Network Queing models

Extra Notes

Random Experiment

• Event: A subset of the sample space whether the even is occured is determined by whether the outcome is an element of the event set

• Random Variable: Denoted by a Captial X, there is nothing random about the random variables. It is a function, just a mapping.

What is a typical example for a mapping - Flipping a coin?

If thats the case, than the sample space is either head or tails. Then if thats the case, the random variable will map the head to a value.

Thus, random experiements outcome would map to a set of real numbers. The distribution function just measures the probability that the outcome from the mapping is less than or equal to certain constant x.

Probability Density Fn: Using lower case f to denote this. The distribution function is also called cumulative distribution function.

Exponential Distribution

The most important distribution for our module.

• Meaning of lambda: Expection of T itself is at the avg entirely, thus lambda is rate (Avg rate of packet arriving)

Why is this good then

Desirable property:

• Memoryless property: IF a random variable follow exponential, then the following equaltion is satisfied (Check slides)