CS485 Sylabus

### The initial performance Analysis of the Aloha protocol

• Initial performance analysis of the Aloha protocol

• Model description:

• An average of G messages are being transmitted per sec:

Analogy:

• We know that:

 There may be collisions Not every transmission will be successful

• Define:

 ``` p = the fraction of transmission attempts that are successful ```

• Then the throughput S is equal to:

 ``` S = # successful transmissions per sec (definition !!!) = # transmission attempts per sec × fraction that are successful = G × p So: S = p × G ```

• \$64,000 question: how do we compute p ???

 ``` p = ????? ```

Fact:

• p is different for

 slotted Aloha unslotted Aloha

• Definition of the time unit

• Fact:

• You can often simplify the Mathematical analysis by:

 Each message (frame) has the same length (= same transmission time)

• Time unit used in the performance analysis:

 Time unit = transmission time of a message

• Note:

• In slotted Aloha, we also have:

 ``` 1 time unit = length of 1 slot ```

Reason:

• Because one message is transmitted in one slot:

We also have:

 Time unit = length (duration) of 1 slot !!!

• An important fact of probability

• Fact:

 The probability of some event X = the fraction of event X

• Example:

• We roll a die

Then:

 ``` Probability of rolling a 6 = 1/6 Fraction of rolls equal 6 = 1/6 ```