Queue

First we know that the queue model is based on Poisson distribution. Here is three characteristics of Poisson distribution:

• The experiment consists of counting the number of events that will occur during a specific interval of time or in a specific distance, area, or volume.
• The probability that an event occurs in a given time, distance, area, or volume is the same.
• Each event is independent of all other events. For example, the number of people who arrive in the first hour is independent of the number who arrive in any other hour.

Little’s Theorem

N = λT

N=average number of customers

λ=Average arrival rate

T=Average sojourn(stay) time of a customer

Apply the Little’s Theorem to the Network Delay environment

We should also add some notation:

ρ: the line’s utilization factor(we can see that $ρ=\frac{λ}{μ}$ later)

X: average transmission time

$ρ=λX$

now introduce the model:

M/M/1 Model

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