Solutions to Chapter 4 - Communication Networks

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Communication Networks (2 nd Edition) Chapter 4 Solutions e. Called-party identification – Each member of a family has a different phone number. Incoming calls have a different ring for each phone number. In the signaling network, multiple numbers can all be routed to the same phone. For each number, however, a different ring signal can be sent to the phone. The phone may have only one ringer, so to differentiate the numbers each ring can have a different duration with different length pauses, similar to Morse code. Thus, one number may be one long ring, while the other number may be two short rings. 53. Consider a 64 kbps connection in ISDN. Solutions follow questions: a. Sketch the layers of the protocol stack in the user plane that are involved in the connection. Assume that two switches are involved in the connection. Only the physical layer in the user plane of the end systems and the two switches are involved in the 64 kbps connection. b. Sketch the layers of the protocol stack in the control plane that are involved in the setting up of the connection. Assume that the two switches in part (a) are involved in the call setup. The physical, data link, network and application layers of the control plane are involved in the setting up of the connection. 54. Explain how the control plane from ISDN can be used to set up a virtual connection in a packetswitching network. Is a separate signaling network required in this case Solution: In order to setup a virtual connection in a packet switched network, the ISDN control plane must first reserve resources during a call setup phase. The circuit does not exist as a physical entity, but rather a sequence of entries in forwarding tables in the packet switched network. As such, each packet in the call follows the same route through the network. 55. Identify the components in the delay that transpires from when a user makes a request for a telephone connection to when the connection is set up. Which of these components increase as the volume of connection requests increases Solution: After the user requests a connection by dialing the phone number, the call setup procedure involves finding a path from the source to the destination. As shown in figure 4.44a, if the two phones are attached directly to the same switch, assuming the switch is non-blocking, the connection can be made and the delay is equal to the processing time in the switch and the short propagation delay of the signal. If the two phones are not connected to the same switch, a path must be selected for the call using the signaling network. The delay from this stage includes, processing time in each of the signaling nodes involved, propagation delay of the signals through the network, and any routing delay overhead. Before a connection can be made, the receiving user has to pick up the phone. This also contributes to the overall connection setup time. The amount of time required for the user to answer the call does not depend on the volume of connection requests in the network. However, if there are many simultaneous requests for connections, the signaling network will have to juggle more requests simultaneously and the routing procedure will take longer. Although there is a fixed minimum propagation delay, as call Leon-Garcia/Widjaja 26
Communication Networks (2 nd Edition) Chapter 4 Solutions requests increase, the propagation delay may also increase because the shortest path route may not be available. 56. Discuss the fault tolerance properties of the STP interconnection structure in the signaling system in Figure 4.52. Solution: The mesh structure means that any STP is connected to any other STP by more than one path. Thus, if a fault occurs on one link, the signaling traffic can be automatically rerouted over another path. If an STP fails, paths are available to a backup STP. 57. A set of trunks has an offered load of 10 Erlangs. How many trunks are required to obtain a blocking probability of 2% Use the following recursive expression for the Erlang B blocking probability: aB( c −1, a) B( c, a) = B(0, a) = 1 c + aB( c −1, a) Solution: Given a = 10 Erlangs and P B = 2% = 0.02, 16 trunks are required to a obtain P B = 2%. C a B(c,a) c a B(c,a) 0 10 1.000 9 10 0.273 1 10 0.909 10 10 0.215 2 10 0.820 11 10 0.163 3 10 0.732 12 10 0.120 4 10 0.647 13 10 0.084 5 10 0.564 14 10 0.057 6 10 0.485 15 10 0.036 7 10 0.409 16 10 0.022 8 10 0.338 17 10 0.013 58. Compare the blocking probabilities of a set of trunks with offered load a = 9 and c = 10 trunks to a system that is obtained by scaling up by a factor of 10, that is, a = 90 and c = 100. Hint: Use the recursion in problem 57 in a spreadsheet or program. Solution: To find the blocking probability of trunks with offered load a = 9 and c = 10, we recursively calculate B(10,9) starting from B(0,9). We use a similar method for the case when a = 90 and c = 100. The results of this process are summarized in the table below. c a B(c,a) c a B(c,a) 0 9 1.000 0 90 1.000 1 9 0.900 1 90 0.989 2 9 0.802 2 90 0.978 3 9 0.706 3 90 0.967 4 9 0.614 4 90 0.956 5 9 0.525 5 90 0.945 6 9 0.441 6 90 0.934 Leon-Garcia/Widjaja 27
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Solutions to Chapter 4 - Communication Networks

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