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Consider a slotted ALOHA system. Assume that the aggregate transmission attempts (including new transmissions as well as retransmissions) by the large number of users are modelled as a Poisson process with average rate of λ packet/s. Each slot has a constant duration equal to the packet transmission time tP. a) What is the probability that a transmission is successful on its first attempt? b) What is the probability that it takes exactly k attempts for a transmission to be successful? c) What is the average number of transmission attempts needed for a packet to be successful? d) Suppose the receivers are improved so that, in case of parallel transmissions in the same slot, a maximum number of two concurrent transmissions can be received correctly. Collision takes place only if three or more packets are sent during the same slot. Express the normalized throughput as a function of the normalized offered traffic.

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