Performance Routing of a Substance to the whole Network

Theorem: For the Routing of a Substance to the whole Network is the required Communication limited by .

Proof:

Assume we have the following situation:

1	Network
1	Administration-Node
s	Sub-Networks in the Network
t	Sub-Sub-Networks in each Sub-Network
c	CNTS in each Sub-Network
l	artificial Lymph Nodes in each Sub-Sub-Network

Now, the Artificial Cell A sends a Substance S to the whole Network.

Workflow of the Routing:

1)	A inserts S to the Node which routes it towards the next Lymph-Nodes.
2) a)	The Lymph-Nodes send S to the neighbour Lymph-Nodes
2) b)	The Lymph-Nodes send S to the CNTS of the Sub-Network
3) a)	The CNTS send S to all other CNTS
4)	All CNTS send it to the Lymph-Nodes of the Sub-Network. Hence, all Lymph-Nodes receive S
5)	All Lymph-Nodes send S to the Nodes using the Bloodstream-Routing and receive it again.

Additionally, the Lymph-Nodes and CNTS store the Substance S for the time-to-live specified in the Substance-Parameters which does not need any Communication.

Definition:

• Distance between two CNTS is
• Distance between CNTS and Lymph-Node is
• Distance between two Lymph-Nodes is
• Distance between Lymph-Node and Nodes is

Calculation of the required Communication:

Communication


Explanation of the Summands:

• Starting Node to Lymph-Nodes
• Lymph-Nodes to neighbour Lymph-Nodes of Sub-Sub-Network
• Lymph_nodes to CNTS
• CNTS to all other CNTS
• CNTS to all Lymph-Nodes
• Lymph-Nodes to Nodes

This can be transformed to:



and this is in



Note: A standard Broadcast needs at least and depends on the Implementation of the Broadcast in the used Network Infrastructure.

"Performance Routing of a Substance to the whole Network" is mentioned on: Routing of Substances