proxy servers, serving content from locations closer to the user. Generally, static files such as HTML/CSS/JS, photos, and videos are served from CDN, although some CDNs such as Amazon's CloudFront support dynamic content. The site's DNS resolution will tell clients which server to contact.

Serving content from CDNs can significantly improve performance in two ways:

  • Users receive content at data centers close to them
  • Your servers do not have to serve requests that the CDN fulfills

Push CDNs

Push CDNs receive new content whenever changes occur on your server. You take full responsibility for providing content, uploading directly to the CDN and rewriting URLs to point to the CDN. You can configure when content expires and when it is updated. Content is uploaded only when it is new or changed, minimizing traffic, but maximizing storage.

Sites with a small amount of traffic or sites with content that isn't often updated work well with push CDNs. Content is placed on the CDNs once, instead of being re-pulled at regular intervals.

Pull CDNs

Pull CDNs grab new content from your server when the first user requests the content. You leave the content on your server and rewrite URLs to point to the CDN. This results in a slower request until the content is cached on the server.

A time-to-live (TTL) determines how long content is cached. Pull CDNs minimize storage space on the CDN, but can create redundant traffic if files expire and are pulled before they have actually changed.

Sites with heavy traffic work well with pull CDNs, as traffic is spread out more evenly with only recently-requested content remaining on the CDN.

Disadvantage(s): CDN

  • CDN costs could be significant depending on traffic, although this should be weighed with additional costs you would incur not using a CDN.
  • Content might be stale if it is updated before the TTL expires it.
  • CDNs require changing URLs for static content to point to the CDN.

Source(s) and further reading

Load balancer


Source: Scalable system design patterns

Load balancers distribute incoming client requests to computing resources such as application servers and databases. In each case, the load balancer returns the response from the computing resource to the appropriate client. Load balancers are effective at:

  • Preventing requests from going to unhealthy servers
  • Preventing overloading resources
  • Helping eliminate single points of failure

Load balancers can be implemented with hardware (expensive) or with software such as HAProxy.

Additional benefits include:

  • SSL termination - Decrypt incoming requests and encrypt server responses so backend servers do not have to perform these potentially expensive operations
  • Session persistence - Issue cookies and route a specific client's requests to same instance if the web apps do not keep track of sessions

To protect against failures, it's common to set up multiple load balancers, either in active-passive or active-active mode.

Load balancers can route traffic based on various metrics, including:

Layer 4 load balancing

Layer 4 load balancers look at info at the transport layer to decide how to distribute requests. Generally, this involves the source, destination IP addresses, and ports in the header, but not the contents of the packet. Layer 4 load balancers forward network packets to and from the upstream server, performing Network Address Translation (NAT).

layer 7 load balancing

Layer 7 load balancers look at the application layer to decide how to distribute requests. This can involve contents of the header, message, and cookies. Layer 7 load balancers terminates network traffic, reads the message, makes a load-balancing decision, then opens a connection to the selected server. For example, a layer 7 load balancer can direct video traffic to servers that host videos while directing more sensitive user billing traffic to security-hardened servers.

At the cost of flexibility, layer 4 load balancing requires less time and computing resources than Layer 7, although the performance impact can be minimal on modern commodity hardware.

Horizontal scaling

Load balancers can also help with horizontal scaling, improving performance and availability. Scaling out using commodity machines is more cost efficient and results in higher availability than scaling up a single server on more expensive hardware, called Vertical Scaling. It is also easier to hire for talent working on commodity hardware than it is for specialized enterprise systems.

Disadvantage(s): horizontal scaling

  • Scaling horizontally introduces complexity and involves cloning servers
    • Servers should be stateless: they should not contain any user-related data like sessions or profile pictures
    • Sessions can be stored in a centralized data store such as a database (SQL, NoSQL) or a persistent cache (Redis, Memcached)
  • Downstream servers such as caches and databases need to handle more simultaneous connections as upstream servers scale out

Disadvantage(s): load balancer

  • The load balancer can become a performance bottleneck if it does not have enough resources or if it is not configured properly.
  • Introducing a load balancer to help eliminate single points of failure results in increased complexity.
  • A single load balancer is a single point of failure, configuring multiple load balancers further increases complexity.

Source(s) and further reading

Reverse proxy (web server)


Source: Wikipedia

A reverse proxy is a web server that centralizes internal services and provides unified interfaces to the public. Requests from clients are forwarded to a server that can fulfill it before the reverse proxy returns the server's response to the client.

Additional benefits include:

  • Increased security - Hide information about backend servers, blacklist IPs, limit number of connections per client
  • Increased scalability and flexibility - Clients only see the reverse proxy's IP, allowing you to scale servers or change their configuration
  • SSL termination - Decrypt incoming requests and encrypt server responses so backend servers do not have to perform these potentially expensive operations
  • Compression - Compress server responses
  • Caching - Return the response for cached requests
  • Static content - Serve static content directly
    • HTML/CSS/JS
    • Photos
    • Videos
    • Etc

Load balancer vs reverse proxy

  • Deploying a load balancer is useful when you have multiple servers. Often, load balancers route traffic to a set of servers serving the same function.
  • Reverse proxies can be useful even with just one web server or application server, opening up the benefits described in the previous section.
  • Solutions such as NGINX and HAProxy can support both layer 7 reverse proxying and load balancing.

Disadvantage(s): reverse proxy

  • Introducing a reverse proxy results in increased complexity.
  • A single reverse proxy is a single point of failure, configuring multiple reverse proxies (ie a failover) further increases complexity.

Source(s) and further reading

Application layer


Source: Intro to architecting systems for scale

Separating out the web layer from the application layer (also known as platform layer) allows you to scale and configure both layers independently. Adding a new API results in adding application servers without necessarily adding additional web servers.

The single responsibility principle advocates for small and autonomous services that work together. Small teams with small services can plan more aggressively for rapid growth.

Workers in the application layer also help enable asynchronism.

Microservices

Related to this discussion are microservices, which can be described as a suite of independently deployable, small, modular services. Each service runs a unique process and communicates through a well-defined, lightweight mechanism to serve a business goal. 1

Pinterest, for example, could have the following microservices: user profile, follower, feed, search, photo upload, etc.

Service Discovery

Systems such as Zookeeper can help services find each other by keeping track of registered names, addresses, ports, etc.

Disadvantage(s): application layer

  • Adding an application layer with loosely coupled services requires a different approach from an architectural, operations, and process viewpoint (vs a monolithic system).
  • Microservices can add complexity in terms of deployments and operations.

Source(s) and further reading

Database


Source: Scaling up to your first 10 million users

Relational database management system (RDBMS)

A relational database like SQL is a collection of data items organized in tables.

ACID is a set of properties of relational database transactions.

  • Atomicity - Each transaction is all or nothing
  • Consistency - Any transaction will bring the database from one valid state to another
  • Isolation - Executing transactions concurrently has the same results as if the transactions were executed serially
  • Durability - Once a transaction has been committed, it will remain so

There are many techniques to scale a relational database: master-slave replication, master-master replication, federation, sharding, denormalization, and SQL tuning.

Master-slave replication

The master serves reads and writes, replicating writes to one or more slaves, which serve only reads. Slaves can also replicate to additional slaves in a tree-like fashion. If the master goes offline, the system can continue to operate in read-only mode until a slave is promoted to a master or a new master is provisioned.


Source: Scalability, availability, stability, patterns

Disadvantage(s): master-slave replication
  • Additional logic is needed to promote a slave to a master.
  • See Disadvantage(s): replication for points related to both master-slave and master-master.

Master-master replication

Both masters serve reads and writes and coordinate with each other on writes. If either master goes down, the system can continue to operate with both reads and writes.


Source: Scalability, availability, stability, patterns

Disadvantage(s): master-master replication
  • You'll need a load balancer or you'll need to make changes to your application logic to determine where to write.
  • Most master-master systems are either loosely consistent (violating ACID) or have increased write latency due to synchronization.
  • Conflict resolution comes more into play as more write nodes are added and as latency increases.
  • See Disadvantage(s): replication for points related to both master-slave and master-master.
Disadvantage(s): replication
  • There is a potential for loss of data if the master fails before any newly written data can be replicated to other nodes.
  • Writes are replayed to the read replicas. If there are a lot of writes, the read replicas can get bogged down with replaying writes and can't do as many reads.
  • The more read slaves, the more you have to replicate, which leads to greater replication lag.
  • On some systems, writing to the master can spawn multiple threads to write in parallel, whereas read replicas only support writing sequentially with a single thread.
  • Replication adds more hardware and additional complexity.
Source(s) and further reading: replication

Federation


Source: Scaling up to your first 10 million users

Federation (or functional partitioning) splits up databases by function. For example, instead of a single, monolithic database, you could have three databases: forums, users, and products, resulting in less read and write traffic to each database and therefore less replication lag. Smaller databases result in more data that can fit in memory, which in turn results in more cache hits due to improved cache locality. With no single central master serializing writes you can write in parallel, increasing throughput.

Disadvantage(s): federation
  • Federation is not effective if your schema requires huge functions or tables.
  • You'll need to update your application logic to determine which database to read and write.
  • Joining data from two databases is more complex with a server link.
  • Federation adds more hardware and additional complexity.
Source(s) and further reading: federation

Sharding


Source: Scalability, availability, stability, patterns

Sharding distributes data across different databases such that each database can only manage a subset of the data. Taking a users database as an example, as the number of users increases, more shards are added to the cluster.

Similar to the advantages of federation, sharding results in less read and write traffic, less replication, and more cache hits. Index size is also reduced, which generally improves performance with faster queries. If one shard goes down, the other shards are still operational, although you'll want to add some form of replication to avoid data loss. Like federation, there is no single central master serializing writes, allowing you to write in parallel with increased throughput.

Common ways to shard a table of users is either through the user's last name initial or the user's geographic location.

Disadvantage(s): sharding
  • You'll need to update your application logic to work with shards, which could result in complex SQL queries.
  • Data distribution can become lopsided in a shard. For example, a set of power users on a shard could result in increased load to that shard compared to others.
    • Rebalancing adds additional complexity. A sharding function based on consistent hashing can reduce the amount of transferred data.
  • Joining data from multiple shards is more complex.
  • Sharding adds more hardware and additional complexity.
Source(s) and further reading: sharding

Denormalization

Denormalization attempts to improve read performance at the expense of some write performance. Redundant copies of the data are written in multiple tables to avoid expensive joins. Some RDBMS such as PostgreSQL and Oracle support materialized views which handle the work of storing redundant information and keeping redundant copies consistent.

Once data becomes distributed with techniques such as federation and sharding, managing joins across data centers further increases complexity. Denormalization might circumvent the need for such complex joins.

In most systems, reads can heavily number writes 100:1 or even 1000:1. A read resulting in a complex database join can be very expensive, spending a significant amount of time on disk operations.

Disadvantage(s): denormalization
  • Data is duplicated.
  • Constraints can help redundant copies of information stay in sync, which increases complexity of the database design.
  • A denormalized database under heavy write load might perform worse than its normalized counterpart.
Source(s) and further reading: denormalization

SQL tuning

SQL tuning is a broad topic and many books have been written as reference.

It's important to benchmark and profile to simulate and uncover bottlenecks.

  • Benchmark - Simulate high-load situations with tools such as ab.
  • Profile - Enable tools such as the slow query log to help track performance issues.

Benchmarking and profiling might point you to the following optimizations.

Tighten up the schema
  • MySQL dumps to disk in contiguous blocks for fast access.
  • Use CHAR instead of VARCHAR for fixed-length fields.
    • CHAR effectively allows for fast, random access, whereas with VARCHAR, you must find the end of a string before moving onto the next one.
  • Use TEXT for large blocks of text such as blog posts. TEXT also allows for boolean searches. Using a TEXT field results in storing a pointer on disk that is used to locate the text block.
  • Use INT for larger numbers up to 2^32 or 4 billion.
  • Use DECIMAL for currency to avoid floating point representation errors.
  • Avoid storing large BLOBS, store the location of where to get the object instead.
  • VARCHAR(255) is the largest number of characters that can be counted in an 8 bit number, often maximizing the use of a byte in some RDBMS.
  • Set the NOT NULL constraint where applicable to improve search performance.
Use good indices
  • Columns that you are querying (SELECT, GROUP BY, ORDER BY, JOIN) could be faster with indices.
  • Indices are usually represented as self-balancing B-tree that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time.
  • Placing an index can keep the data in memory, requiring more space.
  • Writes could also be slower since the index also needs to be updated.
  • When loading large amounts of data, it might be faster to disable indices, load the data, then rebuild the indices.
Avoid expensive joins
Partition tables
  • Break up a table by putting hot spots in a separate table to help keep it in memory.
Tune the query cache
Source(s) and further reading: SQL tuning

NoSQL

NoSQL is a collection of data items represented in a key-value store, document-store, wide column store, or a graph database. Data is denormalized, and joins are generally done in the application code. Most NoSQL stores lack true ACID transactions and favor eventual consistency.

BASE is often used to describe the properties of NoSQL databases. In comparison with the CAP Theorem, BASE chooses availability over consistency.

  • Basically available - the system guarantees availability.
  • Soft state - the state of the system may change over time, even without input.
  • Eventual consistency - the system will become consistent over a period of time, given that the system doesn't receive input during that period.

In addition to choosing between SQL or NoSQL, it is helpful to understand which type of NoSQL database best fits your use case(s). We'll review key-value stores, document-stores, wide column stores, and graph databases in the next section.

Key-value store

Abstraction: hash table

A key-value store generally allows for O(1) reads and writes and is often backed by memory or SSD. Data stores can maintain keys in lexicographic order, allowing efficient retrieval of key ranges. Key-value stores can allow for storing of metadata with a value.

Key-value stores provide high performance and are often used for simple data models or for rapidly-changing data, such as an in-memory cache layer. Since they offer only a limited set of operations, complexity is shifted to the application layer if additional operations are needed.

A key-value store is the basis for more complex systems such as a document store, and in some cases, a graph database.

Source(s) and further reading: key-value store

Document store

Abstraction: key-value store with documents stored as values

A document store is centered around documents (XML, JSON, binary, etc), where a document stores all information for a given object. Document stores provide APIs or a query language to query based on the internal structure of the document itself. Note, many key-value stores include features for working with a value's metadata, blurring the lines between these two storage types.

Based on the underlying implementation, documents are organized in either collections, tags, metadata, or directories. Although documents can be organized or grouped together, documents may have fields that are completely different from each other.

Some document stores like MongoDB and CouchDB also provide a SQL-like language to perform complex queries. DynamoDB supports both key-values and documents.

Document stores provide high flexibility and are often used for working with occasionally changing data.

Source(s) and further reading: document store

Wide column store


Source: SQL & NoSQL, a brief history

Abstraction: nested map ColumnFamily<RowKey, Columns<ColKey, Value, Timestamp>>

A wide column store's basic unit of data is a column (name/value pair). A column can be grouped in column families (analogous to a SQL table). Super column families further group column families. You can access each column independently with a row key, and columns with the same row key form a row. Each value contains a timestamp for versioning and for conflict resolution.

Google introduced Bigtable as the first wide column store, which influenced the open-source HBase often-used in the Hadoop ecosystem, and Cassandra from Facebook. Stores such as BigTable, HBase, and Cassandra maintain keys in lexicographic order, allowing efficient retrieval of selective key ranges.

Wide column stores offer high availability and high scalability. They are often used for very large data sets.

Source(s) and further reading: wide column store

Graph database


Source: Graph database

Abstraction: graph

In a graph database, each node is a record and each arc is a relationship between two nodes. Graph databases are optimized to represent complex relationships with many foreign keys or many-to-many relationships.

Graphs databases offer high performance for data models with complex relationships, such as a social network. They are relatively new and are not yet widely-used; it might be more difficult to find development tools and resources. Many graphs can only be accessed with REST APIs.

相关资源和延伸阅读:图

相关资源和延伸阅读NoSQL

SQL 还是 NoSQL


Source: Transitioning from RDBMS to NoSQL

选择 SQL 的原因:

  • 结构化数据
  • 严格的架构
  • 关系型数据
  • 需要复杂的 joins
  • 事务
  • 清晰的缩放模式
  • 更成熟的开发人员,社区,代码,工具等等
  • 通过索引查找非常快

选择 NoSQL 的原因:

  • 半结构化数据
  • 动态/灵活的模式
  • 非关系型数据
  • 不需要复杂的 joins 操作
  • 可以存储大量 TB/PB 数据
  • 非常数据密集的工作量
  • 非常高的 IOPS 吞吐量

适合 NoSQL 操作的数据:

  • 埋点数据以及日志数据
  • 排行榜或者得分数据
  • 临时数据,比如购物车
  • 需要频繁访问的表
  • 元数据/查找表

相关资源和延伸阅读SQL 还是 NoSQL

缓存


Source: Scalable system design patterns

缓存可以提高页面加载速度,并可以减少服务器和数据库的负载。在这个模型中,分发器先查看请求之前是否被响应过,如果有则将之前的结果直接返回,来省掉真正的处理。

数据库分片均匀分布的读取是最好的。但是热门数据会让读取分布不均匀,这样就会造成瓶颈,如果在数据库前加个缓存,就会抹平不均匀的负载和突发流量对数据库的影响。

客户端缓存

缓存可以位于客户端(操作系统或者浏览器),服务端或者不同的缓存层。

CDN 缓存

CDNs 也被视为一种缓存。

Web 服务器缓存

反向代理和缓存(比如 Varnish可以直接提供静态和动态内容。Web 服务器同样也可以缓存请求,返回相应结果而不必连接应用服务器。

数据库缓存

数据库的默认配置中通常包含缓存级别,针对一般用例进行了优化。调整配置,在不同情况下使用不同的模式可以进一步提高性能。

应用缓存

基于内存的缓存比如 Memcached 和 Redis 是应用程序和数据存储之间的一种键值存储。由于数据保存在 RAM 中它比存储在磁盘上的典型数据库要快多了。RAM 比磁盘限制更多,所以例如 least recently used (LRU)缓存无效算法可以将「热门数据」放在 RAM 中,而对一些比较「冷门」的数据不做处理。

Redis 有下列附加功能:

  • 持久性选项
  • 内置数据结构比如有序集合和列表

有多个缓存级别,分为两大类:数据库查询对象

  • 行级别
  • 查询级别
  • 完整的可序列化对象
  • 完全渲染的 HTML

一般来说,你应该尽量避免基于文件的缓存,因为这使得复制和自动缩放很困难。

数据库查询级别的缓存

当你查询数据库的时候,将查询语句的哈希值与查询结果存储到缓存中。这种方法会遇到以下问题:

  • 很难用复杂的查询删除已缓存结果。
  • 如果一条数据比如表中某条数据的一项被改变,则需要删除所有可能包含已更改项的缓存结果。

对象级别的缓存

将您的数据视为对象,就像对待你的应用代码一样。让应用程序将数据从数据库中组合到类实例或数据结构中:

  • 如果对象的基础数据已经更改了,那么从缓存中删掉这个对象。
  • 允许异步处理workers 通过使用最新的缓存对象来组装对象。

建议缓存的内容:

  • 用户会话
  • 完全渲染的 Web 页面
  • 活动流
  • 用户图数据

何时更新缓存

由于你只能在缓存中存储有限的数据,所以你需要选择一个适用于你用例的缓存更新策略。

缓存


Source: From cache to in-memory data grid

应用从存储器读写。缓存不和存储器直接交互,应用执行以下操作:

  • 在缓存中查找记录,如果所需数据不在缓存中
  • 从数据库中加载所需内容
  • 将查找到的结果存储到缓存中
  • 返回所需内容
def get_user(self, user_id):
    user = cache.get("user.{0}", user_id)
    if user is None:
        user = db.query("SELECT * FROM users WHERE user_id = {0}", user_id)
        if user is not None:
            key = "user.{0}".format(user_id)
            cache.set(key, json.dumps(user))
    return user

Memcached 通常用这种方式使用。

添加到缓存中的数据读取速度很快。缓存模式也称为延迟加载。只缓存所请求的数据,这避免了没有被请求的数据占满了缓存空间。

缓存的缺点:
  • 请求的数据如果不在缓存中就需要经过三个步骤来获取数据,这会导致明显的延迟。
  • 如果数据库中的数据更新了会导致缓存中的数据过时。这个问题需要通过设置 TTL 强制更新缓存或者直写模式来缓解这种情况。
  • 当一个节点出现故障的时候,它将会被一个新的节点替代,这增加了延迟的时间。

直写模式


Source: Scalability, availability, stability, patterns

应用使用缓存作为主要的数据存储,将数据读写到缓存中,而缓存负责从数据库中读写数据。

  • 应用向缓存中添加/更新数据
  • 缓存同步地写入数据存储
  • 返回所需内容

应用代码:

set_user(12345, {"foo":"bar"})

缓存代码:

def set_user(user_id, values):
    user = db.query("UPDATE Users WHERE id = {0}", user_id, values)
    cache.set(user_id, user)

由于存写操作所以直写模式整体是一种很慢的操作,但是读取刚写入的数据很快。相比读取数据,用户通常比较能接受更新数据时速度较慢。缓存中的数据不会过时。

直写模式的缺点:
  • 由于故障或者缩放而创建的新的节点,新的节点不会缓存,直到数据库更新为止。缓存应用直写模式可以缓解这个问题。
  • 写入的大多数数据可能永远都不会被读取,用 TTL 可以最小化这种情况的出现。

回写模式


Source: Scalability, availability, stability, patterns

在回写模式中,应用执行以下操作:

  • 在缓存中增加或者更新条目
  • 异步写入数据,提高写入性能。
回写模式的缺点:
  • 缓存可能在其内容成功存储之前丢失数据。
  • 执行直写模式比缓存或者回写模式更复杂。

刷新


Source: From cache to in-memory data grid

你可以将缓存配置成在到期之前自动刷新最近访问过的内容。

如果缓存可以准确预测将来可能请求哪些数据,那么刷新可能会导致延迟与读取时间的降低。

刷新的缺点:
  • 不能准确预测到未来需要用到的数据可能会导致性能不如不使用刷新。

缓存的缺点:

  • 需要保持缓存和真实数据源之间的一致性,比如数据库根据缓存无效
  • 需要改变应用程序比如增加 Redis 或者 memcached。
  • 无效缓存是个难题,什么时候更新缓存是与之相关的复杂问题。

相关资源和延伸阅读

异步


Source: Intro to architecting systems for scale

异步工作流有助于减少那些原本顺序执行的请求时间。它们可以通过提前进行一些耗时的工作来帮助减少请求时间,比如定期汇总数据。

消息队列

消息队列接收,保留和传递消息。如果按顺序执行操作太慢的话,你可以使用有以下工作流的消息队列:

  • 应用程序将作业发布到队列,然后通知用户作业状态
  • 一个 worker 从队列中取出该作业,对其进行处理,然后显示该作业完成

不去阻塞用户操作,作业在后台处理。在此期间,客户端可能会进行一些处理使得看上去像是任务已经完成了。例如,如果要发送一条推文,推文可能会马上出现在你的时间线上,但是可能需要一些时间才能将你的推文推送到你的所有关注者那里去。

Redis 是一个令人满意的简单的消息代理,但是消息有可能会丢失。

RabbitMQ 很受欢迎但是要求你适应「AMQP」协议并且管理你自己的节点。

Amazon SQS 是被托管的,但可能具有高延迟,并且消息可能会被传送两次。

任务队列

任务队列接收任务及其相关数据,运行它们,然后传递其结果。 它们可以支持调度,并可用于在后台运行计算密集型作业。

Celery 支持调度,主要是用 Python 开发的。

背压

如果队列开始明显增长,那么队列大小可能会超过内存大小,导致高速缓存未命中,磁盘读取,甚至性能更慢。背压可以通过限制队列大小来帮助我们,从而为队列中的作业保持高吞吐率和良好的响应时间。一旦队列填满,客户端将得到服务器忙活着 HTTP 503 状态码,以便稍后重试。客户端可以在稍后时间重试该请求,也许是指数退避

异步的缺点:

  • 简单的计算和实时工作流等用例可能更适用于同步操作,因为引入队列可能会增加延迟和复杂性。

相关资源和延伸阅读

通讯


Source: OSI 7 layer model

超文本传输协议HTTP

HTTP 是一种在客户端和服务器之间编码和传输数据的方法。它是一个请求/响应协议客户端和服务端针对相关内容和完成状态信息的请求和响应。HTTP 是独立的,允许请求和响应流经许多执行负载均衡,缓存,加密和压缩的中间路由器和服务器。

一个基本的 HTTP 请求由一个动词(方法)和一个资源(端点)组成。 以下是常见的 HTTP 动词:

动词 描述 *幂等 安全性 可缓存
GET 读取资源 Yes Yes Yes
POST 创建资源或触发处理数据的进程 No No Yes如果回应包含刷新信息
PUT 创建或替换资源 Yes No No
PATCH 部分更新资源 No No Yes如果回应包含刷新信息
DELETE 删除资源 Yes No No

*多次执行不会产生不同的结果。

HTTP 是依赖于较低级协议(如 TCPUDP)的应用层协议。

传输控制协议TCP


Source: How to make a multiplayer game

TCP 是通过 IP 网络的面向连接的协议。 使用握手建立和断开连接。 发送的所有数据包保证以原始顺序到达目的地,用以下措施保证数据包不被损坏:

如果发送者没有收到正确的响应它将重新发送数据包。如果多次超时连接就会断开。TCP 实行流量控制拥塞控制。这些确保措施会导致延迟,而且通常导致传输效率比 UDP 低。

为了确保高吞吐量Web 服务器可以保持大量的 TCP 连接,从而导致高内存使用。在 Web 服务器线程间拥有大量开放连接可能开销巨大,消耗资源过多,也就是说,一个 memcached 服务器。连接池 可以帮助除了在适用的情况下切换到 UDP。

TCP 对于需要高可靠性但时间紧迫的应用程序很有用。比如包括 Web 服务器数据库信息SMTPFTP 和 SSH。

什么时候使用 TCP over UDP

  • 你需要数据完好无损。
  • 你想对网络吞吐量自动进行最佳评估。

User datagram protocol (UDP)


Source: How to make a multiplayer game

UDP is connectionless. Datagrams (analogous to packets) are guaranteed only at the datagram level. Datagrams might reach their destination out of order or not at all. UDP does not support congestion control. Without the guarantees that TCP support, UDP is generally more efficient.

UDP can broadcast, sending datagrams to all devices on the subnet. This is useful with DHCP because the client has not yet received an IP address, thus preventing a way for TCP to stream without the IP address.

UDP is less reliable but works well in real time use cases such as VoIP, video chat, streaming, and realtime multiplayer games.

Use UDP over TCP when:

  • You need the lowest latency
  • Late data is worse than loss of data
  • You want to implement your own error correction

Source(s) and further reading: TCP and UDP

Remote procedure call (RPC)


Source: Crack the system design interview

In an RPC, a client causes a procedure to execute on a different address space, usually a remote server. The procedure is coded as if it were a local procedure call, abstracting away the details of how to communicate with the server from the client program. Remote calls are usually slower and less reliable than local calls so it is helpful to distinguish RPC calls from local calls. Popular RPC frameworks include Protobuf, Thrift, and Avro.

RPC is a request-response protocol:

  • Client program - Calls the client stub procedure. The parameters are pushed onto the stack like a local procedure call.
  • Client stub procedure - Marshals (packs) procedure id and arguments into a request message.
  • Client communication module - OS sends the message from the client to the server.
  • Server communication module - OS passes the incoming packets to the server stub procedure.
  • Server stub procedure - Unmarshalls the results, calls the server procedure matching the procedure id and passes the given arguments.
  • The server response repeats the steps above in reverse order.

Sample RPC calls:

GET /someoperation?data=anId

POST /anotheroperation
{
  "data":"anId";
  "anotherdata": "another value"
}

RPC is focused on exposing behaviors. RPCs are often used for performance reasons with internal communications, as you can hand-craft native calls to better fit your use cases.

Choose a Native Library aka SDK when:

  • You know your target platform.
  • You want to control how your "logic" is accessed
  • You want to control how error control happens off your library
  • Performance and end user experience is your primary concern

HTTP APIs following REST tend to be used more often for public APIs.

Disadvantage(s): RPC

  • RPC clients become tightly coupled to the service implementation.
  • A new API must be defined for every new operation or use case.
  • It can be difficult to debug RPC.
  • You might not be able to leverage existing technologies out of the box. For example, it might require additional effort to ensure RPC calls are properly cached on caching servers such as Squid.

Representational state transfer (REST)

REST is an architectural style enforcing a client/server model where the client acts on a set of resources managed by the server. The server provides a representation of resources and actions that can either manipulate or get a new representation of resources. All communication must be stateless and cacheable.

There are four qualities of a RESTful interface:

  • Identify resources (URI in HTTP) - use the same URI regardless of any operation.
  • Change with representations (Verbs in HTTP) - use verbs, headers, and body.
  • Self-descriptive error message (status response in HTTP) - Use status codes, don't reinvent the wheel.
  • HATEOAS (HTML interface for HTTP) - your web service should be fully accessible in a browser.

Sample REST calls:

GET /someresources/anId

PUT /someresources/anId
{"anotherdata": "another value"}

REST is focused on exposing data. It minimizes the coupling between client/server and is often used for public HTTP APIs. REST uses a more generic and uniform method of exposing resources through URIs, representation through headers, and actions through verbs such as GET, POST, PUT, DELETE, and PATCH. Being stateless, REST is great for horizontal scaling and partitioning.

Disadvantage(s): REST

  • With REST being focused on exposing data, it might not be a good fit if resources are not naturally organized or accessed in a simple hierarchy. For example, returning all updated records from the past hour matching a particular set of events is not easily expressed as a path. With REST, it is likely to be implemented with a combination of URI path, query parameters, and possibly the request body.
  • REST typically relies on a few verbs (GET, POST, PUT, DELETE, and PATCH) which sometimes doesn't fit your use case. For example, moving expired documents to the archive folder might not cleanly fit within these verbs.
  • Fetching complicated resources with nested hierarchies requires multiple round trips between the client and server to render single views, e.g. fetching content of a blog entry and the comments on that entry. For mobile applications operating in variable network conditions, these multiple roundtrips are highly undesirable.
  • Over time, more fields might be added to an API response and older clients will receive all new data fields, even those that they do not need, as a result, it bloats the payload size and leads to larger latencies.

RPC and REST calls comparison

Operation RPC REST
Signup POST /signup POST /persons
Resign POST /resign
{
"personid": "1234"
}
DELETE /persons/1234
Read a person GET /readPerson?personid=1234 GET /persons/1234
Read a persons items list GET /readUsersItemsList?personid=1234 GET /persons/1234/items
Add an item to a persons items POST /addItemToUsersItemsList
{
"personid": "1234";
"itemid": "456"
}
POST /persons/1234/items
{
"itemid": "456"
}
Update an item POST /modifyItem
{
"itemid": "456";
"key": "value"
}
PUT /items/456
{
"key": "value"
}
Delete an item POST /removeItem
{
"itemid": "456"
}
DELETE /items/456

Source: Do you really know why you prefer REST over RPC

Source(s) and further reading: REST and RPC

Security

This section could use some updates. Consider contributing!

Security is a broad topic. Unless you have considerable experience, a security background, or are applying for a position that requires knowledge of security, you probably won't need to know more than the basics:

  • Encrypt in transit and at rest.
  • Sanitize all user inputs or any input parameters exposed to user to prevent XSS and SQL injection.
  • Use parameterized queries to prevent SQL injection.
  • Use the principle of least privilege.

Source(s) and further reading

Appendix

You'll sometimes be asked to do 'back-of-the-envelope' estimates. For example, you might need to determine how long it will take to generate 100 image thumbnails from disk or how much memory a data structure will take. The Powers of two table and Latency numbers every programmer should know are handy references.

Powers of two table

Power           Exact Value         Approx Value        Bytes
---------------------------------------------------------------
7                             128
8                             256
10                           1024   1 thousand           1 KB
16                         65,536                       64 KB
20                      1,048,576   1 million            1 MB
30                  1,073,741,824   1 billion            1 GB
32                  4,294,967,296                        4 GB
40              1,099,511,627,776   1 trillion           1 TB

Source(s) and further reading

Latency numbers every programmer should know

Latency Comparison Numbers
--------------------------
L1 cache reference                           0.5 ns
Branch mispredict                            5   ns
L2 cache reference                           7   ns                      14x L1 cache
Mutex lock/unlock                          100   ns
Main memory reference                      100   ns                      20x L2 cache, 200x L1 cache
Compress 1K bytes with Zippy            10,000   ns       10 us
Send 1 KB bytes over 1 Gbps network     10,000   ns       10 us
Read 4 KB randomly from SSD*           150,000   ns      150 us          ~1GB/sec SSD
Read 1 MB sequentially from memory     250,000   ns      250 us
Round trip within same datacenter      500,000   ns      500 us
Read 1 MB sequentially from SSD*     1,000,000   ns    1,000 us    1 ms  ~1GB/sec SSD, 4X memory
Disk seek                           10,000,000   ns   10,000 us   10 ms  20x datacenter roundtrip
Read 1 MB sequentially from 1 Gbps  10,000,000   ns   10,000 us   10 ms  40x memory, 10X SSD
Read 1 MB sequentially from disk    30,000,000   ns   30,000 us   30 ms 120x memory, 30X SSD
Send packet CA->Netherlands->CA    150,000,000   ns  150,000 us  150 ms

Notes
-----
1 ns = 10^-9 seconds
1 us = 10^-6 seconds = 1,000 ns
1 ms = 10^-3 seconds = 1,000 us = 1,000,000 ns

Handy metrics based on numbers above:

  • Read sequentially from disk at 30 MB/s
  • Read sequentially from 1 Gbps Ethernet at 100 MB/s
  • Read sequentially from SSD at 1 GB/s
  • Read sequentially from main memory at 4 GB/s
  • 6-7 world-wide round trips per second
  • 2,000 round trips per second within a data center

Latency numbers visualized

Source(s) and further reading

Additional system design interview questions

Common system design interview questions, with links to resources on how to solve each.

Question Reference(s)
Design a file sync service like Dropbox youtube.com
Design a search engine like Google queue.acm.org
stackexchange.com
ardendertat.com
stanford.edu
Design a scalable web crawler like Google quora.com
Design Google docs code.google.com
neil.fraser.name
Design a key-value store like Redis slideshare.net
Design a cache system like Memcached slideshare.net
Design a recommendation system like Amazon's hulu.com
ijcai13.org
Design a tinyurl system like Bitly n00tc0d3r.blogspot.com
Design a chat app like WhatsApp highscalability.com
Design a picture sharing system like Instagram highscalability.com
highscalability.com
Design the Facebook news feed function quora.com
quora.com
slideshare.net
Design the Facebook timeline function facebook.com
highscalability.com
Design the Facebook chat function erlang-factory.com
facebook.com
Design a graph search function like Facebook's facebook.com
facebook.com
facebook.com
Design a content delivery network like CloudFlare cmu.edu
Design a trending topic system like Twitter's michael-noll.com
snikolov .wordpress.com
Design a random ID generation system blog.twitter.com
github.com
Return the top k requests during a time interval ucsb.edu
wpi.edu
Design a system that serves data from multiple data centers highscalability.com
Design an online multiplayer card game indieflashblog.com
buildnewgames.com
Design a garbage collection system stuffwithstuff.com
washington.edu
Add a system design question Contribute

Real world architectures

Articles on how real world systems are designed.


Source: Twitter timelines at scale

Don't focus on nitty gritty details for the following articles, instead:

  • Identify shared principles, common technologies, and patterns within these articles
  • Study what problems are solved by each component, where it works, where it doesn't
  • Review the lessons learned
Type System Reference(s)
Data processing MapReduce - Distributed data processing from Google research.google.com
Data processing Spark - Distributed data processing from Databricks slideshare.net
Data processing Storm - Distributed data processing from Twitter slideshare.net
Data store Bigtable - Distributed column-oriented database from Google harvard.edu
Data store HBase - Open source implementation of Bigtable slideshare.net
Data store Cassandra - Distributed column-oriented database from Facebook slideshare.net
Data store DynamoDB - Document-oriented database from Amazon harvard.edu
Data store MongoDB - Document-oriented database slideshare.net
Data store Spanner - Globally-distributed database from Google research.google.com
Data store Memcached - Distributed memory caching system slideshare.net
Data store Redis - Distributed memory caching system with persistence and value types slideshare.net
File system Google File System (GFS) - Distributed file system research.google.com
File system Hadoop File System (HDFS) - Open source implementation of GFS apache.org
Misc Chubby - Lock service for loosely-coupled distributed systems from Google research.google.com
Misc Dapper - Distributed systems tracing infrastructure research.google.com
Misc Kafka - Pub/sub message queue from LinkedIn slideshare.net
Misc Zookeeper - Centralized infrastructure and services enabling synchronization slideshare.net
Add an architecture Contribute

Company architectures

Company Reference(s)
Amazon Amazon architecture
Cinchcast Producing 1,500 hours of audio every day
DataSift Realtime datamining At 120,000 tweets per second
DropBox How we've scaled Dropbox
ESPN Operating At 100,000 duh nuh nuhs per second
Google Google architecture
Instagram 14 million users, terabytes of photos
What powers Instagram
Justin.tv Justin.Tv's live video broadcasting architecture
Facebook Scaling memcached at Facebook
TAO: Facebooks distributed data store for the social graph
Facebooks photo storage
Flickr Flickr architecture
Mailbox From 0 to one million users in 6 weeks
Pinterest From 0 To 10s of billions of page views a month
18 million visitors, 10x growth, 12 employees
Playfish 50 million monthly users and growing
PlentyOfFish PlentyOfFish architecture
Salesforce How they handle 1.3 billion transactions a day
Stack Overflow Stack Overflow architecture
TripAdvisor 40M visitors, 200M dynamic page views, 30TB data
Tumblr 15 billion page views a month
Twitter Making Twitter 10000 percent faster
Storing 250 million tweets a day using MySQL
150M active users, 300K QPS, a 22 MB/S firehose
Timelines at scale
Big and small data at Twitter
Operations at Twitter: scaling beyond 100 million users
Uber How Uber scales their real-time market platform
WhatsApp The WhatsApp architecture Facebook bought for $19 billion
YouTube YouTube scalability
YouTube architecture

Company engineering blogs

Architectures for companies you are interviewing with.

Questions you encounter might be from the same domain.

Source(s) and further reading

Under development

Interested in adding a section or helping complete one in-progress? Contribute!

  • Distributed computing with MapReduce
  • Consistent hashing
  • Scatter gather
  • Contribute

Credits

Credits and sources are provided throughout this repo.

Special thanks to:

Contact info

Feel free to contact me to discuss any issues, questions, or comments.

My contact info can be found on my GitHub page.

License

Creative Commons Attribution 4.0 International License (CC BY 4.0)

http://creativecommons.org/licenses/by/4.0/