Liberty Holleman
445800543
Tulsa Wednesday 5:30
TCOM 5413
Homework 5
Problem 1 [48 points] (no partial credit will be given here)
There are n cities (say, city 1, city 2, …, city n), each with a given number of terminals to
be connected to a central computer. Each city j has Nj terminals. Every terminal
generates one message, on average, once every M seconds. The average message length
is L bits.
1. If the network connecting these cities has a star topology, then the total incoming
message rate for the network (i.e, ) is equal to:
n
n
N j
a.
j 1
n
n
N j
b.
j 1
L
n
N j
c.
j 1
M
N j
d. L * (
j 1
n
e. Cannot tell
)
2. If the network connecting these cities has a tree topology, then the total incoming
message rate for the network (i.e, ) is equal to:
n
n
N j
a.
j 1
n
n
N j
b.
j 1
L
n
N j
c.
j 1
M
N j
d. L * (
j 1
n
e. Cannot tell
)
3. If the network connecting these cities has a star topology, then the absolute minimum
capacity to assign to each link j connecting city j to the central site is equal to:
a.
Nj
L
a. cannot tell
b.
Nj
M
c. L * N j
d. M * N j
e.
Nj
L*M
f.
L*N j
M
4. If the network connecting these cities has a tree topology, then the absolute minimum
capacity to assign to each link j connecting city j (in a direct or indirect way) to the
central site is equal to:
a.
Nj
L
g. cannot tell
b.
Nj
M
c. L * N j
d. M * N j
e.
Nj
L*M
f.
L*N j
M
5. The company designing the network using a star topology can afford this year a
budget that allows a total of W bps to be allocated among the links in the network.
However, if the company waits until next to design the network using the star
topology, a total of 2*A bps can be allocated among the links. Is the following
statement true or false: “If the company waits until next year, then the optimal
capacity to allocate to each link will double and the minimum average message delay
for the entire network will be reduced by half.”
a. true
b. false
6. The company designing the network using a tree topology can afford this year a total
of W bps to be allocated among the links in the network. However, if the company
waits until next to design the network using the same tree topology, a total of 2*W
bps can be allocated among the links. Is the following statement true or false: “If the
company waits until next year, then the optimal capacity to allocate to each link will
double and the minimum average message delay for the entire network will be
reduced by half.”
a. true
b. false
Problem 2 [52 points] (No partial credit will be given here)
A company has three regions (A, B and C), each region has several terminal sites. Each
terminal generates one message, on average, once every 10 seconds. The average
message length is 100 bits. We want to connect all the sites in each region to a
concentrator in a tree topology, and then connect the three concentrators to a central site
in a star topology. The company can afford to allocate a total of 5000 bps to connect all
the sites in region A to the concentrator in A, a total of 4000 bps to connect all the sites in
region B to the concentrator in B, and a total of 6000 bps to connect all the sites in region
C to the concentrator in C. Also, the company can afford to allocate a total of 10000 bps
to connect all the three concentrators to the central site.
The number of terminals in each site of the three regions is shown in the table below.
Site
1
2
3
4
5
Region A
Number of
terminals
5
5
2
3
10
Site
1
2
3
4
Region B
Number of
terminals
4
8
6
2
Site
1
2
3
4
5
Region C
Number of
terminals
6
5
5
4
12
1. (No partial credit will be given here). For each region, determine the optimal
capacity to allocate each link in the tree in order to minimize the average message
delay in the regional network by filling out the following table.
Region A
Region B
Region C
Link
1
2
3
4
5
Capacity
1547.951672
1024.982797
530.4597767
655.1829936
1241.422761
Link
1
2
3
4
Capacity
Link
1
2
3
4
5
1254.630377
1254.630377
954.3728441
536.3664023
Capacity
1586.127229
1227.452569
847.2293573
753.0636146
1586.127229
2. (No partial credit will be given here). Determine the optimal capacity to allocate to
each of the three links (link A, link B, and link C) to connect the concentrators to the
central site in order to minimize the average message delay in the network connecting
the concentrators to the central site by filling out the following table.
Link
Link A
Link B
Link C
5
Capacity
3300.434918
2928.391935
3771.173146
Link 2
Link 5
2
Link 3
Link 1
1
3
Link 4
A
4
Link A
Link 3
Link 1
3
1
Link B
Central
Site
B
Link 4
Link 2
2
Link C
Link 2
2
Link 3
Link 1
1
3
C
Link 4
Link 5
5
4
4