Throughput of Aloha

Question

The equation for the throughput of Aloha is

S = Ge^-2G

Which can be thought of as G (the rate of transmission attempts) multiplied by e^-2G (the probability of one of those attempts being successful).

I came across this graph and text ...

And it made me question if I really understand what the x-axis represents - offered load.

Why is 0.5 transmission attempts per frame time, referred to as 50% of offered load? (Text above graph).

If there were ten stations and each station attempted one transmission per frame time, would that be 1000% offered load? If yes, why?

I think it's more likely that I have missed a beat somewhere and that I'm not really comprehending what is meant by "offered load".

Any help would be great.

Answer 1

Referring to mathcs.emory.edu, clarifying some terms:

Arrival rate λ = number of new messages that arrives per time unit

Offered load (rate) G = number of (old and new) messages that contend for the channel per time unit

Throughput S = number of messages that are successfully transmitted per time unit

A message is successfully transmitted if its transmission does not collide with any other message transmission

And the offered load G = λ/P[success]

Why is 0.5 transmission attempts per frame time, referred to as 50% of offered load? (Text above graph).

It is just about defining terms (See above linked page for derivation). The packet transmission time is used as time unit here.

If there were ten stations and each station attempted one transmission per frame time, would that be 1000% offered load? If yes, why?

No. The number of successful/unsuccessful transmissions is also relevant for calculating G. See formula for G.

Thanks, muehsi