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CS/EE 577 Final Exam: Networking Questions, Exams of Design and Analysis of Algorithms

The final exam questions for a computer science and electrical engineering (cs/ee) 577 course focused on networking. The exam covers topics such as virtual path/circuit tables, routing memory requirements for single-stage switches, queue control, and network conditions for non-blocking traffic. Students are expected to solve problems related to determining output values for virtual path/circuit tables, calculating required entries and bits per entry for input and output tables, handling cells in a queue, estimating blocking probability using lee’s method, and identifying connections in virtual circuit tables.

Typology: Exams

2012/2013

Uploaded on 03/23/2013

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CS/EE 577 Final Exam
December 17, 1996
This is a closed book exam.
1. (8 points) The virtual path/circuit table shown below is of the type introduced in the
first section of the lecture notes. A copy of the relevant page from the notes is
attached.
base size output VPI VCI
005 05224
153 12151
205 23329
386 34117
414 4 41134
518 2 53315
605 652413
705 771621
822431
943135
10 82224
11 11 54 31
12 15 11 27
13 71812
14 12 12 29
15 11 13 17
16 13 15 18
17 15 22 20
18 12 21 14
19 01235
When a cell with (VPI,VCI)=(3,5) arrives at the input port with this VPI/VCI table,
what output is the cell sent to? What are the values of the (VPI,VCI) field of the
forwarded copy?
Repeat for (2,2), (5,1) and (6,3).
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CS/EE 577 – Final Exam

December 17, 1996

This is a closed book exam.

  1. (8 points) The virtual path/circuit table shown below is of the type introduced in the first section of the lecture notes. A copy of the relevant page from the notes is attached.

base size output VPI VCI (^0 0 5 0 5 22 ) (^1 5 3 1 2 15 ) (^2 0 5 2 3 32 ) (^3 8 6 3 4 11 ) (^4 14 4 4 1 13 ) 5 18 2 5 3 31 5 (^6 0 5 6 5 24 ) (^7 0 5 7 7 16 ) (^8 2 24 ) (^9 4 31 ) (^10 8 22 ) (^11 11 54 ) (^12 15 11 ) (^13 7 18 ) (^14 12 12 ) (^15 11 13 ) (^16 13 15 ) (^17 15 22 ) (^18 12 21 ) 19 0 12 35

When a cell with (VPI,VCI)=(3,5) arrives at the input port with this VPI/VCI table, what output is the cell sent to? What are the values of the (VPI,VCI) field of the forwarded copy?

Repeat for (2,2), (5,1) and (6,3).

  1. (12 points) This problem concerns the amount of routing memory required for single stage switches supporting multicast. For simplicity, assume that the switch supports virtual circuits only and that the virtual path identifier is ignored on the input side and set to zero on the output.

Consider a single-stage switch with 16 ports and using a bus to interconnect the ports. Each input has a virtual circuit table that for point-to-point virtual circuits specifies the output port and output VCI a cell with a given input VCI is to be sent to; for multipoint virtual circuits, it instead specifies a Broadcast Channel Number. The BCN is used at the output ports for another table lookup that yields the outgoing VCI. Assume that we want to support a total of 4096 entries on each input link and each output link and we want to allow up to 500 VCIs on each output to be associated with multicast virtual circuits. How many entries must each of the input tables have and how many bits per entry?

How many entries must each of the output tables have and how many bits per entry, assuming that the output tables are implemented using direct lookup?

How many entries must each of the output tables have and how many bits per entry, assuming that the output tables are implemented using CAMs?

  1. (10 points) Consider a 150 Mb/s link that is experiencing an extended overload period caused by 30 virtual circuits, each sending 4 Kbyte packets continuously at 50 Mb/s. Approximately what fraction of the packets sent on this virtual circuit are lost due to overflow of the queue at the sending end of the link?

Assuming the queue controller does not implement early packet discard, or any similar method of preserving packet integrity, approximately what fraction of the packets sent are corrupted (that is, have at least one of their cells lost)?

Suppose the queue controller does implement early packet discard and that the buffer is large enough to ensure that it never overflows and never becomes empty during the overload period. What fraction of the packets are lost in this case?

Approximately what fraction of the time is the buffer below the threshold?

Suppose we were to add another virtual circuit sending 4 Kbyte packets at 1 Mb/s. Approximately what fraction of packets sent by this new virtual circuit will be lost?

  1. (15 points) What condition must be satisfied in order for Cn,d,r to be strictly nonblocking for point-to-point traffic, assuming b =0 (just write the appropriate inequality).

What condition must be satisfied in order for Cn,d,r to be strictly nonblocking for multipoint traffic, assuming b =0.

What condition must be satisfied in order for Cn,d,r to be reroutably nonblocking for multipoint traffic, assuming b =0 and a first stage fanout restriction of f.

What condition must be satisfied in order for Bn,d to be strictly nonblocking for point-to-point traffic, assuming b =0.

What condition must be satisfied in order for Bn,d ; Bn,d to be reroutably nonblocking for multipoint traffic, assuming b =0.

  1. (10 points) Name the three major categories of single stage switches.

Which of these has the best cost/performance in large configurations?

Which has the worst?

Give two reasons that account for the superiority of the best over the worst.

  1. (6 points) The attached figure from the notes shows a multicast switch in which the components have no internal cell buffers, making it necessary for them to resolve contention in ways other than just locally buffering cells. Suppose that a cell arrives at this switch on the top input with a fanout of 1 and another cell arrives at the next input with a fanout of 8. Assuming there are no other cells present, how many cells will pass through to the outputs of the copy network in the next operational cycle?

If the copy network is replaced with one having 16 outputs and the copy range calculation is changed appropriately, how many cells will pass through to the copy network outputs?

  1. (12 points) Define the following terms:

strictly nonblocking

rearrangeably nonblocking

reroutably nonblocking

  1. (12 points) The table below shows a simplified version of the virtual circuit tables for an eight port configuration of the WU gigabit switch. In this version, virtual paths are omitted and a pair of the form (x,y) in the table represents a (output port,VCI) pair and a pair of the form (x,y) represents a (recycling port,VCI) pair. Make a list of the different connections represented by the table entries shown. For each point-to- point connection, list the (input port, input VCI) and (output port, output VCI). For each one-to-many connection, give the (input port, input VCI) and the set of all (output port, output VCI) pairs to which copies of cells are forwarded. For each many-to-many connection give the set of all (input port, input VCI) pairs from which cells are received and the set of all (output port, output VCI) pairs to which copies of cells are sent.

VCI 0 1 2 3 4 5 6 7 8 9 input 0 (3,3),(7,0) 1 (5,1) 2 (5,2)^ (3,2),(4,0)^ (1,4),(2,8)^ (5,1) 3 (1,7),(2,0) 4 (7,7),(5,9)^ (6,2) 5 (2,6),(6,1) 6 (6,7),(7,2)^ (5,1) 7 (5,9),(7,1)^ (5,1)