Problem
1. (a) Prove that the peak throughput of a pure Aloha system is 112e, where e is the base of the natural algorithm.
(b) Suppose a system has two different packet lengths: T and 2T. Find the throughput of a slotted Aloha system in this case.
2. Suppose that, in a slotted Aloha system, there is a 10% packet error rate due to noise, in addition to the error rate associated with those packet errors due to collisions.
(a) Discuss how the system throughput will be affected.
(b) Repeat the discussion for a carrier-sensitive multiple-access (CSMA) system.