why is thee channel through double in slotted ALOHA compared to pure ALOHA?

Answer 1

Haha, you must be doing homework :-) The only reason ALOHA is usually discussed is for historical purposes when talking about multiple access protocols. The main difference between the two is that slotted ALOHA requires synchronization across all stations, and pure ALOHA does not.

In slotted ALOHA, time is broken up into exact intervals, each interval corresponds to a single frame, and all stations stay synchronized to this timing scheme. This basically converts the "continuous" pure ALOHA into a "discrete" slotted ALOHA.

As for the doubling of throughput, you'll have to do the math. The probability of arrival of a frame at any given time is modeled as a Poisson process. For the continuous pure ALOHA case the maximum throughput works out to be about 18%. For slotted ALOHA is works out to more like 36%. More exactly, the best utilization for slotted ALOHA works out to be 1/e where e is the natural log base value 2.71828 so that gives 36.7%, as opposed to pure ALOHA where it's 1/2e or 18.4%.

Below is a link that explains it along with the math. Just do a web search on pure and slotted aloha and you'll get lots of good results.