Network Models and Addressing

Data communication forms the backbone of modern information systems, transforming raw physical phenomena into structured digital interactions. To build reliable networks, engineers utilize highly structured architectural models and addressing schemes that allow disparate systems to exchange information across complex physical and logical topologies.

1. Physical Structures and Network Topologies

A network is a collection of devices, often called nodes, connected by communication links. A node can be a computer, printer, router, or any other device capable of transmitting or receiving data.

1.1 Connection Types

Before examining topologies, we must classify how links connect devices:

Point-to-Point: A dedicated link exists between exactly two devices. The entire capacity of the link is reserved for transmission between those two devices.
Multipoint (Multidrop): More than two specific devices share a single link. The capacity of the channel is shared either spatially (simultaneously) or temporally (timesharing).

1.2 Topologies

The term physical topology refers to the structural representation of how links and nodes are physically arranged.

text

    MESH TOPOLOGY                 STAR TOPOLOGY
       Node---Node                    Node
      /  \   /  \                      \
     /    \ /    \                      \
  Node-----X-----Node        Node-------[ HUB ]-------Node
     \    / \    /                      /
      \  /   \  /                      /
       Node---Node                    Node
 
    BUS TOPOLOGY                  RING TOPOLOGY
  [Node]  [Node]  [Node]              Node----Node
    |       |       |                /            \
  =====================             Node          Node
      (Backbone Cable)               \            /
                                      Node----Node

Mesh Topology

In a fully connected mesh topology, every device has a dedicated point-to-point link to every other device. For $N$ devices, the network parameters are:

$\text{Total physical duplex links} = \frac{N(N - 1)}{2}$

$\text{Input/Output (I/O) ports per device} = N - 1$

Advantages: Robustness (if one link fails, it does not affect the others), privacy and security (dedicated lines), and easy fault identification.
Disadvantages: Extreme cabling redundancy and expensive installation.

Star Topology

Each device has a dedicated point-to-point link only to a central controller, usually called a hub or switch. Devices do not communicate directly with each other.

Advantages: Less expensive than a mesh; easy installation and reconfigurability; robustness (single node link failure does not disable the network).
Disadvantages: High dependency on the central hub; if the hub goes down, the entire network fails.

Bus Topology

A multipoint configuration. One long cable acts as a backbone to link all devices in the network via drop lines and taps.

Advantages: Easy installation and sparse cabling.
Disadvantages: A fault or break in the backbone stops all transmission. Signal reflections at the ends require terminators.

Ring Topology

Each device has a dedicated point-to-point connection with only the two devices on either side of it. A signal is passed along the ring in one direction from device to device until it reaches its destination.

Advantages: Relatively easy to install and reconfigure. Fault isolation is simplified.
Disadvantages: Unidirectional traffic means a break in the ring can disable the entire network (unless a dual-ring configuration is used).

2. Theoretical Foundations: Analog and Digital Signals

To travel through a medium, data must be transformed into electromagnetic signals. Signals can be classified as either analog or digital.

2.1 Periodic Analog Signals

A periodic analog signal repeats a pattern over a continuous time frame. The sine wave is the fundamental periodic analog signal and can be described mathematically as:

$s(t) = A \sin(2\pi f t + \phi)$

Where:

$A$ is the peak amplitude (measured in Volts, $V$ ).
$f$ is the frequency (measured in Hertz, $Hz$ ), representing the rate of change.
$\phi$ is the phase (measured in degrees or radians), representing the waveform's offset relative to time $t = 0$ .

Frequency and Period

Frequency ( $f$ ) and period ( $T$ ) are inversely related:

$f = \frac{1}{T} \quad \text{and} \quad T = \frac{1}{f}$

| Unit of Period ( $T$ ) | Equivalent in Seconds ( $s$ ) | Unit of Frequency ( $f$ ) | Equivalent in Hertz ( $Hz$ ) | | :--- | :--- | :--- | :--- | | Seconds ( $s$ ) | $1\text{ s}$ | Hertz ( $Hz$ ) | | | Milliseconds () | | Kilohertz () | | | Microseconds () | | Megahertz () | | | Nanoseconds () | | Gigahertz () | |

Phase Shifts

A phase shift describes the position of the wave relative to time origin $t = 0$ :

text

    Phase = 0 degrees (In Phase)          Phase = 90 degrees (1/4 Cycle Offset)
          /\    /\    /\                      /\    /\    /\
        _/  \  /  \  /  \                    /  \  /  \  /  \
       /     \/    \/    \                  /    \/    \/    \
      0-------------------> t              0-------------------> t

$0^\circ$ Shift: Starts at $0$ and goes up.
$90^\circ$ Shift (or $\pi/2$ rad): Starts at its positive peak value.
$180^\circ$ Shift (or rad): Starts at and goes down.

Wavelength ( $\lambda$ )

Wavelength binds the period or frequency of a simple sine wave to the propagation speed ( $c$ ) of the medium:

$\lambda = c \times T = \frac{c}{f}$

For light or electromagnetic waves in a vacuum, $c \approx 3 \times 10^8\text{ m/s}$ . In a physical cable, the propagation speed is lower (e.g., $c \approx 2.4 \times 10^8\text{ m/s}$ ).

2.2 Time and Frequency Domains

An analog signal can be visualized in two ways:

Time-Domain Plot: Shows amplitude changes over time.
Frequency-Domain Plot: Shows amplitude versus frequency. A complete sine wave in the time domain is represented by a single spike in the frequency domain.

text

       TIME DOMAIN                           FREQUENCY DOMAIN
    Amplitude                              Amplitude
       ^     /\    /\                         ^
       |    /  \  /  \                        |      | (Single Spike at f1)
       |   /    \/    \                       |      |
       +-----------------> Time               +------+-------------> Frequency
       0         T                            0      f1

According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases.

Periodic Composite Signals: Decompose into a series of signals with discrete frequencies.
Nonperiodic Composite Signals: Decompose into an infinite combination of sine waves with continuous frequencies.

The bandwidth ( $B$ ) of a composite signal is the difference between its highest ( $f_h$ ) and lowest ( $f_l$ ) frequencies:

$B = f_h - f_l$

3. Transmission Impairments and Performance Metrics

Signals travel through imperfect transmission media. This imperfection causes signal degradation, meaning the received signal differs from the transmitted one.

text

    [Transmitted Signal] ------> [ TRANSMISSION MEDIUM ] ------> [Received Signal]
                                           ^
                                           |
                                  - Attenuation (Power Loss)
                                  - Distortion (Phase Delay)
                                  - Noise (Thermal, Crosstalk, External)

3.1 Attenuation (Power Loss)

Attenuation represents a loss of energy. When a signal travels through a medium, some of its energy is lost as heat. Engineers use the decibel (dB) to measure the relative strength or loss of a signal:

$\text{dB} = 10 \log_{10}\left(\frac{P_2}{P_1}\right)$

Where $P_1$ is the input power and $P_2$ is the output power.

A negative decibel value indicates attenuation (loss). For example, if a signal's power is halved ( $P_2 = 0.5 P_1$ ): $\text{dB} = 10 \log_{10}(0.5) \approx -3\text{ dB}$

3.2 Noise and Signal-to-Noise Ratio (SNR)

Noise is unwanted background energy that corrupts a signal. The Signal-to-Noise Ratio (SNR) measures the ratio of signal power to noise power:

$\text{SNR} = \frac{P_{\text{signal}}}{P_{\text{noise}}}$

$\text{SNR}_{\text{dB}} = 10 \log_{10}(\text{SNR})$

3.3 Network Performance Metrics

Latency (Delay)

Latency is the total time it takes for a message to travel from source to destination:

$\text{Latency} = T_{\text{prop}} + T_{\text{trans}} + T_{\text{queue}} + T_{\text{proc}}$

Propagation Time ( $T_{\text{prop}}$ ): The time required for a single bit to travel from the source to the destination. $T_{\text{prop}} = \frac{\text{Distance}}{\text{Propagation Speed}}$

Bandwidth-Delay Product (BDP)

The Bandwidth-Delay Product (BDP) defines the volume of a communication link. It represents the maximum number of bits that can fill the link at any given moment:

$\text{BDP} = \text{Bandwidth (bps)} \times \text{Delay (seconds)}$

text

    Visualizing the Link as a Pipe:
    |<------------------------- Delay ------------------------->|
    =============================================================
    ===> Bits in transit: [0][1][1][0][1][0][1][0][0][1][1][0]  | ---> Cross-Sectional Area
    =============================================================    (Bandwidth)

4. Channel Capacity and Data Rate Limits

A key concern in networking is how fast data can be sent over a channel. This speed depends on three factors: available bandwidth, signal levels, and noise.

4.1 Noiseless Channels: Nyquist Bit Rate

For a noiseless channel, the Nyquist formula defines the theoretical maximum bit rate:

$\text{Bit Rate} = 2 \times B \times \log_2(L)$

Where:

$B$ is the bandwidth of the channel in Hertz.
$L$ is the number of discrete signal levels used to represent data.

Increasing the number of signal levels ( $L$ ) allows more bits to be sent per level ( $\log_2(L)$ ), but it also increases system complexity and error susceptibility in the presence of even minimal noise.

4.2 Noisy Channels: Shannon Capacity

Real-world channels are noisy. Claude Shannon developed a formula to determine the absolute theoretical limit of a noisy channel's data rate, regardless of how many signal levels are used:

$C = B \times \log_2(1 + \text{SNR})$

Where $C$ is the channel capacity in bits per second (bps).

4.3 Practical Implementation: Combining Nyquist and Shannon

In network design, the Shannon formula gives the upper limit of what is physically possible. The Nyquist formula is then used to determine the number of signaling levels ( $L$ ) required to achieve the target rate.

5. Layered Network Architectures: OSI vs. TCP/IP

To handle the complexity of network communications, functions are organized into layered models. Each layer performs specific tasks and provides services to the layer above it.

5.1 The ISO/OSI Model

The Open Systems Interconnection (OSI) model is a theoretical seven-layer framework developed by the International Standards Organization (ISO).

text

           OSI MODEL                         TCP/IP SUITE
    +-----------------------+          +-----------------------+
  7 |      Application      |          |                       |
    +-----------------------+          |      Application      |
  6 |     Presentation      |          |                       |
    +-----------------------+          +-----------------------+
  5 |        Session        |          |       Transport       |
    +-----------------------+          +-----------------------+
  4 |       Transport       |          |        Network        |
    +-----------------------+          +-----------------------+
  3 |        Network        |          |       Data Link       |
    +-----------------------+          +-----------------------+
  2 |       Data Link       |          |       Physical        |
    +-----------------------+          +-----------------------+
  1 |       Physical        |
    +-----------------------+

7. Application Layer: Responsible for providing services directly to the user (e.g., HTTP, FTP, SMTP).
6. Presentation Layer: Manages data translation, compression, and encryption.
5. Session Layer: Coordinates dialog control, session establishment, and synchronization.
4. Transport Layer: Ensures process-to-process delivery of the entire message. It manages segmentation, flow control, and error recovery.
3. Network Layer: Handles source-to-destination packet delivery across multiple links. It is responsible for logical routing and path selection.
2. Data Link Layer: Responsible for hop-to-hop frame delivery over a single physical link. It manages physical addressing (MAC), framing, and node-level flow/error control.
1. Physical Layer: Responsible for transmitting individual raw bits over a physical medium (e.g., copper wire, fiber optics).

5.2 The TCP/IP Protocol Suite

The TCP/IP model is the practical, five-layer architectural framework that powers the modern Internet. It combines the Session and Presentation layers of the OSI model into a single Application layer:

Application
Transport
Network (Internet)
Data Link
Physical

5.3 Encapsulation

As data travels down the protocol stack at the transmitter, each layer adds its own control information, called a header (and sometimes a trailer). This process is known as encapsulation. At the receiver, this process is reversed (decapsulation).

text

    Layer          Data Unit                  Process
    -----------------------------------------------------------------
    Application    [   Data   ]               Raw Message
                        |
    Transport      [H4][ Data ]               Segment / User Datagram
                        |
    Network        [H3][H4][ Data ]           Datagram / Packet
                        |
    Data Link      [H2][H3][H4][ Data ][T2]   Frame
                        |
    Physical       01101010100101011101       Bitstream Transmission

6. Addressing Schemes in TCP/IP Networks

Four distinct levels of addressing are used in a TCP/IP network to route data from a source application to a destination application:

text

    +-----------------------+------------------------------------------+
    | Address Level         | TCP/IP Layer / Scope                     |
    +-----------------------+------------------------------------------+
    | Specific Addresses    | Application Layer (e.g., email / URL)    |
    | Port Addresses        | Transport Layer (16-bit process port)    |
    | Logical Addresses     | Network Layer (IPv4 / IPv6)              |
    | Physical Addresses    | Data Link/Physical Layer (MAC address)   |
    +-----------------------+------------------------------------------+

6.1 Physical (MAC) Address

Scope: Local-link (hop-to-hop).
Format: Typically a 48-bit (6-byte) hexadecimal address written as twelve hexadecimal digits grouped in pairs (e.g., 07:01:02:01:2C:4B).
Behavior: The source and destination physical addresses change at every router hop along the path.

6.2 Logical (IP) Address

Scope: Global-network (source-to-destination).
Format: 32-bit (IPv4) or 128-bit (IPv6).
Behavior: Logical addresses remain constant from the source host to the destination host, regardless of how many router hops the packet passes through.

6.3 Port Address

Scope: Process-level (process-to-process).
Format: A 16-bit integer representing a specific running application process (e.g., port 80 for HTTP, port 443 for HTTPS).
Behavior: Port addresses remain constant from the source to the destination.

7. The Internet Protocol (IP) Datagram and Fragmentation

The network layer uses the Internet Protocol (IP) to transport data across physical boundaries. Packets at this layer are called datagrams.

7.1 IPv4 Datagram Header Format

An IPv4 datagram consists of a variable-length header (20 to 60 bytes) and a data payload. The header is typically represented in 32-bit (4-byte) rows:

text

     0                   1                   2                   3
     0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |Version|  HLEN |    DSCP/ECN   |          Total Length         |  Row 1
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |         Identification        |Flags|      Fragment Offset    |  Row 2
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |  Time to Live |    Protocol   |        Header Checksum        |  Row 3
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                         Source IP Address                     |  Row 4
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                      Destination IP Address                   |  Row 5
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                   Options (Variable, 0 to 40 bytes)           |  Row 6...
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

Version (4 bits): Defines the IP version (e.g., 0100 for IPv4).
HLEN (4 bits): Header length represented in 4-byte words. $\text{Header Length (bytes)} = \text{HLEN} \times 4$ The minimum value is $5$ ( $20$ bytes) and the maximum is $15$ ( $60$ bytes).
Total Length (16 bits): Defines the entire size of the datagram (header + data) in bytes. The maximum size is .

7.2 Fragmentation Mechanics

Different networks have different limits on the maximum frame size they can carry, known as the Maximum Transfer Unit (MTU). When an IP datagram's total length exceeds a network's MTU, it must be divided into smaller pieces through a process called fragmentation.

Fragmentation Fields

Identification (16 bits): A unique identifier shared by all fragments of the same original datagram.
Flags (3 bits):
- Bit 0: Reserved (must be 0).
- Bit 1 (DF): Don't Fragment. If set to 1, the packet cannot be fragmented. If it exceeds an MTU, it is discarded, and an ICMP error is returned.
- Bit 2 (MF): More Fragments. If set to 1, more fragments follow. If set to 0, this is the last fragment.
Fragment Offset (13 bits): Indicates the position of the fragment's payload relative to the beginning of the original unfragmented data payload, measured in 8-byte units. $\text{Actual byte position} = \text{Fragment Offset} \times 8$

Step-by-Step Fragmentation Example

Consider an original IP datagram with a total length of 4020 bytes (including a standard 20-byte header, so the data payload is 4000 bytes) that needs to pass through a network with an MTU of 1420 bytes.

text

    [Original Datagram: Total Length = 4020, Header = 20, Payload = 4000]
                                   |
              +--------------------+--------------------+
              |                                         |
     [Fragment 1]                              [Fragment 2]
     Total Length = 1420                       Total Length = 1420
     Header = 20                               Header = 20
     Payload = 1400 (Bytes 0-1399)             Payload = 1400 (Bytes 1400-2799)
     MF = 1, Offset = 0                        MF = 1, Offset = 175
              |
              +--------------------+
              |
     [Fragment 3]
     Total Length = 1220
     Header = 20
     Payload = 1200 (Bytes 2800-3999)
     MF = 0, Offset = 350

Fragment 1:
- Max payload size allowed: $1420 - 20 = 1400\text{ bytes}$ .
- Payload bytes sent: $0$ to $1399$ (length $= 1400$ bytes, which is divisible by 8).
- Header fields:
  - Total Length = $1420$ bytes

8. Summary

Physical Topologies determine how links are arranged in a network. Mesh topologies offer high redundancy but require complex cabling. Star topologies centralize connections through a hub or switch, making them easier to manage.
Signals can be periodic analog (represented by sine waves) or nonperiodic digital. The bandwidth of a composite signal is the difference between its highest and lowest frequency components.
Transmission Impairments include attenuation, distortion, and noise. Net signal loss or gain across cascaded systems can be calculated by adding their individual decibel (dB) values.
Data Rate Limits are governed by the Nyquist limit for noiseless channels ( $2 B \log_2(L)$ ) and the Shannon capacity limit for noisy channels ( $B \log_2(1 + \text{SNR})$ ).

Assessed progress

Network Models and Addressing

Key Concepts

OSI Reference Model

TCP/IP Protocol Suite

Shannon Capacity & Nyquist Rate

IP Fragmentation & Offset

Hierarchical Addressing

Quick Check

Computer Networks

Computer Networks