Consider a slotted ALOHA system. Assume that the aggregate transmission attempts (including new…

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.