So far in this tutorial, we didn't care about the unit of measurement yet. It was assumed they are in the same unit.
For a formula to be correct, the units between variables must also be correct and consistent.
The capacity matrix is simply weighted adjacency matrix. Thus, you can set the unit of capacity matrix. For example, for transport related application, capacity can be measured either as number of lanes or road width or vehicle per hour or vehicle per day.
The stochastic matrix has no unit (unit less because it is probability).
The flow matrix has unit of flow. The meaning of flow can be anything from vehicles flow, money flow, energy flow, entropy flow and so on depending on your applications. For road transport related application, the unit of flow can be 'vehicle per hour' or 'vehicle per day'. Since flow is a function of stochastic and kappa (=total flow), the unit of flow comes from kappa because stochastic is unitless.
The congestion matrix is unitless. Since congestion is a division between flow and capacity, there must be a unit conversion factor to make the capacity to be at the same unit as the flow. For example, if the capacity is on number of lanes and the flow is in vehicles per hour then we need to convert the number of lanes into vehicles per hour by a conversion factor. If the capacity is on road width and the unit of flow is in passenger car unit per day then we need a conversion factor to convert road width in meter into passenger car unit per day.
The virtual lab below is an attempt to set the multiplying factor in order to convert the units such that the model would become consistent.
Lab Tool: Capacity to Congestion
You can use the program below to convert capacity matrix into a Congestion Matrix via proportioal capacity approximation.
End each row by a semicolon. Separate each data in one row by comma or a space.
You network must be strongly connected.
Values in capacity matrix represents
Input: Capacity matrix
Input: capacity multiplier
Input: total flow, kappa
