Solutions to Chapter 4 - Communication Networks

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Communication Networks (2 nd Edition) Chapter 4 Solutions The spacing in Hertz is: Frequency Bandwidth = 8 (3∗10 )(0.75 ∗10 −9 2 (1550 ∗10 ) −9 ) = 93.65GHz Thus, the maximum achievable bit rate that each wavelength can achieve using on-off modulation is 2 × 93.65 = 187 Gbps. Each signal carries 2.5 Gbps of traffic, so we see that because of the relatively large guard bands needed, WDM wavelengths have a very large spacing compared to their width. 23. How does WDM technology affect the hierarchical SONET ring topology in Figure 4.29 In other words, what are the consequences of a single fiber providing large number of high-bandwidth channels Solution: WDM allows for much more aggregate bandwidth on each fiber. Thus, in the context of the hierarchical SONET ring topology, the high-tier ring can use WDM in order to increase its bandwidth and the number of channels it can support and, in turn, the number of lower-tier rings that it can service. WDM allows it to achieve this increased service ability without the need to lay down more physical fibers over its links. On the other hand, the use SONET ring topology mean that each wavelength is associated with a separate SONET ADM, and this creates a problem in terms of interconnecting traffic across rings. 24. WDM and SONET can be used to create various logical topologies over a given physical topology. Discuss how WDM and SONET differ and explain what impact these differences have in the way logical topologies can be defined. Solution: Both WDM and SONET define logical topologies by setting up semi-permanent paths between nodes in the network. WDM creates these paths by assigning lightpaths between nodes. WDM without wavelength conversion has an inherent restriction imposed on the logical topologies that it can create, because no two lightpaths that share the same link can use the same wavelength. In SONET, since tributaries are electrically defined, the only restriction imposed on the topologies is the total bandwidth utilized on each link. 25. Compare the operation of a multiplexer, an add-drop multiplexer, a switch, and a digital crossconnect. Solution: A multiplexer is a 1:N device. It takes N separate signals on N different inputs and combines them into one higher rate signal on one output port. An add-drop multiplexer takes in N signals on one input port and replaces one of them with a new signal from a separate input port. The new aggregate signal is routed to an output port and the signal that was replaced is “dropped” to a separate output port. Leon-Garcia/Widjaja 12
Communication Networks (2 nd Edition) Chapter 4 Solutions A switch takes in N inputs and routes them to N different outputs. Frequently each input to a switch contains a number of multiplexed connections. These connections can be demultiplexed and routed to different output ports where they are aggregated prior to exiting the switch. Generally, switches are configured using signaling that establishes paths across the network. A digital cross-connect is similar to a switch except that it is semi-permanent, usually configured by network operators rather than signaling processes. Their configuration is also done on a larger time scale (days or weeks). Digital cross-connects provide a basic network topology on which routing can be applied. 26. Consider a crossbar switch with n inputs and k outputs. Solutions follow questions: a. Explain why the switch is called a concentrator when n > k. Under what traffic conditions is this switch appropriate This switch is a concentrator because traffic comes in on n lines and is concentrated onto k lines. Traffic on the output lines is higher than that of the input lines by a factor of n/k on average. The switch has inherent multiplexing functionality. b. Explain why the switch is called an expander when n > k. Under what traffic conditions is this switch appropriate This switch is an expander because the number of lines is expanded from n to k. This switch is appropriate when the outgoing lines carry less traffic than the incoming lines. One such example is at the egress of a backbone network to an access network. The switch has inherent demultiplexing functionality. c. Suppose an N x N switch consists of three stages: an N x k concentration stage; a k x k crossbar stage; and a k x N expansion stage. Under what conditions is this arrangement appropriate The number of crosspoints in an N x N crossbar switch is N 2 . If the traffic load on the inputs is relatively low, this configuration may save on hardware costs. The number of crosspoints needed in the three-stage switch described is: k 2 + 2kN Depending on the values of N and k, k 2 + 2kN may be less than N 2 , especially if N is much greater than k. d. When does the three-stage switch in part (c) fail to provide a connection between an idle input and an idle output line Assuming unicast traffic, if more than k inputs require a path to one of the third stage’s n outputs at the same time, blocking will occur in the first stage, since it only has k outputs. Leon-Garcia/Widjaja 13
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Solutions to Chapter 4 - Communication Networks

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