---
# System prepended metadata

title: Traffic load 與 buffer size 的關係 (QoS)

---

# Traffic load 與 buffer size 的關係 (QoS)

Author: WhoAmI
Date: 20230126
email: kccddb@gmail.com
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: $\mu$
![](https://i.imgur.com/vuj39MT.png)

![](https://i.imgur.com/ctq8Eto.png)

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




![](https://i.imgur.com/EMWRlkG.jpg)
![](https://i.imgur.com/5ZANUQg.jpg)
![](https://i.imgur.com/K02EMkd.jpg)
:::info
當 $\rho=\lambda/\mu$ 增加 惡化更快 (通常非線性)
:::
<h2>Input Queue</h2>


![](https://i.imgur.com/NX2bdCM.jpg)

![](https://i.imgur.com/JkZ4EVx.jpg)

<h2> Output Queue</h2>

![](https://i.imgur.com/5gwR3GF.png)
![](https://i.imgur.com/Cz5JaYv.png)

![](https://i.imgur.com/pe2XQ2j.jpg)