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Suppose you are asked to design a highway control system (or remote monitoring of public area) where all the sensors share a 15 Mbps link to the control center. Each sensor (e.g., camera) requires 1 Mbps when transmitting, but it only transmits with probability 0.1.
1. How many sensors can be supported using circuit switching?
2. Suppose there are N sensors, and packet switching is used. Find the probability that at any give time, exactly k sensors are transmitting simultaneously.
3. How many sensors can be supported using packet switching such that the probability of exceeding the link capacity is no more than 0.005?
4. Compared to circuit switching, what are the main advantages and disadvantages of packet switching?
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