Performance

Bandwidth

• $\text{data rate}=\frac{\text{data transmitted}}{\text{time}}$
  • (bit rate $R$) (קצב נתונים)
    • $\text{bit-rate}=\frac{\text{data transmitted}\text{[bits]}}{\text{time}\text{[sec]}}$ (unit: bits per second (or bps))

• data bandwidth (or digital bandwidth or simply bandwidth)

• network throughput (or just throughput) (in bps)
  • “The amount of data that a medium transmits, either theoretically or practically, during a given period of time.” (West, 2021)
  • “Throughput at any point in a network is defined as the number of bits passing through the point in a second, which is actually the transmission rate of data at that point.” (Forouzan, 2012)
• “The throughput is a measure of how fast we can actually send data through a network. Although, at first glance, bandwidth in bits per second and throughput seem the same, they are different. …the bandwidth is a potential measurement of a link; the throughput is an actual measurement of how fast we can send data.” (Forouzan, 2012)
• “The terms bandwidth and throughput are often used interchangeably” (Kozierok, 2005)

Latency

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

• latency

  • the amount of time it takes for a packet of data to travel between two points across a network connection
  • ”The delay between the transmission of a signal and its receipt” (West, 2021)

• 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)

  • (internet layer) “The time a packet waits in input and output queues in a router” (Forouzan, 2012)

• (Processing delay)

  • (internet layer) “Time required to process a packet in a router or a destination host” (Forouzan, 2012)

• 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

  • $\text{RTT}\approx 2\times t_{\text{prop}}$

• (packet switched network with $S$ switches (i.e. $S+1$ links))

  • $\text{source}\to {\text{switch}}_1\to \cdots \to {\text{switch}}_S\to \text{destination}$
  • (store-and-forward) $T=(S+1)\cdot (t_{\text{tx}}+t_{\text{prop}})$ (time to send a packet from source to destination)
  • (cut-through) $T=t_{\text{tx}}+(S+1)\cdot t_{\text{prop}}+S\cdot \frac{H}{R}$.
    • $H$ is the header size (in bits)
    • $\frac{H}{R}$ is the cut-through delay at each switch

• (effective throughput) $\frac{\text{size}\text{[bits]}}{\text{RTT}+\frac{\text{size}\text{[bits]}}{\text{bandwidth}\text{[bps]}}}$

• (stop-and-wait)

  • $\text{throughput}\text{[bps]}=\frac{\text{packet-size}\text{[bits]}}{\text{RTT}}$
    • $\text{RTT}=N\cdot \left(\frac{\text{packet-size}\text{[bits]}+\text{ack-size}\text{[bits]}}{\text{bandwidth}\text{[bps]}}+2\cdot t_{\text{prop}}\right)$
      • $N$ is the number of links in one direction

Bandwidth-delay product

• bandwidth-delay product (in bits)
  • $\text{RTT}\times \text{bandwidth}$
  • the amount of data that can be in transit in the network at any given time
  • ”The bandwidth-delay product defines the number of bits that can fill the link.” (Forouzan, 2012)
  • link utilization = $\frac{\text{data in flight}}{\text{bandwidth-delay product}}$

File transfer time

• $T_{\text{total}}=t_{\text{handshake}}+t_{\text{data}}+t_{\text{prop}}$
  • $t_{\text{handshake}}=h\times \text{RTT}$, where $h$ is the number of RTTs needed for handshaking
    • (often $h=2$)
  • $t_{\text{prop}}\approx \frac{\text{RTT}}{2}$
  • $N=\lceil \frac{\text{file-size}\text{[bits]}}{\text{packet-size}\text{[bits]}}\rceil$ is the number of packets needed to transmit the file
  • $t_{\text{tx}}=\frac{\text{packet-size}\text{[bits]}}{\text{bandwidth}\text{[bps]}}$ is the transmission time for one packet
  • $N\cdot t_{\text{tx}}\approx \frac{\text{file-size}\text{[bits]}}{\text{bandwidth}\text{[bps]}}$ is the total transmission time for all packets
  • (Continuous pipeline)
    • $t_{\text{data}}=N\cdot t_{\text{tx}}$
  • (Stop-and-wait)
    • $t_{\text{data}}=N\cdot t_{\text{tx}}+(N-1)\cdot \text{RTT}$
  • (window limited to $W$ packets)
    • $t_{\text{data}}=(K-1)\cdot \text{RTT}$
      • $K=\lceil \frac{N}{W}\rceil$ (number of RTT rounds needed to send all packets)
      • $W$ is the window size (packets can be sent per RTT)
  • (exponential increase)
    • $t_{\text{data}}=(\lceil {\log }_2(N+1)\rceil -1)\cdot \text{RTT}$

draft

• (Channel utilization) $U=\frac{\text{throughput}}{R}$

References

• West, Jill (2021). Data Communication and Computer Networks. Course Technology.
• Forouzan, B. A. (2012). Data Communications and networking. McGraw-Hill Education.
• Kozierok, C. M. (2005). The TCP/IP guide: A Comprehensive, Illustrated Internet Protocols Reference. No Starch Press.