Solutions to Chapter 4 - Communication Networks

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Communication Networks (2 nd Edition) Chapter 4 Solutions Solutions follow questions: a. Explain how a multicast connection may be implemented in a crossbar switch. In a crossbar switch, multicasting can be implemented by copying the multicast input to multiple outputs. b. How does the presence of multicast connections affect blocking performance of a crossbar switch Are unicast calls adversely affected Unlike unicast switches, flow in multicast switches is not conserved. Generally, if multicasting is implemented in a switch, the total traffic flow out of the switch is more than the flow into the switch. Thus the probability of blocking is increased because the traffic inside the switch is higher. Unicast traffic is also affected by this increased flow because fewer resources in the switch are available. c. Explain how multicast connections should be implemented in a multistage switch. Should the multicast branching be done as soon as possible or as late as possible In a multistage switch with a given multicast traffic profile, each branching procedure represents an increase in traffic flow beyond the branch point. Thus, to keep traffic load in the switch to a minimum, branching should be done as late as possible. 31. Do a web search for crosspoint switching chips. What specifications do you find for number of ports, bit rate/port Are dualcasting and multicasting supported Do the crosspoints need to be changed together or can they be changed independently What considerations determine how fast the crosspoints can be changed Solution: Some specs for Crosspoint fabrics chips: Switch size: 2x2, 4x4, 17x17, 34x34, 36x37, 68x69, 64x64, 72x72, 144x144 Port speed: 1.6 Gbps, 2.5 Gbps, 3.2 Gbps, 3.6 Gbps Dualcasting and multicasting is usually supported by crosspoint chips, as well as masking particular ports, and also programming a single port or a subset of ports independently. The speed of changes depend on the clock recovery and signal synchronization at the port interfaces (receivers and transmitters at input and output ports of the crosspoint fabric), and also the speed of programming the I/O Table registers. 32. What is the delay incurred in traversing a TSI switch Solution: The arriving frame is written onto the switch register and after the frame is completely written in, it needs to be read out in permuted order. 33. Explain how the TSI method can be used to build a time-division multiplexer that takes four T-1 lines and combines them into a single time-division multiplexed signal. Be specific in terms of the number of registers required and the speeds of the lines involved. Solution: Leon-Garcia/Widjaja 16
Communication Networks (2 nd Edition) Chapter 4 Solutions Each input line carries T-1 traffic. The input frame size is n = 24 slots. Each frame that is output is of length 4n = 96 slots. After a full set of 96 slots is written into the 4 registers, the slots are read out in the outgoing line. 1.544 Mbps AA 24 slots 1.544 Mbps B A 24 slots AA BA C A AD 1.544 Mbps C A 1.544 Mbps AD 24 slots 24 slots 6.176 Mbps 34. Suppose that the TDM frame structure is changed so that each frame carries two PCM samples. Does this affect the maximum number of channels that can be supported using TSI switching Note: The solution to this problem is currently being reviewed and may be revised. Solution: Yes. Now each slot requires two memory reads and two memory writes. Thus, the maximum number of channels that can be supported is: Max = 125µ s 4 × mem In other words, one half as many slots per frame can be supported as compared to when each slot requires one PCM sample. 35. Examine the time-space-time circuit-switch architecture and explain the elements that lead to greater compactness, that is, smaller physical size in the resulting switching system. Solution: In a space switch, n inputs are switched simultaneously in a switching time of T seconds. The space-time circuit switch switches each of the n inputs in succession with a switching time of T/n each, for a total switching time of T. By switching the inputs one at a time instead of simultaneously, the switching matrix needed at any given time is reduced in size accordingly and greater hardware compactness is achieved. The implicit tradeoff, however, is that higher line and switch speeds are needed. 36. Consider the three-stage switch in problem 4.26c. Explain why a space-time-space implementation of this switch makes sense. Identify the factors that limit the size of the switches that can be built using this approach. Solution: A space-time-space implementation would have the middle stage replaced by a TSI switch stage, and thus reduce hardware costs. The maximum number of slots in a TSI switch, say M, is limited Leon-Garcia/Widjaja 17
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Solutions to Chapter 4 - Communication Networks

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