Reference Card

1 Probability and Related Topics:

Notation

\(O_i\) denotes sample point \(i\).
\(\mathcal{S}\) denotes the sample space.
\(P\{O_{i}\}\) denotes the probability of \(O_i\).
\(f(x)\) denotes the probability that the random variable \(X\) takes on the value \(x\).
\(E(X)\) denotes the expected value of the random variable \(X\).
\(P(A)\) denotes the probability of event \(A\).
\(P(A|B)\) denotes the conditional probability of event \(A\) given event \(B\).
\(\lambda\) denotes the arrival rate.
\(\mu\) denotes the service rate.

Important Facts/Results

\( P(A \mbox{ or } B \mbox{ or both}) = P(A) + P(B) - P(A \mbox{ and } B) \)

\( P(A \mbox{ and } B) = P(A|B) \cdot P(B) \)

Assuming certain assumptions are satisfied, the expected size of a queueing system is given by \(\lambda / (\mu - \lambda)\).

Assuming certain assumptions are satisfied, the expected time in a queueing system is given by \(1 / (\mu - \lambda)\).

2 File Sharing and Related Topics:

Notation

\(N\) denotes the number of machines that want the file
\(F\) denotes the size of the file (in bits)
\(u_S\) denotes the source's upload rate
\(u_i\) denotes the upload rate of machine \(i\)
\(d_i\) denotes the download rate of machine \(i\)
\(d_{\mbox{min}} = \min\{d_1, d_2, \ldots, d_N\}\)
\(D\) denotes the total time

Important Facts/Results

\( D_{\text{Clint-Server}} = \max \left\{ \frac{NF}{u_S}, \frac{F}{d_{\mbox{min}}} \right\} \)

\( D_{\text{Peer-to-Peer}} \approx \max \left\{ \frac{F}{u_S}, \frac{F}{d_{\mbox{min}}}, \frac{NF}{u_\mbox{total}} \right\} \)

3 Some HTML Elements:

The entire document is contained between an <html> tag and an </html> tag.

Metadata (i.e., data about the document) is contained between optional <head> and </head> tags.

The main part of the document is contained between a <body> tag and a </body> tag.

Paragraphs are contained between <p> and </p> tags. Paragraphs can contain text and other elements (e.g., images and links).

Images are specified using <img/> tags. They have a src attribute that contains the URL of the image file. The value of the src attribute follows the = character and is in quotes (e.g., <img src="DukeDog.png" />).

Links (or anchors) are specified using <a> and </a> tags. The URL of the link (i.e., the file to retrieve when the link is clicked) is specified with the href attribute. The value of the href follows the = character and is in quotes. The text of the link (i.e., the text that the user can click on to retrieve the URL) is contained between the <a> and </a> tags (e.g., <a href="http://www.cs.jmu.edu/index.html">JMU CS<a>).

4 Flow Control and Related Topics:

Notation

\(L\) denotes the length of the frame
\(R\) denotes the transmission rate
\(d_{\text{trans}} = L/R\) denotes the frame transmission delay
\(d_{\text{prop}}\) denotes the propagation delay
\(RTT = 2 \cdot d_{\text{prop}}\) denotes the round-trip time (i.e., round-trip propagation delay)
\(d_{\text{ack}}\) denotes the ACK transmission delay
\(d_{\text{proc}}\) denotes the processing time
\(d_{\text{total}} = d_{\text{trans}} + RTT + d_{\text{ack}} + 2 \cdot d_{\text{proc}}\)
\(U\) denotes the utilization rate (and is defined as \(d_{\text{trans}}/d_{\text{total}}\))

Important Facts/Results

\(U_\text{Stop-and-Wait} = \frac{1}{1 + \left(\frac{RTT}{d_{\text{trans}}}\right)}\)

\(U_\text{Fixed Window} = \frac{w}{w + \left(\frac{RTT}{d_{\text{trans}}}\right)}\)

5 Graphs and Networks:

Notation

\(V\) is a non-empty, finite set of vertices (or nodes)
\(L\) is a finite set of unordered pairs of distinct elements of \(V\) called links (or edges or arcs)
A simple graph, \(G\), is an ordered pair \((V,L)\)

6 Waves, Data, Signals and Related Topics:

Notation

\(\lambda\) denotes the wavelength
\(f\) denotes the frequency
\(v = \lambda f\) denotes the velocity
\(M\) denotes the maximum data rate (in bits per second)
\(H\) denotes the bandwidth of the channel (in Hz)
\(V\) denotes the number of discrete levels in the signal (in levels per cycle)
\(S/N\) denotes the signal to noise ratio

Important Facts/Results

In a perfect (i.e., noiseless) channel:
\( M = 2 H \log_{2}(V) \)

In a noisy channel (under appropriate assumptions):
\( M = H \log_{2}(1 + S/N) \)

7 Ethernet and Related Topics:

Notation

\(d_{\text{prop}}\) denotes the time to transmit a maximum size frame

Important Facts/Results

\(U_\text{Ethernet} = \frac{1}{1 + 5 d_{\text{prop}} / d_{\text{max}}}\)

8 IP Addresses and TCP/UDP Ports:

Addresses

Class A addresses (in binary) start with 0.
Class B addresses (in binary) start with 10.
Class C addresses (in binary) start with 110.
Class D addresses (in binary) start with 1110.

Addresses in the following ranges are private addresses:

10.0.0.0 - 10.255.255.255
172.16.0.0 - 172.31.255.255
192.168.0.0 - 192.168.255.255

Some Well-Known Ports

13 - Daytime
17 - Quote of the Day
20 - File Transfer Protocol (FTP) data
21 - FTP control
22 - Secure Shell (SSH)
23 - Telnet
25 - Simple Mail Transfer Protocol (SMTP)
67 - Dynamic Host Configuration Protocol (DHCP) server
68 - Dynamic Host Configuration Protocol (DHCP) client
80 - Hypertext Transfer Protocol (HTTP)
109 - Post Office Protocol (POP) v2
110 - POP v3
220 - IMAP v3
389 - LDAP
443 - HTTPS
520 - Routing Information Protocol (RIP)
989 - FTPS data
990 - FTPS control

9 Frame/Packet/Datagram/Message Formats:

Ethernet

Preamble (7 octets)
Alert (1 octets)
MAC Destination (6 octets)
MAC Source (6 octets)
Length (2 octets)
Payload (46-1500 octets)
Frame Check Sequence/CRC (4 octets)

Version (4 bits)
Header Length (4 bits)
Type of Service (8 bits)
Total Length (16 bits)
Identification (16 bits)
Flags (3 bits)
Fragment Offset (13 bits)
Time to Live (8 bits)
Protocol (8 bits)
Header Checksum (16 bits)
Source Address (32 bits)
Destination Address (32 bits)
Options (Variable)
Payload (Variable)

TCP

Source Port (16 bits)
Destination Port (16 bits)
Sequence Number (32 bits)
Acknowledgement (32 bits)
Header Length (4 bits)
Reserved (3 bits)
NS Flag (1 bit)
CWR Flag (1 bit)
ECE Flag (1 bit)
URG Flag (1 bit)
ACK Flag (1 bit)
PSH Flag (1 bit)
RST Flag (1 bit)
SYN Flag (1 bit)
FIN Flag (1 bit)
Receiver Window Size (16 bits)
Checksum (16 bits)
Urgent Pointer (16 bits)
Options (Variable)
Payload (Variable)

UDP

Source Port (16 bits)
Destination Port (16 bits)
Total Length in Octets (16 bits)
Checksum (16 bits)