User talk:Shrachik agrahari

Topology From Wikipedia, the free encyclopedia Not to be confused with topography. This article is about the branch of mathematics. For other uses, see Topology (disambiguation). Möbius strips, which have only one surface and one edge, are a kind of object studied in topology.

Topology (from the Greek τόπος, "place", and λόγος, "study") is the mathematical study of shapes and topological spaces. It is an area of mathematics concerned with the properties of space that are preserved under continuous deformations including stretching and bending, but not tearing or gluing. This includes such properties as connectedness, continuity and boundary.

Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation. Such ideas go back to Leibniz, who in the 17th century envisioned the geometria situs (Greek-Latin for "geometry of place") and analysis situs (Greek-Latin for "picking apart of place"). The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. By the middle of the 20th century, topology had become a major branch of mathematics.

Topology has many subfields:

   General topology establishes the foundational aspects of topology and investigates properties of topological spaces and investigates concepts inherent to topological spaces. It includes point-set topology, which is the foundational topology used in all other branches (including topics like compactness and connectedness).
   Algebraic topology tries to measure degrees of connectivity using algebraic constructs such as homology and homotopy groups.
   Differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.
   Geometric topology primarily studies manifolds and their embeddings (placements) in other manifolds. A particularly active area is low dimensional topology, which studies manifolds of four or fewer dimensions. This includes knot theory, the study of mathematical knots.

A three-dimensional depiction of a thickened trefoil knot, the simplest non-trivial knot

See also: topology glossary for definitions of some of the terms used in topology, and topological space for a more technical treatment of the subject.

Contents

   1 History
   2 Introduction
   3 Concepts
       3.1 Topologies on Sets
       3.2 Continuous functions and homeomorphisms
       3.3 Manifolds
   4 Topics
       4.1 General topology
       4.2 Algebraic topology
       4.3 Differential topology
       4.4 Geometric topology
       4.5 Generalizations
   5 Applications
       5.1 Biology
       5.2 Computer science
       5.3 Physics
       5.4 Robotics
   6 See also
   7 References
   8 Further reading
   9 External links

History The Seven Bridges of Königsberg was a problem solved by Euler.

Topology began with the investigation of certain questions in geometry. Leonhard Euler's 1736 paper on the Seven Bridges of Königsberg[1] is regarded as one of the first academic treatises in modern topology.

The term "Topologie" was introduced in German in 1847 by Johann Benedict Listing in Vorstudien zur Topologie,[2] who had used the word for ten years in correspondence before its first appearance in print. The English form topology was first used in 1883 in Listing's obituary in the journal Nature[3] to distinguish "qualitative geometry from the ordinary geometry in which quantitative relations chiefly are treated". The term topologist in the sense of a specialist in topology was used in 1905 in the magazine Spectator.[citation needed] However, none of these uses corresponds exactly to the modern definition of topology.

Modern topology depends strongly on the ideas of set theory, developed by Georg Cantor in the later part of the 19th century. In addition to establishing the basic ideas of set theory, Cantor considered point sets in Euclidean space as part of his study of Fourier series.

Henri Poincaré published Analysis Situs in 1895,[4] introducing the concepts of homotopy and homology, which are now considered part of algebraic topology.

Unifying the work on function spaces of Georg Cantor, Vito Volterra, Cesare Arzelà, Jacques Hadamard, Giulio Ascoli and others, Maurice Fréchet introduced the metric space in 1906.[5] A metric space is now considered a special case of a general topological space. In 1914, Felix Hausdorff coined the term "topological space" and gave the definition for what is now called a Hausdorff space.[6] Currently, a topological space is a slight generalization of Hausdorff spaces, given in 1922 by Kazimierz Kuratowski.[citation needed]

For further developments, see point-set topology and algebraic topology. Introduction

Topology can be formally defined as "the study of qualitative properties of certain objects (called topological spaces) that are invariant under a certain kind of transformation (called a continuous map), especially those properties that are invariant under a certain kind of transformation (called homeomorphism)."

Topology is also used to refer to a structure imposed upon a set X, a structure that essentially 'characterizes' the set X as a topological space by taking proper care of properties such as convergence, connectedness and continuity, upon transformation.

Topological spaces show up naturally in almost every branch of mathematics. This has made topology one of the great unifying ideas of mathematics.

The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. For example, the square and the circle have many properties in common: they are both one dimensional objects (from a topological point of view) and both separate the plane into two parts, the part inside and the part outside.

One of the first papers in topology was the demonstration, by Leonhard Euler, that it was impossible to find a route through the town of Königsberg (now Kaliningrad) that would cross each of its seven bridges exactly once. This result did not depend on the lengths of the bridges, nor on their distance from one another, but only on connectivity properties: which bridges are connected to which islands or riverbanks. This problem in introductory mathematics called Seven Bridges of Königsberg led to the branch of mathematics known as graph theory. A continuous deformation (a type of homeomorphism) of a mug into a doughnut (torus) and back

Similarly, the hairy ball theorem of algebraic topology says that "one cannot comb the hair flat on a hairy ball without creating a cowlick." This fact is immediately convincing to most people, even though they might not recognize the more formal statement of the theorem, that there is no nonvanishing continuous tangent vector field on the sphere. As with the Bridges of Königsberg, the result does not depend on the shape of the sphere; it applies to any kind of smooth blob, as long as it has no holes.

To deal with these problems that do not rely on the exact shape of the objects, one must be clear about just what properties these problems do rely on. From this need arises the notion of homeomorphism. The impossibility of crossing each bridge just once applies to any arrangement of bridges homeomorphic to those in Königsberg, and the hairy ball theorem applies to any space homeomorphic to a sphere.

Intuitively, two spaces are homeomorphic if one can be deformed into the other without cutting or gluing. A traditional joke is that a topologist cannot distinguish a coffee mug from a doughnut, since a sufficiently pliable doughnut could be reshaped to a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.

Homeomorphism can be considered the most basic topological equivalence. Another is homotopy equivalence. This is harder to describe without getting technical, but the essential notion is that two objects are homotopy equivalent if they both result from "squishing" some larger object. Equivalence classes of the English alphabet: Homeomorphism Homotopy equivalence Alphabet homeo.png Alphabet homotopy.png

An introductory exercise is to classify the uppercase letters of the English alphabet according to homeomorphism and homotopy equivalence. The result depends partially on the font used. The figures use the sans-serif Myriad font. Homotopy equivalence is a rougher relationship than homeomorphism; a homotopy equivalence class can contain several homeomorphism classes. The simple case of homotopy equivalence described above can be used here to show two letters are homotopy equivalent. For example, O fits inside P and the tail of the P can be squished to the "hole" part.

Homeomorphism classes are:

   no holes,
   no holes three tails,
   no holes four tails,
   one hole no tail,
   one hole one tail,
   one hole two tails,
   two holes no tail, and
   a bar with four tails (the "bar" on the K is almost too short to see).

Homotopy classes are larger, because the tails can be squished down to a point. They are:

   one hole,
   two holes, and
   no holes.

To be sure that the letters are classified correctly, we need to show that two letters in the same class are equivalent and two letters in different classes are not equivalent. In the case of homeomorphism, this can be done by selecting points and showing their removal disconnects the letters differently. For example, X and Y are not homeomorphic because removing the center point of the X leaves four pieces; whatever point in Y corresponds to this point, its removal can leave at most three pieces. The case of homotopy equivalence is harder and requires a more elaborate argument showing an algebraic invariant, such as the fundamental group, is different on the supposedly differing classes.

Letter topology has practical relevance in stencil typography. For instance, Braggadocio font stencils are made of one connected piece of material. Concepts Topologies on Sets Main article: Topological space

The term topology also refers to a specific mathematical idea which is central to the area of mathematics called topology. Informally, a topology is used to tell how elements of a set are related spatially to each other. The same set can have different topologies. For instance, the real line, the complex plane, and the Cantor set can be thought of as the same set with different topologies.

Formally, let X be a set and let τ be a family of subsets of X. Then τ is called a topology on X if:

   Both the empty set and X are elements of τ
   Any union of elements of τ is an element of τ
   Any intersection of finitely many elements of τ is an element of τ

If τ is a topology on X, then the pair (X, τ) is called a topological space. The notation Xτ may be used to denote a set X endowed with the particular topology τ.

The members of τ are called open sets in X. A subset of X is said to be closed if its complement is in τ (i.e., its complement is open). A subset of X may be open, closed, both (clopen set), or neither. The empty set and X itself are always both closed and open. An open set containing a point x is called a 'neighborhood' of x.

A set with a topology is called a topological space. Continuous functions and homeomorphisms Main articles: Continuous function and homeomorphism

A function or map from one topological space to another is called continuous if the inverse image of any open set is open. If the function maps the real numbers to the real numbers (both spaces with the Standard Topology), then this definition of continuous is equivalent to the definition of continuous in calculus. If a continuous function is one-to-one and onto, and if the inverse of the function is also continuous, then the function is called a homeomorphism and the domain of the function is said to be homeomorphic to the range. Another way of saying this is that the function has a natural extension to the topology. If two spaces are homeomorphic, they have identical topological properties, and are considered topologically the same. The cube and the sphere are homeomorphic, as are the coffee cup and the doughnut. But the circle is not homeomorphic to the doughnut. Manifolds Main article: Manifold

While topological spaces can be extremely varied and exotic, many areas of topology focus on the more familiar class of spaces known as manifolds. A manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot. Topics General topology Main article: General topology

General topology is the branch of topology dealing with the basic set-theoretic definitions and constructions used in topology.[7][8] It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.

The fundamental concepts in point-set topology are continuity, compactness, and connectedness. Intuitively, continuous functions take nearby points to nearby points; compact sets are those which can be covered by finitely many sets of arbitrarily small size; and connected sets are sets which cannot be divided into two pieces which are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.

Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces. Algebraic topology Main article: Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.[9] The basic g

Local area network From Wikipedia, the free encyclopedia Computer network types by spatial scope

   Nanoscale
   Near-field (NFC)
   Body (BAN)
   Personal (PAN)
   Controller (CAN)
   Near-me (NAN)
   Local (LAN)
       Home (HAN)
       Storage (SAN)
   Campus (CAN)
   Backbone
   Metropolitan (MAN)
   Wide (WAN)
   Cloud (IAN)
   Internet
   Interplanetary Internet

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A local area network (LAN) is a computer network that interconnects computers within a limited area such as a home, school, computer laboratory, or office building, using network media.[1] The defining characteristics of LANs, in contrast to wide area networks (WANs), include their smaller geographic area, and non-inclusion of leased telecommunication lines.[citation needed]

ARCNET, Token Ring and other technology standards have been used in the past, but Ethernet over twisted pair cabling, and Wi-Fi are the two most common technologies currently used to build LANs.

Contents

   1 History
       1.1 Standards evolution
       1.2 Cabling
       1.3 Wireless
   2 Technical aspects
   3 See also
   4 References
   5 External links

History A conceptual diagram of a local area network using 10BASE5 Ethernet

The increasing demand and use of computers in universities and research labs in the late 1960s generated the need to provide high-speed interconnections between computer systems. A 1970 report from the Lawrence Radiation Laboratory detailing the growth of their "Octopus" network[2][3] gave a good indication of the situation.

Cambridge Ring (computer network) was developed at Cambridge University in 1974[4] but was never developed into a successful commercial product.

Ethernet was developed at Xerox PARC in 1973–1975,[5] and filed as U.S. Patent 4,063,220. In 1976, after the system was deployed at PARC, Metcalfe and Boggs published a seminal paper, "Ethernet: Distributed Packet-Switching for Local Computer Networks."[6]

ARCNET was developed by Datapoint Corporation in 1976 and announced in 1977.[7] It had the first commercial installation in December 1977 at Chase Manhattan Bank in New York.[8] Standards evolution

The development and proliferation of personal computers using the CP/M operating system in the late 1970s, and later DOS-based systems starting in 1981, meant that many sites grew to dozens or even hundreds of computers. The initial driving force for networking was generally to share storage and printers, which were both expensive at the time. There was much enthusiasm for the concept and for several years, from about 1983 onward, computer industry pundits would regularly declare the coming year to be “the year of the LAN”.[9][10][11]

In practice, the concept was marred by proliferation of incompatible physical layer and network protocol implementations, and a plethora of methods of sharing resources. Typically, each vendor would have its own type of network card, cabling, protocol, and network operating system. A solution appeared with the advent of Novell NetWare which provided even-handed support for dozens of competing card/cable types, and a much more sophisticated operating system than most of its competitors. Netware dominated[12] the personal computer LAN business from early after its introduction in 1983 until the mid-1990s when Microsoft introduced Windows NT Advanced Server and Windows for Workgroups.

Of the competitors to NetWare, only Banyan Vines had comparable technical strengths, but Banyan never gained a secure base. Microsoft and 3Com worked together to create a simple network operating system which formed the base of 3Com's 3+Share, Microsoft's LAN Manager and IBM's LAN Server - but none of these was particularly successful.

During the same period, Unix computer workstations from vendors such as Sun Microsystems, Hewlett-Packard, Silicon Graphics, Intergraph, NeXT and Apollo were using TCP/IP based networking. Although this market segment is now much reduced, the technologies developed in this area continue to be influential on the Internet and in both Linux and Apple Mac OS X networking—and the TCP/IP protocol has now almost completely replaced IPX, AppleTalk, NBF, and other protocols used by the early PC LANs. Cabling

Early LAN cabling had generally been based on various grades of coaxial cable. Shielded twisted pair was used in IBM's Token Ring LAN implementation, but in 1984, StarLAN showed the potential of simple unshielded twisted pair by using Cat3 cable—the same simple cable used for telephone systems. This led to the development of 10Base-T (and its successors) and structured cabling which is still the basis of most commercial LANs today.

Fiber-optic cabling is common for links between switches, but fiber to the desktop is uncommon. Wireless

As well as traditional cabling, many LANs are now based partly or wholly on wireless technologies. Almost all of today's smartphoness, tablets and laptops have wireless support built-in so a wireless local area network, or WLAN, gives users the ability to move around within a local coverage area and still be connected to the network. Wireless networks have become popular in domestic homes due to ease of installation, and in commercial complexes to offer easy network access to their staff. Visiting guest are often offered internet access via a hotspot service. Technical aspects

Network topology describes the layout of interconnections between devices and network segments. At the Data Link Layer and Physical Layer, a wide variety of LAN topologies have been used, including ring, bus, mesh and star, but the most common LAN topology in use today is switched Ethernet. At the higher layers, the Internet Protocol (TCP/IP) has become the standard, replacing NetBEUI, IPX/SPX, AppleTalk and others.

Simple LANs generally consist of one or more switches. A switch can be connected to a router, cable modem, or ADSL modem for Internet access. Complex LANs are characterized by their use of redundant links with switches using the spanning tree protocol to prevent loops, their ability to manage differing traffic types via quality of service (QoS), and to segregate traffic with VLANs. A LAN can include a wide variety of network devices such as switches, firewalls, routers, load balancers, and sensors.[13]

LANs can maintain connections with other LANs via leased lines, leased services, or the Internet using virtual private network technologies. Depending on how the connections are established and secured in a LAN, and the distance involved, a LAN may also be classified as a metropolitan area network (MAN) or a wide area network (WAN). See also Portal icon Computer networking portal Portal icon Computer Science portal

   IEEE 802 family of IEEE standards
   Ethernet physical layer
   LAN messenger
   LAN party
   Network card

References

Gary A. Donahue (June 2007). Network Warrior. O'Reilly. p. 5. Samuel F. Mendicino (1970-12-01). "Octopus: The Lawrence Radiation Laboratory Network". Rogerdmoore.ca. Archived from the original on 2010-10-11. "THE LAWRENCE RADIATION LABORATORY OCTOPUS". Courant symposium series on networks (Osti.gov). 29 Nov 1970. OSTI 4045588. "A brief informal history of the Computer Laboratory". University of Cambridge. 20 December 2001. Archived from the original on 2010-10-11. "Ethernet Prototype Circuit Board". Smithsonian National Museum of American History. Retrieved 2007-09-02. "Ethernet: Distributed Packet-Switching For Local Computer Networks". Acm.org. Retrieved 2010-10-11. "ARCNET Timeline". ARCNETworks magazine. Fall 1998. Archived from the original on 2010-10-11. Lamont Wood (2008-01-31). "The LAN turns 30, but will it reach 40?". Computerworld.com. Retrieved 2010-10-11. "'The Year of The LAN' is a long-standing joke, and I freely admit to being the comedian that first declared it in 1982...", Robert Metcalfe, InfoWorld Dec 27, 1993 "...you will remember numerous computer magazines, over numerous years, announcing 'the year of the LAN.'", Quotes in 1999 "...a bit like the Year of the LAN which computer industry pundits predicted for the good part of a decade...", Christopher Herot Wayne Spivak (2001-07-13). "Has Microsoft Ever Read the History Books?". VARBusiness. Archived from the original on 2010-10-11.

   "A Review of the Basic Components of a Local Area Network (LAN)". NetworkBits.net. Retrieved 2008-04-08.

External links

O. S .I. LAYER .- (OPEN SYSTEM INTRCONNECT) BY- SHRACHIK AGRAHARI(PRANJUL)

OSI model From Wikipedia, the free encyclopedia OSI model by layer 7. Application[show] 6. Presentation[show] 5. Session[show] 4. Transport[show] 3. Network[show] 2. Data link[show] 1. Physical[show]

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The Open Systems Interconnection model (OSI) is a conceptual model that characterizes and standardizes the internal functions of a communication system by partitioning it into abstraction layers. The model is a product of the Open Systems Interconnection project at the International Organization for Standardization (ISO), maintained by the identification ISO/IEC 7498-1.

The model groups communication functions into seven logical layers. A layer serves the layer above it and is served by the layer below it. For example, a layer that provides error-free communications across a network provides the path needed by applications above it, while it calls the next lower layer to send and receive packets that make up the contents of that path. Two instances at one layer are connected by a horizontal connection on that layer. Communication in the OSI-Model (example with layers 3 to 5)

Contents

   1 History
   2 Description of OSI layers
       2.1 Layer 1: physical layer
       2.2 Layer 2: data link layer
       2.3 Layer 3: network layer
       2.4 Layer 4: transport layer
       2.5 Layer 5: session layer
       2.6 Layer 6: presentation layer
       2.7 Layer 7: application layer
   3 Cross-layer functions
   4 Interfaces
   5 Examples
   6 Comparison with TCP/IP model
   7 See also
   8 References
   9 External links

History

In the late 1970s, two projects began independently, with the same goal: to define a unifying standard for the architecture of networking systems.[citation needed] One was administered by the International Organization for Standardization (ISO), while the other was undertaken by the International Telegraph and Telephone Consultative Committee, or CCITT (the abbreviation is from the French version of the name). These two international standards bodies each developed a document that defined similar networking models.

In 1983, these two documents were merged to form a standard called The Basic Reference Model for Open Systems Interconnection. The standard is usually referred to as the Open Systems Interconnection Reference Model, the OSI Reference Model, or simply the OSI model. It was published in 1984 by both the ISO, as standard ISO 7498, and the renamed CCITT (now called the Telecommunications Standardization Sector of the International Telecommunication Union or ITU-T) as standard X.200.

OSI had two major components, an abstract model of networking, called the Basic Reference Model or seven-layer model, and a set of specific protocols.

The concept of a seven-layer model was provided by the work of Charles Bachman at Honeywell Information Services. Various aspects of OSI design evolved from experiences with the ARPANET, NPLNET, EIN, CYCLADES network and the work in IFIP WG6.1. The new design was documented in ISO 7498 and its various addenda. In this model, a networking system was divided into layers. Within each layer, one or more entities implement its functionality. Each entity interacted directly only with the layer immediately beneath it, and provided facilities for use by the layer above it.

Protocols enabled an entity in one host to interact with a corresponding entity at the same layer in another host. Service definitions abstractly described the functionality provided to an (N)-layer by an (N-1) layer, where N was one of the seven layers of protocols operating in the local host.

The OSI standards documents are available from the ITU-T as the X.200-series of recommendations.[1] Some of the protocol specifications were also available as part of the ITU-T X series. The equivalent ISO and ISO/IEC standards for the OSI model were available from ISO, but only some of them without fees.[2] Description of OSI layers

The recommendation X.200 describes seven layers, labeled 1 to 7. Layer 1 is the lowest layer in this model. OSI Model Layer Data unit Function[3] Examples Host layers 7. Application Data High-level APIs, including resource sharing, remote file access, directory services and virtual terminals HTTP, FTP, SMTP 6. Presentation Translation of data between a networking service and an application; including character encoding, data compression and encryption/decryption ASCII, EBCDIC, JPEG 5. Session Managing communication sessions, i.e. continuous exchange of information in the form of multiple back-and-forth transmissions between two nodes RPC, PAP 4. Transport Segments Reliable transmission of data segments between points on a network, including segmentation, acknowledgement and multiplexing TCP, UDP Media layers 3. Network Packet/Datagram Structuring and managing a multi-node network, including addressing, routing and traffic control IPv4, IPv6, IPsec, AppleTalk 2. Data link Bit/Frame Reliable transmission of data frames between two nodes connected by a physical layer PPP, IEEE 802.2, L2TP 1. Physical Bit Transmission and reception of raw bit streams over a physical medium DSL, USB

At each level N two entities at the communicating devices (layer N peers) exchange protocol data units (PDUs) by means of a layer N protocol. Each PDU contains a payload, called the service data unit (SDU), along with protocol-related headers and/or footers.

Data processing by two communicating OSI-compatible devices is done as such:

   The data to be transmitted is composed at the topmost layer of the transmitting device (layer N) into a protocol data unit (PDU).
   The PDU is passed to layer N-1, where it is known as the service data unit (SDU).
   At layer N-1 the SDU is concatenated with a header, a footer, or both, producing a layer N-1 PDU. It is then passed to layer N-2.
   The process continues until reaching the lowermost level, from which the data is transmitted to the receiving device.
   At the receiving device the data is passed from the lowest to the highest layer as a series of SDUs while being successively stripped from each layer's header and/or footer, until reaching the topmost layer, where the last of the data is consumed.

Some orthogonal aspects, such as management and security, involve all of the layers (See ITU-T X.800 Recommendation[4]). These services are aimed at improving the CIA triad - confidentiality, integrity, and availability - of the transmitted data. In practice, the availability of a communication service is determined by the interaction between network design and network management protocols. Appropriate choices for both of these are needed to protect against denial of service.[citation needed] Layer 1: physical layer

The physical layer has the following major functions:

   It defines the electrical and physical specifications of the data connection. It defines the relationship between a device and a physical transmission medium (e.g., a copper or fiber optical cable). This includes the layout of pins, voltages, line impedance, cable specifications, signal timing, hubs, repeaters, network adapters, host bus adapters (HBA used in storage area networks) and more.
   It defines the protocol to establish and terminate a connection between two directly connected nodes over a communications medium.
   It may define the protocol for flow control.
   It defines transmission mode i.e. simplex, half duplex, full duplex.
   It defines topology.
   It defines a protocol for the provision of a (not necessarily reliable) connection between two directly connected nodes, and the modulation or conversion between the representation of digital data in user equipment and the corresponding signals transmitted over the physical communications channel. This channel can involve physical cabling (such as copper and optical fiber) or a wireless radio link.

The physical layer of Parallel SCSI operates in this layer, as do the physical layers of Ethernet and other local-area networks, such as Token Ring, FDDI, ITU-T G.hn, and IEEE 802.11 (Wi-Fi), as well as personal area networks such as Bluetooth and IEEE 802.15.4. Layer 2: data link layer

The data link layer provides node-to-node data transfer -- a reliable link between two directly connected nodes, by detecting and possibly correcting errors that may occur in the physical layer. The data link layer is divided into two sublayers:

   Media Access Control (MAC) layer - responsible for controlling how devices in a network gain access to data and permission to transmit it.
   Logical Link Control (LLC) layer - controls error checking and packet synchronization.

The Point-to-Point Protocol (PPP) is an example of a data link layer in the TCP/IP protocol stack.

The ITU-T G.hn standard, which provides high-speed local area networking over existing wires (power lines, phone lines and coaxial cables), includes a complete data link layer that provides both error correction and flow control by means of a selective-repeat sliding-window protocol. Layer 3: network layer

The network layer provides the functional and procedural means of transferring variable length data sequences (called datagrams) from one node to another connected to the same network. It translates logical network address into physical machine address. A network is a medium to which many nodes can be connected, on which every node has an address and which permits nodes connected to it to transfer messages to other nodes connected to it by merely providing the content of a message and the address of the destination node and letting the network find the way to deliver ("route") the message to the destination node. In addition to message routing, the network may (or may not) implement message delivery by splitting the message into several fragments, delivering each fragment by a separate route and reassembling the fragments, report delivery errors, etc.

Datagram delivery at the network layer is not guaranteed to be reliable.

A number of layer-management protocols, a function defined in the management annex, ISO 7498/4, belong to the network layer. These include routing protocols, multicast group management, network-layer information and error, and network-layer address assignment. It is the function of the payload that makes these belong to the network layer, not the protocol that carries them. Layer 4: transport layer

The transport layer provides the functional and procedural means of transferring variable-length data sequences from a source to a destination host via one or more networks, while maintaining the quality of service functions.

An example of a transport-layer protocol in the standard Internet stack is Transmission Control Protocol (TCP), usually built on top of the Internet Protocol (IP).

The transport layer controls the reliability of a given link through flow control, segmentation/desegmentation, and error control. Some protocols are state- and connection-oriented. This means that the transport layer can keep track of the segments and retransmit those that fail. The transport layer also provides the acknowledgement of the successful data transmission and sends the next data if no errors occurred. The transport layer creates packets out of the message received from the application layer. Packetizing is a process of dividing the long message into smaller messages.

OSI defines five classes of connection-mode transport protocols ranging from class 0 (which is also known as TP0 and provides the fewest features) to class 4 (TP4, designed for less reliable networks, similar to the Internet). Class 0 contains no error recovery, and was designed for use on network layers that provide error-free connections. Class 4 is closest to TCP, although TCP contains functions, such as the graceful close, which OSI assigns to the session layer. Also, all OSI TP connection-mode protocol classes provide expedited data and preservation of record boundaries. Detailed characteristics of TP0-4 classes are shown in the following table:[5] Feature name TP0 TP1 TP2 TP3 TP4 Connection-oriented network Yes Yes Yes Yes Yes Connectionless network No No No No Yes Concatenation and separation No Yes Yes Yes Yes Segmentation and reassembly Yes Yes Yes Yes Yes Error recovery No Yes Yes Yes Yes Reinitiate connectiona No Yes No Yes No Multiplexing / demultiplexing over single virtual circuit No No Yes Yes Yes Explicit flow control No No Yes Yes Yes Retransmission on timeout No No No No Yes Reliable transport service No Yes No Yes Yes a If an excessive number of PDUs are unacknowledged.

An easy way to visualize the transport layer is to compare it with a post office, which deals with the dispatch and classification of mail and parcels sent. Do remember, however, that a post office manages the outer envelope of mail. Higher layers may have the equivalent of double envelopes, such as cryptographic presentation services that can be read by the addressee only. Roughly speaking, tunneling protocols operate at the transport layer, such as carrying non-IP protocols such as IBM's SNA or Novell's IPX over an IP network, or end-to-end encryption with IPsec. While Generic Routing Encapsulation (GRE) might seem to be a network-layer protocol, if the encapsulation of the payload takes place only at endpoint, GRE becomes closer to a transport protocol that uses IP headers but contains complete frames or packets to deliver to an endpoint. L2TP carries PPP frames inside transport packet.

Although not developed under the OSI Reference Model and not strictly conforming to the OSI definition of the transport layer, the Transmission Control Protocol (TCP) and the User Datagram Protocol (UDP) of the Internet Protocol Suite are commonly categorized as layer-4 protocols within OSI. Layer 5: session layer

The session layer controls the dialogues (connections) between computers. It establishes, manages and terminates the connections between the local and remote application. It provides for full-duplex, half-duplex, or simplex operation, and establishes checkpointing, adjournment, termination, and restart procedures. The OSI model made this layer responsible for graceful close of sessions, which is a property of the Transmission Control Protocol, and also for session checkpointing and recovery, which is not usually used in the Internet Protocol Suite. The session layer is commonly implemented explicitly in application environments that use remote procedure calls. Layer 6: presentation layer

The presentation layer establishes context between application-layer entities, in which the application-layer entities may use different syntax and semantics if the presentation service provides a big mapping between them. If a mapping is available, presentation service data units are encapsulated into session protocol data units, and passed down the protocol stack.

This layer provides independence from data representation (e.g., encryption) by translating between application and network formats. The presentation layer transforms data into the form that the application accepts. This layer formats and encrypts data to be sent across a network. It is sometimes called the syntax layer.[6]

The original presentation structure used the Basic Encoding Rules of Abstract Syntax Notation One (ASN.1), with capabilities such as converting an EBCDIC-coded text file to an ASCII-coded file, or serialization of objects and other data structures from and to XML. Layer 7: application layer

The application layer is the OSI layer closest to the end user, which means both the OSI application layer and the user interact directly with the software application. This layer interacts with software applications that implement a communicating component. Such application programs fall outside the scope of the OSI model. Application-layer functions typically include identifying communication partners, determining resource availability, and synchronizing communication. When identifying communication partners, the application layer determines the identity and availability of communication partners for an application with data to transmit. When determining resource availability, the application layer must decide whether sufficient network or the requested communication exists. In synchronizing communication, all communication between applications requires cooperation that is managed by the application layer. Some examples of application-layer implementations include:

   On OSI stack:
       FTAM File Transfer and Access Management Protocol
       X.400 Mail
       Common Management Information Protocol (CMIP)
   On TCP/IP stack:
       Hypertext Transfer Protocol (HTTP),
       File Transfer Protocol (FTP),
       Simple Mail Transfer Protocol (SMTP),
       Simple Network Management Protocol (SNMP), etc.

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