Consider a packet switched network with two intermediate nodes between sender A

Question

Consider a packet switched network with two intermediate nodes between sender A and receiver B (that is, A x y B.). Define C as The capacity of The links in bps. Define D as The bit size of application data. Define H as The header size in bits. Define P as The number of packets for this application data. Assume no processing and propagation delays. Nodes receive The whole packet and then transmit to The next node. Derive a formula for The end-to-end delay for that particular application data. Given that C = 5,000 bps, D = 50:000 bits, H = 500 bits, what would be The optimum number of packets that minimizes The total end-to-end delay? Calculate The delay too.

Explanation / Answer

T end to end = (P+2)*(H + (D/P))/C

to get optimum value of P i.e to get the value of P at which the equation becomes minimum

derive it with respect to P and equate it to zero

T end to end =(PH + D + 2H +2D/P ) / C

deriving the above will become

H + 0 + 0 -2D/P2 =0

=> P2 = (2D/H)  

=> P = 2D/H

for C=5000bps , D=50000 bits H=500bits

Popt = sqrt(2D/H) = sqrt(2*50000/500) = sqrt(200) = 14.14

rounding it to nearest intiger will become 14

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