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.