Greeting,

My name is Pooria, an Optical Telecommunications student. I have been working on Flexible Bandwidth Optical Networks since 2009. However, in my current project, I got a question that I thought maybe you can help me to solve. Well, I need to introduce a quantitative criterion for judging the degree of spectral fragmentation in the network links. I will explain the problem in a simple way, hence, it is highly appreciated if you could guide me.

Assuming, we have a row of twelve chairs. Five people will randomly sit on them. We take two possible cases:

- They sit on the five first chairs respectively. We named this case “The Compact case”.

- In the second case, which we named “The Fragmented case”, people sit on chairs in the following order:

- Man 1 – Chair 1, Man 2 – Chair 4, Man 3 – Chair 6, Man 4 – Chair 8, Man 5 – Chair 10.

Now, I would like to introduce a factor that showsHow faris the fragmented case form the compact case. More difficult, what will be this factor if people need random number of chairs as well. For example:

- Man 1 needs 2 chairs, Man 2 needs 1 chair, Man 3 needs 1 chair, Man 4 needs 1 chair, Man 5 needs 3 chairs.

I will be grateful if you could guide me through this problem. Thank you very much.

Looking forward to hear you,

Cheers,

Pooria