The basic idea of an ALOHA system is simple. Users transmit whenever they have data to be sent. There will be collisions, of course, and collision frames will be destroyed. However, due to the feedback property of broadcasting, a sender can always find out whether or not its frame was destroyed by listening to the channel. the same way other users do. If the frame was destroyed, the sender just waits a random amount of time and sends it again.
The waiting time must be random or the same frames will collide over and over, in lockstep. Systems in which multiple users share a common channel in a way that can lead to conflicts are widely known as contention systems.
Figure 6.4 illustrates the transmission of a frame in pure Aloha. In pure Aloha, frames are transmitted at completely arbitrary times.

We have made the frames all of the same length because the throughput of Aloha systems is maximized by having a uniform frame size rather than allowing variable length frames.
Whenever two frames try to occupy the channel at the same time, there will be a collision and both will be confused. If the first bit of a new frame overlaps with just the last bit of a frame almost finished, both frames will be totally destroyed and both will have to be transmitted later.
Now we will discuss about efficiency of an Aloha channel. Let us consider an infinite collection of interactive users sitting at their computers (stations). A user is always in one of the two steps: typing or waiting.
Initially, all users are in the typing state; when a line is finished, the user stops typing, waiting for a response. The station then transmits a frame containing the line and checks the channel to see if it was successful. If so, the user sees the reply and goes back to typing. If not, the user continues to wait and the frame is retransmitted over and over until it has been successfully sent.
Let the `frame time' denote the amount of time needed to transmit the standard, fixed length frame (that is, the frame length divided by the bit rate). At this point, we assume that the infinite population of users generates new frames according to Poisson distribution with mean S frames per frame time.
If S > 1, the user community is generating frames at a higher rate than the channel can handle and nearly every frame will suffer a collision. It is reasonable to expect 0 < S < 1.
In addition to the new frames, the stations also generate retransmissions of frames that previously suffered collisions.
Let us further assume that the probability of k transmission attempts per frame time, old and new combined, is also a Poisson distribution with mean G per frame time. Clearly, G > = S. At low load (that is, S = 0), there will be few collisions, and hence retransmissions. Therefore, G = S. At high load, there will be many collisions, and G > S.
Under all loads, the throughput is just the offered load, G times the probability of a transmission being successful, that is, S = GPO 0, where PO is the probability that a frame does not suffer a collision.
A frame will not suffer a collision if no other frames are sent within one frame time of its start as shown in Figure.

In fact, the shaded frame's fate was already sealed even before the first time it was sent, but since in pure Aloha a station does not listen to the channel before transmitting, it has no way of knowing that another frame was already underway. Similarly, any other frame started between to + t and to + 2t will bump into the end of the shaded frame.
The probability that k frames are generated during a given frame time is given by the Poisson distribution:

So the probability of zero frames is just e -G. In an interval two frame times long, the mean number of frames generated is 2G. The probability of no other traffic being initiated during the entire vulnerable (harmed) period is thus given by Po = e-G. Using S = GPo, S = Ge 2c.
Figure 6.6 illustrates pure Aloha and slotted Aloha.

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