Consider sending a large amount of data over a lossy link. Each bit can be indep

Question

Consider sending a large amount of data over a lossy link. Each bit can be independently
in error with a probability of b. Packets with any bit (data or header) in error are dropped
by the receiver. Each packet contains an h bit header and a d-bit data payload. The raw capacity
of the link is C bits per second.
(a) What is the probability that a packet gets dropped at the receiver?
(b) Compute the throughput over the link. Throughput is defined as the maximum
number of data bits received per second by the application. Assume that the sender is
sending packets back-to-back.
(c) Assume h = 100 and b = 10^(-5). What is the value of d that maximizes the
throughput over the link? Do not use a program to find the answer. Use algebra and
calculus; show your work.

Explanation / Answer

Answer a:

The probability of losing a packet is proportional to the number of bits transmitted, or the number of packets depends on both aspect.

Here, each packet having total number of bits (h+d) bits.

Transmitted data bits =(h+d)bits per packet.

Lets consider there are n number of packets.

So total number of bits=(h+d) * n;

Considering each bit can be independently in error with probability of b.

So the probability of packet getting dropped out of n number of data packets is

P= ((h+d)cb)*n) if taking error.

Or p =(((h+d)c b)/8)*n)

Answer b:

Approximate data throughput=(total number of received bytes /transmission time)*(8/1000) kbps.

=(((h+d)*n)/Ts)*(8/1000)kbps.

Ts=( h+d)/c)

Answer c:

Transmission time =(100+ 50) / 1000;

                                       =0.15 second.

Lets take d =50 bits and n= 5 packets.

Here, ignoring packet loss.

Through put =(((100+50) * 5) /0.15) *(8/1000)

                          = 40 bits /seconds

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