## Ideal Flow Network Virtual Lab

Welcome to IFN Virtual Lab. The material in this pages would give you an informal introduction and motivation about the ideal flow theory and mostly about its applications. These pages are still under development, so it is incomplete and still has many inaccuracy.

Several blind men were asked about how an elephant look like. Those who touch the trunk would say elephant looks like a hose. The man who touch the feet would describe elephant as a trunk of a tree. The man who touch the body of the elephant would say it looks like a wall. Similarly, Ideal Flow Network (IFN) seems to be different things to different people.

There are certain proportions in nature, which balance, produce certain optimality such as harmony in musical frequencies as well as Fibonacci sequence in flowers and plants. In investigating the nature of traffic congestion through the work of mathematics and computer simulation, we discovered astonishing patterns of link capacity proportion in the network produces balance in congestion level that theoretically can be brought down to the absolute minimum. We called the pattern premagic to represent the line sum symmetric where the sum of rows of the capacity matrix would be exactly equal to the transpose of the sum of columns. The heart of this pattern lies on the ideal flow network, which is basically *a steady state of relative flow conservation in a strongly connected network.*

IFN itself is purely mathematics. It is one of the laws of nature about closed system equilibrium. The basic philosophy of IFN is if each part (i.e., node) were in equilibrium, the whole system (i.e., network) would be automatically in equilibrium, as long as the system is closed.

IFN initially began as a transportation-engineering tool. That is why many of the terminologies (such as lanes, capacity, flow, and congestion) remains intact as historical reason. Modelers in other fields would be easier to imagine the meaning of these terminologies because road transportation is what we used in our daily activities. Everyone could comments and give opinion on how traffic congestion can be solved but he or she has no tool to measure, to prove his or her opinion. IFN gives anyone valuable tool for those who have opinion to solve traffic congestion in their own place to check the effect of their own policy scenarios. The main applications of IFN theory would be for traffic flow in road networks. Ideal Flow on Network (IFN) is a very useful modeling metaphor based on assigning flows in a transportation network. IFN can be applied to many applications range from machine learning of computer science to engineering, natural and social science. To use IFN as your modeling tool, you need to formulate the problems at hand can be formulated as flow equilibrium in a strongly connected network graph.

It turns out that the same principles and models can be used for numerous other fields as long as the four axioms of IFN and the definition of IFN is hold. Even if you intent to apply IFN only in your own field and you have no intention to solve any traffic network, learning the IFN theory and applications to transportation network would give a lot of valuable insight before you apply IFN on your area of interest.

The topics of this tutorial is as follow:

### Basic IFN

- What is Ideal Flow Network?
- IFN Lab: Matrix and Network
- Capacity to Stochastic
- Stochastic to Ideal Flow
- Capacity to Congestion