2 PROBLEM SOLUTIONS FOR CHAPTER 1
8. Call the routers A, B, C, D, and E. There are ten potential lines: AB, AC,
AD, AE, BC, BD, BE, CD, CE, and DE. Each of these has four possibilities
(three speeds or no line), so the total number of topologies is 4
10
= 1,048,576.
At 100 ms each, it takes 104,857.6 sec, or slightly more than 29 hours to
inspect them all.
9. The mean router-router path is twice the mean router-root path. Number the
levels of the tree with the root as 1 and the deepest level as n. The path from
the root to level n requires n − 1 hops, and 0.50 of the routers are at this level.
The path from the root to level n − 1 has 0.25 of the routers and a length of
n − 2 hops. Hence, the mean path length, l, is given by
l = 0.5 × (n − 1) + 0.25 × (n − 2) + 0.125 × (n − 3) +
...
or
l =
i =1
Σ
∞
n (0.5)
i
−
i =1
Σ
∞
i(0.5)
i
This expression reduces to l = n − 2. The mean router-router path is thus
2n − 4.
10. Distinguish n + 2 events. Events 1 through n consist of the corresponding
host successfully attempting to use the channel, i.e., without a collision. The
probability of each of these events is p(1 − p)
n − 1
. Event n + 1 is an idle
channel, with probability (1 − p)
n
. Event n + 2 is a collision. Since these
n + 2 events are exhaustive, their probabilities must sum to unity. The proba-
bility of a collision, which is equal to the fraction of slots wasted, is then just
1 − np(1 − p)
n − 1
− (1 − p)
n
.
11. Among other reasons for using layered protocols, using them leads to break-
ing up the design problem into smaller, more manageable pieces, and layering
means that protocols can be changed without affecting higher or lower ones,
12. No. In the ISO protocol model, physical communication takes place only in
the lowest layer, not in every layer.
13. Connection-oriented communication has three phases. In the establishment
phase a request is made to set up a connection. Only after this phase has been
successfully completed can the data transfer phase be started and data trans-
ported. Then comes the release phase. Connectionless communication does
not have these phases. It just sends the data.
14. Message and byte streams are different. In a message stream, the network
keeps track of message boundaries. In a byte stream, it does not. For exam-
ple, suppose a process writes 1024 bytes to a connection and then a little later
writes another 1024 bytes. The receiver then does a read for 2048 bytes.
With a message stream, the receiver will get two messages, of 1024 bytes
