Performance

Bandwidth

• $\text{data rate}=\frac{\text{data transmitted}}{\text{time taken}}$
• $\text{Bit rate}=\frac{\text{ \# bits transmitted}}{\text{Time taken}}$ (unit: bits per second, bps)
• The bit rate $R$ (קצב נתונים) is the number of bits transmitted per a unit of time (unit: bps, bits per second)
• The data bandwidth (or digital bandwidth or simply bandwidth) is the maximum data rate that can be transmitted over a communication channel
• transmission rate?todo

Throughput

• Network throughput (or just throughput) (in bps) is a measurement of the average amount of data that actually passes through a network in a specific time frame, taking into account the impact of latency

Latency

$\text{Latency}=t_{\text{prop}}+t_{\text{tx}}+t_{\text{queue}}$

• latency is the amount of time it takes for a packet of data to travel between two points across a network connection
• latency (also called delay (?)todo) is the time it takes for data to pass from one point on a network to another
• (Propagation delay) $t_{\text{prop}}=\frac{d}{v}$
  • $d$ is the length of the physical link (in $\mathrm{m}$)
  • $v$ is the propagation speed in the medium (in $m/s$).
    • (Typically, $v\approx \frac{2}{3}c$, where $c$ is the speed of light in vacuum.)
• (Transmission delay) $t_{\text{tx}}=\frac{L}{R}=\frac{\text{length}\text{[bits]}}{\text{transmission rate}\text{[bps]}}$
• (Queueing delay)
• (Processing delay)
• round-trip time (RTT) (or (round-trip delay (RTD)): the time it takes for a signal to travel from the source to the destination and back again
  • $\text{RTT}\approx 2\times t_{\text{prop}}$

Bandwidth-delay product

• The bandwidth-delay product, $\text{RTT}\times \text{bandwidth}$, in bits, is the amount of data that can be in transit in the network at any given time

Stop-and-wait

$\text{Throughput}\text{[bps]}=\frac{\text{frame size}\text{[bits]}}{\text{RTT}}$

File transfer time

• Minimum transfer time: $\text{RTT}+t_{\text{tx}}$

• $T_{\text{total}}=t_{\text{handshake}}+t_{\text{data}}$

  • $t_{\text{handshake}}=k\times \text{RTT}$, where $k$ is the number of RTTs needed for handshaking
    • $2\times \text{RTT}$todo
  • (Continuous pipeline) $t_{\text{data}}=N\cdot t_{\text{tx}}+t_{\text{prop}}$
  • (Stop-and-wait) $t_{\text{data}}=(N-1)\cdot (t_{\text{tx}}+\text{RTT})+t_{\text{tx}}+t_{\text{prop}}$
  • (window-limited) $t_{\text{data}}=(K-1)\cdot \text{RTT}+t_{\text{prop}}$
    • $K=\lceil \frac{N}{W}\rceil$
    • $W$ is the window size (packets per RTT)
  • $N=\lceil \frac{\text{File Size}}{\text{Packet Size}}\rceil$ is the number of packets needed to transmit the file