---
# System prepended metadata

title: II or Rate Discussion
tags: [Discussions]

---

# II or Rate Discussion

###### Tags: `Discussions`

### Introduction

Using rate:
+) The term rate is dynamic - sounds suitable for DS
-) Expressions are really *hard* to understand

Using II:
+) Simple linear expressions
-) The term *II* is static - sounds suitable for SS

### Formulation - rate

![](https://i.imgur.com/ptHaavg.jpg =400x)

```
r = r' = min(1/IIp, 1/IIg, 1/IIs)
```

![](https://i.imgur.com/7ZZSBMT.jpg =300x)

The start and return can be considered as rate = 0

MUX/DEMUX expression: 
*(Both components have a single-port end and a double-port end. p is the probablity to go to port 1 at the double-port end.)*

```
1/single_port_rate = 1/double_port_1_rate*p+1/double_port_2_rate*(1-p)

double_port_1_rate = single_port_rate*p
double_port_2_rate = single_port_rate*(1-p)
```
### Formulation - II
![](https://i.imgur.com/hWH7N9k.jpg =400x)

```
1/r = 1/r' = max(IIp, IIg, IIs)
```

![](https://i.imgur.com/tFUbq5f.jpg =300x)

The start and return can be neglected

MUX/DEMUX expression: 
*(Both components have a single-port end and a double-port end. p is the probablity to go to port 1 at the double-port end.)*

    II_single = II_double1*p+II_double2*(1-p)

    II_double1 = II_single/p
    II_double2 = II_single/(1-p)


Or put this figure...
Each edge has a rate and each component has an II.

![](https://i.imgur.com/qZYWXD4.jpg =300x)


