Tutorial 10

Tutorial 10 - IERG4020 Tutorial 10 FENG Shen 1 MEAN SD MAX...

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IERG4020 Tutorial 10 FENG Shen 1
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QUIZ 4 DISCUSSION 2 MEAN 5.02 SD 2.21 MAX 9.50 MIN 0.50 MEDIAN 5.00
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Problem 1 Consider a feedback shuffle-exchange network with nodes 00, 01, 10, and 11. Suppose that there is a packet at each of the nodes and the source-destination mapping is 00 10, 01 00, 10 11, 11 01. Show the sequence of nodes traversed by each of the packets on route to its destination node. Is there contention among packets? (3 pts) Ans : 00 01 10 (via link 001 & 010) 01 10 00 (via link 010 & 100) 10 01 11 (via link 101 & 011) 11 10 01 (via link 110 & 101) From the output links traversed, we observed there is no contention among packets. 3
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Problem 2 Consider a copy network. An input packet can request 1, 2, or 3 copies. How many bits are needed to encode the copy number? (2 pts) Ans : The number of bits needed to encode the copy number is 4 2 log 3 2  
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Problem 3 (a) Derive p and q in terms of ρ . (2 pts) p is the success probability of one packet . Suppose there is a packet A at the input of a node. The probability that there is another packet B at the other input of this node is ρ . B is destined for the same output as A with probability 1/2. In this case, B wins contention with probability 1/2. Therefore the deflection probability of A is thus 5 1 2 3 Figure 1 11 22 4 q   4 pq 
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Problem 3 (b) Derive the throughput per node of this network in terms of ρ . What is the value of ρ that maximizes the throughput? (3 pts) Let T i be the expected number of additional nodes a packet in state i will traverse before reaching the destination. From the state diagram we have 6 p 0 1 q Figure 2 0 1 10 1 0 14 1 4 T T Tp T q T p  
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Problem 3 By Little’s law, 6 input links in total Hence the throughput per node is Taking derivative for Therefore ρ = 1 maximizes the throughput Λ . 7 p 0 1 q Figure 2 1 6 T 2 1 2( 4 ) 2 32 2 T    2 22 0 2 d d     (0,1) 
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CHAPTER 6 REVIEW – MULTICAST SWITCH & PATH SWITCHING 8
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MULTICAST SWITCH 9
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Multicast When we want to make a point-to-multi-point
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This note was uploaded on 12/08/2010 for the course IEG IEG4020 taught by Professor Fengshen during the Spring '10 term at CUHK.

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Tutorial 10 - IERG4020 Tutorial 10 FENG Shen 1 MEAN SD MAX...

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