- 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
- An average of
G messages are being
transmitted per sec:
- 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
- p is
different for
- Fact:
- You can often
simplify the
Mathematical analysis by:
- Adopting a different time unit
- You can often
simplify the
Mathematical analysis by:
- Recall the follow assumption:
- 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 !!!
- In slotted Aloha, we
also have:
- 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
- We roll
a die