Networking Equations

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  • Propagation delay = distance traveled / propagation speed
  • Transmission delay = # of bytes to transfer / transmission speed (or bandwidth)
  • Signal-to-noise ratio (dB)  = 10 log10 (S/N)
  • Attenuation in decibels = 10 log10 (Transmitted power/received power)
  • Nyquist Theorem : Maximum data rate = 2 H log2V bits/sec   where H is in Hz and V is # of levels
  • Shannon’s Result : Maximum number of bits/sec = H log2 (1+S/N)    where H is in Hz

 

  • Pure ALOHA  throughput          T = Ge-2G      Max throughput occurs at G = 0.5

T = throughput per frame time           e = 2.718

G = attempts per packet time

Throughput in bits per sec = T x transmission speed

Vulnerable period = 2 x frame transmission time

 

  • Slotted ALOHA throughput      T=Ge-G    Max throughput occurs at G = 1
  • TCP round-trip time

RTT = α RTTOLD + M(1 – α)                               RTTOLD = previously observed round-trip time

α = smoothing factor
M = observed round-trip time (actual time to receive an ACK)

D = βDOLD + (1 – β) · |RTT – M|                         DOLD = previously observed standard deviation

β = smoothing factor (may be α)
TCP Timeout = RTT + 4D

 

  • Ethernet / IEEE 802.3  (p. 280)

Channel efficiency = t / (t + 2G/A)

t = ave time to transmit a frame

G = end-to-end propagation time (time for frame to traverse entire Ethernet network)
2G = duration of each time slot

A = probability that some station acquires channel in a particular contention slot

= kP(1 – P)k-1

k = # of stations ready to transmit

P = probability that each station transmits during a contention slot

Channel efficiency = 1/(1 + 2BLe/cF)

B = network bandwidth                                       c = signal propagation speed

L = cable length                                                    F = frame length

e = contention slots per frame (2.718)

Maximum throughput = channel efficiency x transmission speed

Minimum frame length = 2 x propagation delay x transmission speed (data rate)
* 802.3 minimum frame length = 64 bytes