Solution to Homework 1

Solution#1.3

Number of routers= 5
Therefore,
Number of point to point links in fully connected network = 5C2 = 10
There are four possibilities for each link-
  1. No connection
  2. High-speed line
  3. Medium-speed line
  4. Low-speed line
So total number of topologies= 410
Time to inspect one topology= 100 ms
Total time to inspect all topologies and find the best= 100 x 410 ms 
                                      = 104,857.6 sec
                                      ~ 29 hours (answer)


Solution#1.14

Probability that the frame is damaged = p
So, probability of successful frame transmission = (1-p)

Let k be the mean number of transmissions required to send a frame successfully.
So for (k-1) times the frame is damaged.

Probability of successful frame transmission= Number of suceessful transmissions/ Total number of transmissions 
i.e.                         1-p = 1/k



Therefore,
                               k = 1/1-p     (answer)

Solution#1.17

With n layers and h bytes added per layer, the total number of header bytes per message is hn, so fraction of the space wasted on headers is hn/(M + nh).


Solution#1.22

Bits carried by dog = 21 gigabytes or 168 gigabits.
speed = 18 km/hour = 0.005 km/sec
Data Rate = 155 Mbps
Time required to fill up the tape, t = 168 x 230 / 155 x 106 sec
Maximum distance that can be covered in time t, d = speed x t 
                                     = 0.005 x 168 x 230 / 155x106 km
                                     = 5.4 km
Therefore for d < 5.4 km dog has a higher rate than ATM line.