Solutions to Chapter 4 - Communication Networks

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Communication Networks (2 nd Edition) Chapter 4 Solutions P b Load [Erlangs] 1% 43.342 10% 56.059 b. Explain why requests for channels from handoffs should receive priority over requests for channels from new calls. How does this change the Erlang load calculations In telephone conversations, service interruption is less acceptable than denial of service due to a busy network. The calculations in part (a) assumed equal priority for all calls. If priority is given to current calls that are being handed off, the Erlang load calculations are more complicated. Newly attempted calls in this scenario have a lower priority and, thus, a higher P b . 64. Suppose that an analog cellular telephone system is converted to digital format by taking each channel and converting it into n digital telephone channels. Solutions follow questions: a. Find an expression for the number of channels that can be provided in the digital system using the parameters introduced in problem 62. Assuming that there will be n times more control channels in this new scheme, the number of channels in each cell is: B ( 1− a) b n R b. Consider the AMPS system and assume that it is converted to digital format using n = 3. How many Erlangs of traffic and the new system support at 1% blocking probability 5% This calculation is exactly the same as that in problem 4.62, except that now the number of trunks is tripled, so c = 160. To support 1% blocking or 5% blocking, the traffic can be: P b Load [Erlangs] 1% 141.167 5% 157.046 65. Suppose that a CDMA system has the same number of channels as the digital system in problem 64, but with a reuse factor of 1. Solutions follow questions: a. How many Erlangs of traffic can be supported in each cell by this system at 1% blocking probability 5% This CDMA system has 416 channels. Assuming that 21 channels are still used for call setup and the reuse factor is 1, each cell has 395 channels, so we have: c = 395 a = Erlangs of traffic Leon-Garcia/Widjaja 30
Communication Networks (2 nd Edition) Chapter 4 Solutions The probability of blocking in this system is given by: P b = c a c! c a j j j= 0 ! Thus we have: P b Load [Erlangs] 1% 370.410 5% 401.856 b. Suppose the per capita traffic generated in a city is 0.10 Erlangs during the busiest hour of the day. The city has a population of 1 million residents and the traffic is generated uniformly throughout the city. Estimate the number of cells required to meet the cities traffic demand using the system in part (a). For a probability of blocking of 1%, Total number of cells in city = (0.10 Erlangs/person)(1 000 000 people) / (370.410Erlangs/cell) = 270 Cells For a probability of blocking of 5%, Total number of cells in city = (0.10 Erlangs/person)(1 000 000 people) / (401.856 Erlangs/cell) = 249 Cells 66. Consider the equipment involved in providing a call between mobile and wireline telephones. Solutions follow questions: a. Sketch a diagram showing the various equipment and facilities between an originating mobile telephone to a wireline destination telephone. Suppose first that the mobile carries analog voice; then suppose it carries digital voice. The mobile phone or mobile subscriber unit (MSU) transmits and receives signals to and from the cell base station (BS) in the area where the phone is located. The cell base station exchanges the signals with the mobile switching center (MSC) located at the mobile telephone switching office (MTSO). All cell base stations are connected to the mobile telephone switching office through wire or microwave channels. The mobile switching center is also connected to the local public switched telephone network (PSTN). The mobile switching center switches the calls among the base stations and also between the base stations and the wireline telephone network. In analog cellular networks, the signal from the mobile phone arrives in analog form and is then digitized for switching and transmission. In digital cellular systems the signal from the mobile user arrives in digital form. However cellular phones use high performance speech coding formats that require conversion PCM prior to switching in the digital telephone network. Leon-Garcia/Widjaja 31
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Solutions to Chapter 4 - Communication Networks

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