Queuing transaction rates and the yield curve

Rather than use transaction rates to map to the yield curve, use inter arrival times. The optimization problem is, How can one minimize variance on queue size with the most idle time. So, 30 year term structures are things that happen on 30 year intervals, like building a highway or establishing a family neighborhood.

Sample period is the average inter arrival period, so we convert to sample periods. The question becomes, How many sample frequencies do we need to estimate queue sizes? Well, we are restricted to computing equilibrium moments, then the question becomes, How many sampling frequencies do I need to sample gaussian noise. And the the distribution of sampling frequencies becomes the Fourier transform of that, which is again Gaussian. So, we pick sampling frequencies along the yield curve, which is Gaussian at stability. Use the constant measurement error to limit the dimensionality. Do one of a number of decompositions of NGDP, in time, and pick the top five modes. They should be distributed to minimize inter nodal errors due to measurement uncertainty, which one can check against the actual real yield curves.

In the multi-stage queue model, all distribution chains will adapt to these sampling rates, dividing up production and lot sizes to meet a specific production structure, with capital investment decisions agglomerating about the sample period. So, in the queuing model, introduce lot size, again getting back to price theory as lot size ratios.

So, when a yield curve is steep, there is a tendency for long term capital investments to hold, for a long time; and variations from planned output will be managed by lower lever, shorter term queues. Our curve is steep, whatever we have decided long term can be changed by a double dip recession and restart (asymmetry) ; or it can be made to work.