# Traffic load 與 buffer size 的關係 (QoS)

Author: WhoAmI
Date: 20230126
email: [e-mail]
Copyright: CC BY-NC-SA

<style>
.blue {
color: blue;
}
.bgblue {
color: blue;
font-size: 24px;
font-weight: bold;
}
.red {
color: red;
font-size: 24px;
font-weight: bold;
}
h1 {text-align: center;}
h2 {text-align: center;}
</style>

input rate: $\lambda$
output rate: $\mu$


An M/M/1 queue is a stochastic process whose state space is the set {0,1,2,3,...} where the value corresponds to the number of customers in the system, including any currently in service.

Arrivals occur at rate λ according to a Poisson process and move the process from state i to i + 1.
Service times have an exponential distribution with rate parameter μ in the M/M/1 queue, where 1/μ is the mean service time.

**utilization $\rho=\frac{\lambda}{\mu}$**

:::info
當 $\rho=\lambda/\mu$ 增加 惡化更快 (通常非線性)
:::
<h2>Input Queue</h2>



<h2> Output Queue</h2>