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Exam 2, Part A
April 16, 1999
You may use one page of notes. Write your answers in the space provided.
- (15 points) Consider the version of the “broadcast packet switch” shown below.
- 8 - 2 -
- 1 - 8 -
- 10 - 4 -
- 10 - 11 -
- 8 - 10 -
- 1 - 6 -
- 10 - 1 -
- 10 - 14 -
- 8 - 2 -
- 1 - 8 -
- 10 - 4 -
- 10 - 11 -
- 8 - 10 -
- 1 - 6 -
- 10 - 1 -
- 10 - 14 -
0 1 2 3 4
MI
0 1 2 3 4
VCI
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15
fanout,MI
output
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15
In this system, the IPP routing tables specify the outputs for unicast cells and they also specify the fanout and MI values for multicast cells. The copy network replicates cells as specified by the fanout, the multicast routing tables specify the outputs for multicast cells (using the MI) and the routing network delivers cells to their outgoing links. In the copy network, copying is delayed as long as possible and SEs that don’t copy cells distribute them randomly over all their outputs, in order to balance the load. Assume that if a cell with an odd fanout value is copied at an SE the fanout value is split as evenly as possible with the top SE output getting the “extra copy.” Given the table entries shown, how much bandwidth will be used on links (1,3) and (3,9) of the routing network as a result of cells arriving at input 4 with VCI 1, assuming that the rate at which cells arrive is 160 Mb/s. (Note that links (1,3) and (3,9) in the routing network on emphasized with heavier lines.)
How much bandwidth will be used on links (1,3) and (3,9) of the routing network as a result of cells arriving at input 6 with VCI 3, assuming that the rate at which cells arrive is 80 Mb/s?
How much bandwidth will be used on links (1,3) and (3,9) of the routing network as a result of cells arriving at input 9 with VCI 2, assuming that the rate at which cells arrive is 800 Mb/s?
- (15 points) Fill in the following table.
x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 3 ; 6 (x)
What is ( 2 ; 117 ) in D 243 ; 3?
What is ( 2 ; 117 ) in Y 243 ; 3?
- (20 points) For each of the following systems give the speed advantage needed to make them nonblocking for unicast traffic. Assume there is no minimum virtual circuit rate and that the highest virtual circuit rate equals the link rate. Static routing network with topology C (^5123) ; 32 ; 48
Static routing network with topology B 256 ; 4
For each of the following systems give the speed advantage needed to make them strictly nonblocking for multicast traffic. Assume there is no minimum virtual circuit rate and that the highest virtual circuit rate equals the link rate. Static routing network with topology B 256 ; 4 ; B 256 ; 4 , assuming that routes are setup with a maximum fanout of 16 in each of the two subnetworks.
Dynamic routing network with topology D 1024 ; 4 ; 3.
- (15 points) How many paths are there from input 68 to output 742 in D 1024 ; 4 ; 2?
Link ( 3 ; 134 ) is on one of these paths. List two other links in stage 3 that are also?
Name one link in stage 4 that is on a path from input 68 to output 742?
- (15 points) C 18 ; 3 ; 3 is rearrangeably nonblocking for unicast connections when B = b = = 1 and. Why is this true?
C 18 ; 3 ; 3 is also rearrangeably nonblocking for unicast connections when B = b = 1 =2, = 1. Why is this true?
Exam 2, Part B
April 16, 1999
On this part of the exam, you may use one page of notes. Write your answers in the space provided.
- (60 points) Suppose you are required to design a new high speed network for a company. There are 7,168 employees that each require a desktop PC with a 150 Mb/s network connection and there are 256 servers that each require a 600 Mb/s network connection. Vendor A offers a family of switching systems that can be configured with n 1 ports at 150 Mb/s plus n 2 ports at 600 Mb/s for any values of n 1 and n 2. However, the cost of such a system (in dollars) is
50 n 1 + 100 n 2 + (n 1 + 4 n 2 )^2
Approximately, how much will the switching for the network cost if you use a single large switch from vendor A?
How much will the switching cost if you use multiple switches in which each switch is limited in the bandwidth to no more than 128 150 Mb/s? Assume that the access switches have a 1:1 concentration ratio.
Suppose your boss decides that the network should support high quality video conferencing, where each channel uses a bandwidth of 15 Mb/s. He also wants point-to-point video connections to never block. Describe how would you modify the network in the previous part of the problem to satisfy this additional requirement. By approximately how much does this requirement increase the cost of the network?
Vendor B offers a similar family of switching systems but with a different cost characteristic. In particular, for vendor B’s products, the cost of the system with n 1 ports at 150 Mb/s plus n 2 ports at 600 Mb/s is
50 n 1 + 100 n 2 + 2 (n 1 + 4 n 2 ) log 2 (n 1 + 4 n 2 )
How much will the switching for the network cost if you use a single large switch from vendor B?
Consider an alternative design using binary cell replication and recycling. Specify the topology you would use in this case, assuming that you use dedicated recycling ports to handle the recycling required for multicast. How many dedicated recycling ports do you need, assuming that up to 25% of the output traffic can be multicast and that the maximum virtual circuit rate is 600 Mb/s? What bandwidth is required on the internal links? How many components does your design require?
How much routing table memory is required in this design? How does this compare to what would be required by a switching system with 1024 inputs and 1024 outputs that only supports unicast?
