All formulas used in Computer Networks till GATE 2020



This article consists of all formulas used in GATE examination till 2019 paper in CSE branch. I made this cause I could not find collection of all formulas at one place. If I missed any formula please mention it in comment so I can include it.
I hope this helps to people in need.

Delays :-

\[Transmission\thinspace delay\thinspace :\thinspace T_d,\thinspace \thinspace \thinspace \thinspace Frame\thinspace size\thinspace in\thinspace bits:\thinspace L, \thinspace \thinspace \thinspace \thinspace Bandwidth:\thinspace B\]\[Propagation\thinspace delay\thinspace :\thinspace P_d,\thinspace \thinspace \thinspace \thinspace Distance :\thinspace L, \thinspace \thinspace \thinspace \thinspace Speed:\thinspace B\]
\[T_d=L/B\]
\[P_d=D/S\]
\[Total\thinspace delay = T_d+P_d\]


Capacity:-

\[Half\thinspace\thinspace duplex\thinspace \thinspace \thinspace \thinspace C=B*P_d\]
\[Full\thinspace\thinspace duplex\thinspace \thinspace \thinspace \thinspace C=2*B*P_d\]


Stop and Wait :-

\[Efficiency:\eta,\thinspace\thinspace\thinspace \alpha = P_d/T_d\]
\[\eta = \frac{1}{1+2\alpha}\]
\[Throughput = \eta * B\thinspace\thinspace\thinspace =\thinspace\thinspace \frac{Total\thinspace data}{Total\thinspace time}\]

Sliding Window:-

\[window\thinspace size = 1+2\alpha\]
\[Minimum\thinspace number\thinspace of\thinspace bits\thinspace for\thinspace sequence\thinspace field = \left \lceil \log_2 (1+2\alpha ) \right \rceil\]


Time Division Multiplexing (TDM):-

\[each\thinspace slot\thinspace is\thinspace P_d+T_d\]
\[\eta =\frac{1}{1+\alpha }\]

Polling:-

\[Time\thinspace take\thinspace for\thinspace a\thinspace poll\thinspace : \thinspace T_{poll}\]
\[time\thinspace per \thinspace station = T_{poll}+P_d+T_d\]
\[\eta =\frac{T_d}{T_{poll}+P_d+T_d}\]

CSMA/CD:-

\[T_d\geq 2*P_d\]
\[L\geq 2*P_d*B\]
\[\eta = \frac{1}{1+6.44*\alpha }\]


ALOHA:-

Pure ALOHA:

\[\eta = G * e^{-2G}\] 
\[\eta_m_a_x = 0.184\thinspace\thinspace\thinspace at\thinspace\thinspace G=1/2\]

Slotted ALOHA:

\[\eta = G * e^{-G}\]
\[\eta_m_a_x = 0.368\thinspace\thinspace\thinspace at\thinspace\thinspace G=1\]


Max Data Rate:-

Noiseless channel (Nquist bit rate) :

\[L : Number\thinspace of\thinspace signal\thinspace levels\]
\[Bit\thinspace Rate=2*Bandwidth*\log_2L\]

Noisy channel (shannon capacity):

\[C=Bandwidth*\log_2(1+S/N)\]
\[S/N \thinspace is\thinspace signal\thinspace to\thinspace noise\thinspace ratio\thinspace in\thinspace dB\]
\[X\thinspace dB = 10\log_{10}(S/N)\]

Hamming distance:-

\[Number\thinspace of\thinspace correction\thinspace bits\thinspace with\thinspace e\thinspace errors= 2*e+1\]


Token bucket:-

\[M:\thinspace max\thinspace burst,\thinspace\thinspace\thinspace\thinspace P:\thinspace rate\thinspace of\thinspace arrival,\thinspace\thinspace\thinspace\thinspace C:\thinspace capacity\thinspace of\thinspace bucket\]
\[S=\frac{C}{M-P}\]


RSA:-

\[private\thinspace key (d,n) \thinspace\thinspace\thinspace\thinspace\thinspace public\thinspace key (e,n)\]
\[p\thinspace\thinspace and\thinspace\thinspace q\thinspace are\thinspace large\thinspace primes\]
\[n=p*q \thinspace\thinspace ,\thinspace\thinspace z=(p-1)*(q-1)\]
\[d\thinspace is\thinspace a\thinspace relative\thinspace prime\thinspace to\thinspace z\thinspace\]
\[find\thinspace e\thinspace such\thinspace that\thinspace\thinspace\thinspace (e*d)mod\thinspace z = 1\]

Encryption:

\[C:cypher\thinspace text\]
\[C = P^{e}mod\thinspace n\]

Decryption:

\[P:plain\thinspace text\]
\[P = C^{d}mod\thinspace n\]


Diffie-Hellman:-

\[N\thinspace is\thinspace a\thinspace large\thinspace prime\thinspace such\thinspace that\thinspace (N-1)/2\thinspace\thinspace is\thinspace\thinspace also\thinspace a\thinspace\thinspace prime\]
\[G\thinspace is\thinspace a\thinspace prime\thinspace number\]
\[Sender\thinspace chooses\thinspace a\thinspace large\thinspace random\thinspace number\thinspace x\]
\[R1=G^{x}mod\thinspace N\]
\[then\thinspace sends\thinspace it\thinspace to\thinspace receiver\]
\[Receiver\thinspace chooses\thinspace a\thinspace large\thinspace random\thinspace number\thinspace y\]
\[R2=G^{y}mod\thinspace N\]
\[then\thinspace sends\thinspace it\thinspace to\thinspace sender\]
\[Sender\thinspace calculates\thinspace \thinspace\thinspace\thinspace\thinspace K=(R2)^{x}mod\thinspace N\]
\[Receiver\thinspace calculates\thinspace \thinspace\thinspace\thinspace\thinspace K=(R1)^{y}mod\thinspace N\]
\[K\thinspace is\thinspace symetric\thinspace key\]

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