Editing ALOHAnet (section)

=== Pure ALOHA ===
[[file:Pure ALOHA1.svg|thumb|alt=Graph of frames being sent from 4 different stations according to the pure ALOHA protocol with respect to time, with overlapping frames shaded to denote collision.|Pure ALOHA protocol. Boxes indicate frames. Shaded boxes indicate frames that have collided.]]

The original version of the protocol (now called Pure ALOHA, and the one implemented in ALOHAnet) was quite simple:

* If you have data to send, send the data
* If, while you are transmitting data, you receive any data from another station, there has been a message collision. All transmitting stations will need to try resending ''later''.

Pure ALOHA does not check whether the channel is busy before transmitting. Since collisions can occur and data may have to be sent again, ALOHA cannot efficiently use 100% of the capacity of the communications channel. How long a station waits until it retransmits, and the likelihood a collision occurs are interrelated, and both affect how efficiently the channel can be used. This means that the concept of ''retransmit later'' is a critical aspect; The quality of the backoff scheme chosen significantly influences the efficiency of the protocol, the ultimate channel capacity, and the predictability of its behavior.

To assess Pure ALOHA, there is a need to predict its throughput, the rate of (successful) transmission of frames.<ref name="tann">{{Cite book |last=Tanenbaum |first=A. S. |url=https://archive.org/details/computernetworks00tane_2 |title=Computer Networks |publisher=Prentice Hall PTR |year=2003 |isbn=9780130661029 |author-link=Andrew S. Tanenbaum |url-access=registration |via=The Internet Archive}}</ref> First make a few simplifying assumptions:

* All frames have the same length.
* Stations cannot generate a frame while transmitting or trying to transmit. That is, while a station is sending or trying to resend a frame, it cannot be allowed to generate more frames to send.
* The population of stations attempting to transmit (both new transmission and retransmissions) follows a [[Poisson distribution]].

Let {{Math|T}} refer to the time needed to transmit one frame on the channel, and define ''frame-time'' as a unit of time equal to {{math|T}}. Let {{math|G}} refer to the mean used in the Poisson distribution over transmission-attempt amounts. That is, on average, there are {{math|G}} transmission attempts per ''frame-time''.

[[file:Pure ALOHA.svg|thumb|alt=Graph of 3 frames with respect to time. The earlier green frame overlaps with the yellow frame sent at time t0, which overlaps with the later purple frame.|Overlapping frames in the pure ALOHA protocol. Frame-time is equal to 1 for all frames.]]

Consider what needs to happen for a frame to be transmitted successfully. Let {{Math|t}} refer to the time at which it is intended to send a frame. It is preferable to use the channel for one frame-time beginning at {{Math|t}}, and all other stations to refrain from transmitting during this time.

For any frame-time, the probability of there being {{Math|k}} transmission-attempts during that frame-time is:

<math>\frac{G^k e^{-G}}{k!}</math>

[[file:Aloha PureVsSlotted.svg|thumb|alt=Throughput vs. Traffic Load of Pure Aloha and Slotted Aloha.|Comparison of Pure Aloha and Slotted Aloha shown on Throughput vs. Traffic Load plot.]]

The average number of transmission-attempts for two consecutive frame-times is {{math|2G}}. Hence, for any pair of consecutive frame-times, the probability of there being {{Math|k}} transmission attempts during those two frame-times is:

:<math>\frac{(2G)^k e^{-2G}}{k!}</math>

Therefore, the probability (<math>Prob_{pure}</math>) of there being zero transmission-attempts between {{math|t-T}} and {{math|t+T}} (and thus of a successful transmission for us) is:

:<math>Prob_{pure}=e^{-2G}</math>

The throughput can be calculated as the rate of transmission attempts multiplied by the probability of success, and it can be concluded that the throughput (<math>S_{pure}</math>) is:

:<math>S_{pure}=Ge^{-2G}</math>

The maximum throughput is {{math|0.5/e}} frames per frame-time (reached when <math>G=0.5</math>), which is approximately 0.184 frames per frame-time. This means that, in Pure ALOHA, only about 18.4% of the time is used for successful transmissions.