Consider a square city that is 100 km. Suppose you design a cellular system for this...

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Consider a square city that is 100 km². Suppose you design a cellular system for this city with square cells, where every cell (regardless of cell size) has 100 channels so can support 100 active users (in practice the number of users that can be supported per cell is mostly independent of cell size as long as the propagation model and power scale appropriately). (a) What is the total number of active users that your system can support for a cell size of 1 km²? (b) What cell size would you use if you require that your system support 250,000 active users? Now we consider some financial implications based on the fact that users do not talk continuously. Assume that Friday from 5-6 pm is the busiest hour for cell phone users. During this time, the average user places a single call, and this call lasts 2 minutes. Your system should be designed such that the subscribers will tolerate no greater than a 2% blocking probability during this peak hour. Note that the blocking probability is computed using the Erlang B model: P = where C is the number of channels and A = UμH for U the number of users, the average number of call requests per unit time, and H the average duration of a call. (See any basic networking book or search this definition via Google for more details). = AC C!x=0 Ak, (c) How many total subscribers can be supported in the macrocell system (1 km² cells) and in the microcell system (with cell size from part (b))? (d) If a base station costs $500,000, what are the base station costs for each system? (e) If users pay $50 a month in both systems, what will be the monthly revenue in each case. How long will it take to recoup the infrastructure (base station) cost for each system? Consider a square city that is 100 km². Suppose you design a cellular system for this city with square cells, where every cell (regardless of cell size) has 100 channels so can support 100 active users (in practice the number of users that can be supported per cell is mostly independent of cell size as long as the propagation model and power scale appropriately). (a) What is the total number of active users that your system can support for a cell size of 1 km²? (b) What cell size would you use if you require that your system support 250,000 active users? Now we consider some financial implications based on the fact that users do not talk continuously. Assume that Friday from 5-6 pm is the busiest hour for cell phone users. During this time, the average user places a single call, and this call lasts 2 minutes. Your system should be designed such that the subscribers will tolerate no greater than a 2% blocking probability during this peak hour. Note that the blocking probability is computed using the Erlang B model: P = where C is the number of channels and A = UμH for U the number of users, the average number of call requests per unit time, and H the average duration of a call. (See any basic networking book or search this definition via Google for more details). = AC C!x=0 Ak, (c) How many total subscribers can be supported in the macrocell system (1 km² cells) and in the microcell system (with cell size from part (b))? (d) If a base station costs $500,000, what are the base station costs for each system? (e) If users pay $50 a month in both systems, what will be the monthly revenue in each case. How long will it take to recoup the infrastructure (base station) cost for each system?

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a For a cell size of 1 km the total number of active users the system can support can be found using the given information Each cell regardless of siz... View the full answer