Question: Consider an unslotted CSMA/CD system in which the propagation delay is negligible compared to the time β required for a node to detect that the channel is idle or busy. Assume that each packet requires one time unit for transmission. Assume that β time units after either a successful transmission or a collision ends, all backlogged nodes attempt transmission after a random delay and that the composite process of initiation times is Poisson of rate G (up to time β after the first initiation). For simplicity, assume that each collision lasts for β time units.

(a) Find the probability that the first transmission initiation after a given idle detection is successful.

(b) Find the expected time from one idle detection to the next.

(c) Find the throughput (for the given assumptions).

(d) Optimize the throughput numerically over G.