Solutions to Chapter 4 - Communication Networks

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Communication Networks (2 nd Edition) Chapter 4 Solutions by the length of the memory cycle. This limitation means that N/n ≤ M, which in turn places a limitation on N, the number of inputs to the switch (since n has a maximum that is determined by technological constraints). The limitation on the number of slots M suggests that the approach is suitable when concentration can be used in the input stage because of light loading in the input lines. 37. Consider n digital telephones interconnected by a unidirectional ring. Suppose that transmissions in the ring are organized into frames with slots that can hold one PCM sample. Solutions follow questions: a. Suppose each telephone has designated slot numbers into which it inserts its PCM sample in the outgoing direction and from which it extracts its received PCM sample from the incoming direction. Explain how a TSI system can be used to provide the required connections in this system. At some point in the ring, TSI is carried out to interchange the information in the time slots between all pairs of connected users b. Explain how the TSI system can be eliminated if the pairs of users are allowed to share a time slot If all user pairs share a time slot, for any connected pair of users we can assign the same timeslot to both. To communicate, each of the users inserts outgoing PCM samples on the slot and extracts incoming PCM samples from the same slot. c. How would connections be established in parts (a) and (b) In the system described in part (a) the TSI switch monitors all of the slots continuously for connection request made by the users. If user A requests a connection to user B, the central switch controller makes the connection if the slot corresponding to user B is available. In the system described in part (b) a mechanism is needed to coordinate the sharing of slots between all the pairs of users. The most efficient mechanism would have half as many timeslots as users. The central switching mechanism would assign each pair of users a timeslot to communicate over. Call setup would require all users to communicate with the central switch on a setup slot that would have to be accessed via a MAC protocol. An alternative simple distributed mechanism would involve each user monitoring their own timeslot. Assuming that the users have time slot tunability, a call could be initiated by sending a sample on the intended receivers time slot (provided it is free). Communication would occur on the receiver’s time slot in this scenario. The drawback of this mechanism is that no more than half of the available bandwidth would ever be used. 38. Consider the application of a crossbar structure for switching optical signals. a. Which functions are the crosspoints required to implement The crosspoints must be able to open, close, hold open, and hold closed connections. b. Consider a 2 x 2 crossbar switch and suppose that the switch connection pattern is (1 → 1, 2 → 2) for T seconds and (1 → 2, 2 → 1) for T seconds. Suppose it takes τ seconds to change between connection patterns, so the incoming optical signals must have guardbands to allow for this. Calculate the relationship between the bit rate R of the information in the optical signals, the number of bits in each “frame”, and the values T and τ For R in the range from 1 Leon-Garcia/Widjaja 18
Communication Networks (2 nd Edition) Chapter 4 Solutions gigabit/second to 1 terabit/second and τ in the range of 1 microsecond to 1 millisecond, find values of T that yield 50% efficiency in the use of the transmission capacity. The transition time is τ seconds, and the hold time is T seconds. The optical transmission rate is R bps and the actual information bit rate is R effective , and letting n be the number of bits per frame (including overhead), we have: R effective = (total bit rate of connection)(proportion of useful bits) = T n R ∗ ( ) = T + τ T + τ The value of T that yields 50% efficiency is T = τ. For T = τ = 1 microsecond, we have n = RT which gives frame size of n = 1000 bits at 1 Gbps and n = 1000000 bits at 1 Tbps. For T = τ = 1 millisecond, the frame sizes are 1000 times longer. 39. Suppose an optical signal contains n wavelength-division multiplexed signals at wavelengths λ 1 , λ 2 , …, λ n . Consider the multistage switch structure in Figure 4.35 and suppose that the first stage switches consist of an element that splits the incoming optical signal into n separate optical signals each at one of the incoming wavelengths. The jth such signal is routed to jth crossbar switch in the middle stage. Explain how the resulting switch structure can be used to provide a rearrangeable optical switch. Solution: In the resulting architecture, the second-stage inputs to any given switching element have the same wavelength. Thus, each single wavelength signal input to the second stage can be directed to any one of the third stage elements. Each third stage element corresponds to a single output port. It is assumed that the third stage consists of elements that recombine the n incoming signals, each with a different wavelength, into a WDM signal. The operation of this switch is very similar to that of the switch in figure 4.35 However, it differs in that there is only one possible route for each input-output-wavelength combination. 40. Consider the equipment involved in providing a call between two telephone sets. Solutions follow questions: a. Sketch a diagram showing the various equipment and facilities between the originating telephone through a single telephone switch and on to the destination telephone. Suppose first that the local loop carries analog voice; then suppose it carries digital voice. In an analog connection, the telephone set is connected by a pair of wires to the telephone office. The wires are terminated in a line card that digitizes the voice signal and transfers the digital signal to a digital switching system. The digital signal travels along a fixed path from the telephone switch in the originating office to the telephone switch in the destination office. The two or more offices are interconnected by digital transmission lines. If the telephone set were to generate digital voice then a digital signal would be transmitted along the local loop that connects the telephone to the central office. The operation of the line card would differ, as the arriving signal would already be in digital form. b. Repeat part (a) in the case where the two telephone calls are in different LATAs. Leon-Garcia/Widjaja 19
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Solutions to Chapter 4 - Communication Networks

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