Computer Network Unit 1 q what are the topologies in computer n/w ?

Q 11. Give mathematical derivation to sketch out efficiency of pure ALOHA & slotted ALOHA . draw a graph between system throughput and offered load.
Ans: Suppose N stations have packets to send

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  meach transmits in slot with probability p
  
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  mprob. successful transmission S is:
  
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  by single node:
  

S= p (1-p)^(N-1)

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  by any of N nodes
  

S = Prob (only one transmits) = N p (1-p^)(N-1)
Pure ALOHA
The value of p (p*) that maximizes the efficiency of
ALOHA is:
E(p) =Np(1 - p)2(N-1)
E’(p) =N(1 - p) 2N-2 – Np2(N-1)(1 - p) 2(N-3)
= N(1-p) 2(N-3) ((1 - p)-p2(N- 1))
E’(p) = 0 => p* = 1/(2N-1)
Using this value, the max efficiency of ALOHA is;
lim (N-> infinity) E(p*)= ½ * 1/e =1/2e
Slotted ALOHA
The value of p (p*) that maximises the efficiency of
slotted ALOHA is:
E(p) =Np(1 - p)N-1
E’(p) =N(1 - p) N-1- Np(N-1)(1 - p) N-2
= N(1-p) N-2((1 - p)-p(N- 1))
E’(p) = 0 => p* = 1/N
Using this value, the max efficiency of slotted ALOHA is;
E(p*)=N 1/N(1-1/N) N-1= (1-1/N) N-1= (1-1/N) N/(1-1/N)
lim (N-> infinity) (1-1/N) = 1 lim (N-> infinity) (1-1/N) N = 1/e
Thus: lim (N-> infinity) E(p*)= 1/e




Q 12. Explain
Stop and wait Protocol :

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  Stop-and-wait is a method used in telecommunications to send information between two connected devices.
  
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  It ensures that information is not lost due to dropped packets and that packets are received in the correct order.
  
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  It is the simplest kind of automatic repeat-request (ARQ) method. A stop-and-wait ARQ sender sends one frame at a time; it is a special case of the general sliding window protocol with both transmit and receive window sizes equal to 1.
  
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  After sending each frame, the sender doesn't send any further frames until it receives an acknowledgement (ACK) signal. After receiving a good frame, the receiver sends an ACK. If the ACK does not reach the sender before a certain time, known as the timeout, the sender sends the same frame again.