Question

Consider a packet of length L bits which begins at end host A and travels over two links to a destination end host B. These two links are connected by a router. Let di, si and Ri denote the length, propagation speed and the transmission rate of link i, for i = 1, 2. Assume the router delays each packet by dproc. Assuming no queuing delays, in terms of di, si and Ri, (i = 1, 2), and L, write down a formula for the total end-to-end delay for the packet. b) Suppose now the packet is 1000 Bytes, the propagation speed on both links is 3 * 108 m/sec, the transmission rate for both links is 1 Mbps, the router processing delay is 2 msec, the length of the first link is 3000 km and the length of the second link is 2000 km. For these values, compute the end-to-end delay

Answer 1

Packet length = L

Router delay = dproc

Distance or length = d_i

Propagation speed = s_i

Transmission Rate = R_i

a)

b)

Given,

Packet size (L) = 1000 Bytes = 1000 x 8 bits

Propagation speed = S₁ = S₂ = 3 X 10⁸ m/sec

Router processing delay = dproc = 2 msec

Transmission rates = R1 = R2 = 1 Mbps = 1 x 2²⁰ bps

Length of link1 = d1 = 3000 km

Length of link1 = d2 = 2000 km

End to End delay = (1000 x 8) / (2 x 10⁶) + (1000 x 8) / (2 x 10⁶) + (3000 x 10³) / (3 x 10⁸ ) + (2000 x 10³) / (3 x 10⁸ ) + (2ms)

End to End delay = ( 4 x 10^-3) + ( ( 4 x 10^-3) + (10 x 10^-2) + (6.6 x 10^-3) + (2ms)

End to end delay = 4 + 4 + 10 + 6.6 + 2 = 26.6 ms