CS/EE 577 Final Exam December 17, 1996

Transcription

1 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 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

2 2. (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? 2

3 3. (10 points) Consider a queue with a capacity of B cells. When implementing the control for such a queue, one must determine how to handle cells that arrive when the queue is full. The simplest thing to do in such cases is to always discard cells that arrive when the queue is full. However, it is possible to avoid discarding such cells when the first cell in the queue is leaving, since the bytes of the arriving cell can be written into the memory locations vacated by the departing cell. Which of these two options is implemented by the queue represented by the finite state model shown below? (This finite state model is for a queue in which, at each each time step, a cell arrives with a fixed probability λ and leaves with a fixed probability µ.) Show how you would modify the model to implement the other option. 3

4 4. (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? 4

5 5. (15 points) What condition must be satisfied in order for C n,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 C n,d,r to be strictly nonblocking for multipoint traffic, assuming b=0. What condition must be satisfied in order for C n,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 B n,d to be strictly nonblocking for point-to-point traffic, assuming b=0. What condition must be satisfied in order for B n,d ;B n,d to be reroutably nonblocking for multipoint traffic, assuming b=0. 5

6 6. (12 points) Define the series operator for constructing networks. Define the parallel operator. What is the associative property for the series operator? What is the associative property for the parallel operator? 6

7 7. (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. 7

8 8. (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? 9. (12 points) Define the following terms: strictly nonblocking rearrangeably nonblocking reroutably nonblocking 8

9 10. (8 points) Give an expression for estimating the blocking probability of the following network using Lee s method. In your expression, use p to denote the probability that an input port of the network is busy. You may assume that p is no more than ¾. 9

10 11. (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-topoint 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 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) 10