Assume that you are the network engineer of an ISP (Internet Service Provider), and you need...

 

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Assume that you are the network engineer of an ISP (Internet Service Provider), and you need to calculate the requirements for a multiplexer that will be installed in a telephone exchange. You assume that a user who will be connected to the multiplexer independently transmits data at the peak rate of c when there is data to send and zero otherwise, and there are N users. Also, you are given the average transmission rate of a user as r. a. Derive the formula for probability of k users transmitting data at the peak rate simultaneously. b. The multiplexer is said to be in the "overflow mode" if there are more than n users (n being an operational parameter of the multiplexer) transmitting data simultaneously. Derive the formula for overflow probability the multiplexer. Assume that you are the network engineer of an ISP (Internet Service Provider), and you need to calculate the requirements for a multiplexer that will be installed in a telephone exchange. You assume that a user who will be connected to the multiplexer independently transmits data at the peak rate of c when there is data to send and zero otherwise, and there are N users. Also, you are given the average transmission rate of a user as r. a. Derive the formula for probability of k users transmitting data at the peak rate simultaneously. b. The multiplexer is said to be in the "overflow mode" if there are more than n users (n being an operational parameter of the multiplexer) transmitting data simultaneously. Derive the formula for overflow probability the multiplexer.