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Topology - Design and Analysis of Switching Systems - Exam, Exams of Design and Analysis of Algorithms

Main points of this exam paper are: Networks Shown, Parallel Connection, Operations, Topology Construction, Standard, Network Type, Appropriate Symbol, Particular Topology, Benes Network, Speed Advantage Needed

Typology: Exams

2012/2013

Uploaded on 03/23/2013

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CS/EE 577 Exam 2
12/8/00
1. (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 18 19
τ4,5(x)
What is σ(2,95) in D125,5?
What is σ(3,520) in Y1024,4?
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pf4
pf5
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CS/EE 577 — Exam 2

1. (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 18 19

τ4,5(x)

What is σ(2,95) in D 125,5?

What is σ(3,520) in Y 1024,4?

2. (15 points) For each of the networks shown below, given an expression for the topology

using the series and parallel connection operations and the other topology construction

operations. For each network topology that corresponds to a “standard” network type (e.g.

a Benes network), also give the name and the appropriate symbol for the particular topology

(e.g. B 8,2).

  1. (15 points) Explain why the network X (^) 10 , 5 ⊗ X 10 , 10 ⊗ X 5 , 10 is rearrangeably nonblocking for

unicast reservations when B = b =β=1/2. Describe a procedure for selecting a set of compatible

routes for a given set of compatible unicast reservations.

5. (15 points) Give an expression the blocking probability for the following networks using

Lee's method. Assume each external link and internal link can carry just one virtual circuit

at a time. Let p denote the probability that each network input is busy.

C 50 , 10 , 15

( X (^) 2 , 2 × X 2 , 2 )⊗ X 2 , 2 ⊗ X 4 , 4

D 64 , 2 , 2

7. (15 points) In the WUGS architecture, many-to-many multicast can be implemented in one

of two ways. Either you can use separate one-to-many multicast trees for each participant,

or you can use a single shared tree. Consider a many-to-many multicast with 20 participants

(each can both send and receive) and an output bandwidth of 100 Mb/s (that is, each output

link that is participating in the multicast sees a total of 100 Mb/s, so each participating input

link contributes an average of 5 Mb/s).

Using separate multicast trees, how many multicast routing table entries are needed? How

many are needed with a shared tree?

What is the total recycling bandwidth used with separate multicast trees? What is the

recycling bandwidth with a single shared tree?

How many control cells are needed to modify routing table entries when adding another

participant, if we use separate multicast trees? If we use a single shared tree?

8. (15 points) One potential improvement to the WUGS architecture is to provide each IPP

with virtual output queues (one queue for each switch output) and then control the sending

rates for these queues, so as to prevent congestion at any output. Using this approach, traffic

for congested outputs accumulates in the IPP queues and does not interfere with traffic

trying to reach other outputs. However, there is a complication when we combine this

improvement with the WUGS multicast mechanism. The simplest way to combine these is

to do each binary copy operation in the IPPs, allowing the two copies to be placed in

separate virtual output queues. One consequence of doing this is an increase in the

bandwidth used at the interface between the IPPs and the switching network. Consider

such a system in which h of the system’s n ports are used only for recycling traffic. Assume

that multicast cells arriving on input links are always forwarded to a recycling port without

being copied at the input port. Give a lower bound on the value of h needed for nonblocking

multicast. Your expression should be in terms of n , B , β, and δ.