what is difference between open and mixed queue

Question

please consider this image:

In this picture that I got it from Here write said that Network C is Open,B is Mixed and A is Closed.

I want to know why C isn't mixed? Video Server 1,2,...m are closed so C is mixed.

Video Server 1,2,...m is like Admin...

please guide me why C is open and B is mixed

thanks

Answer 1

If you look very closely, the arrow are going out... in network C.

$$ \leftarrow \boxed{\cdot} $$

So $C$ is "open", while $B$ has information going in and out. It is mixed:

$$ \leftarrow \boxed{\cdot} \leftarrow $$

$A$ is closed since no information is coming in or out:

$$\boxed{\cdot \leftarrow \cdot} $$

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$$ \boxed{ \cdot \to \boxed{\boxed{\cdot}_C \leftarrow \cdot }_B\to \cdot}_A$$

Please look at the exercise on box algebra by knot-theorist Lou Kaufmann, or this article on the little 2-cubes operad by Jim Stasheff

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$$ \boxed{\text{Users} \leftrightarrow \boxed{\boxed{\text{Proxy } \leftrightarrow \text{Video Server}}_A \leftrightarrow \text{Admin}}_B}_C $$

Here are the definitions from your notes:

• Open model in which jobs departing from one queue arrive at another queue (or possibly the same queue)
• Closed Closed queueing network: No external arrivals or departures; Total number of jobs in the system is constant
• Mixed Open for some workloads and closed for others ⇒ Two classes of jobs.

Network C is open to external information. A is closed there nothing going in and out. B is open to user jobs but closed to admin jobs.