Question: Consider a slotted Aloha system with "perfect capture." That is, if more than one packet is transmitted in a slot, the receiver "locks onto" one of the transmissions and receives it correctly; feedback immediately informs each transmitting node about which node was successful and the unsuccessful packets are retransmitted later.
(a) Give a convincing argument why expected delay is minimized if all waiting packets attempt transmission in each slot.
(b) Find the expected system delay assuming Poisson arrivals with overall rate λ. Hint: Review Example.
(c) Now assume that the feedback is delayed and that if a packet is unsuccessful in the slot, it is retransmitted on the kth subsequent slot rather than the first subsequent slot. Find the new expected delay as a function of k. Hint: Consider the system as k subsystems, the ith subsystem handling arrivals in slots j such that j mod k = i.
Example: We have m traffic streams of equal-length packets arriving according to a Poisson process with rate λ/m each. If the traffic streams are frequency-division multiplexed on m sub channels of an available channel, the transmission time of each packet is m time units.