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# Erlang Problems

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1) A cellular system has a total of 756 channels available. Each subscriber makes an average of 3 calls per hour and each call lasts about 2.5 minutes. The system operator estimates network capacity based on a 3 percent blocking probability.

(a) The first system design is based on a k=12 frequency reuse pattern with omnidirectional cells. How many subscribers can be served in each cell?

(b) The first approach wasn't quite good enough, so the new plan uses a k=7 frequency reuse with 120 degree sectors in every cell. Now how many subscribers can be served in each cell?

(c) Under plan (b), each cell has a radius of 2 km. To support the same number of subscribers per square km, what should the cell radius be in plan (a)?

2) A network has 50 channels available and serves 315 subscribers. Assume each subscriber makes an average of 2 calls per hour and each call lasts an average of 4 minutes.

(a) What is the blocking probability?

(b) It turns out that 8 of the 315 subscribers stay connected all the time, effectively monopolizing eight of the channels. What is the blocking probability for the other subscribers (assuming averages of 2 calls per hour and 4 minutes per call)?

(c) Under the conditions of part (b), how many channels must the network have available to provide the same blocking probability as in part (a)?