Question: There is a network where two workstations are connected by two modems, modem A and modem B. Both of these modems are faulty. It has

There is a network where two workstations are connected by two modems, modem A and modem B. Both of these modems are faulty. It has been observed that modem A drops packets with a probability of 0.29, while modem B drops packets with a probability of 0.08

A. If the modems are connected in series (i.e. the packets have to go through both modems one after the other), what is the probability that any given packet send from one workstation will arrive at the other? Note that the packets are not retransmitted in case of a failure.

B. If the modems are connected parallely and the transmitting workstation transmits the same packet on both paths, each of which has one of the modems, what is the probability that the receiving workstation receives the packet at least once?

C. The setup is that of problem B. But it is noticed that each modem is more likely to drop packets when there is a power surge at the modem compared to the situation when there is no surge. It is to be noted that the blocking probabilities of the modems in the environment have not changed. The two modems use two different electricity infrastructure providers that are independent of each other. The probability of a power surge during a packets transmission at modem A is 0.37 while at modem B it is 0.24. It is also found that the probability of a drop during a surge for modem A is 0.31 while for modem B it is 0.3. What is the probability of any given packet being received at least once? What is the probability of drop at each modem when there is no power surge?

D. To solve the problem in C. devices are installed that can cancel the power surges. We want to buy the same surge-protector device for both modems, one for each. The company manufacturing the power-surge-protectors provide a measure that tells us what percentage of surges are cancelled by them. Let’s assume that during a packet transmission at most one surge can happen, what should be the rating of the power-surge-protectors if we want to increase the successful packet reception rate to 96%. How about if achieving a successful packet reception rate of 94.5%

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