Call me irresponsible
Call me unreliable
Throw in undependable, too
So what is reliability?
My Blog, my rules. This
is longer and more technical than my typical postings, but so it goes.
The extra time added in order to be reliable is proposed
to be
δ*(1-exp (-(TTI-1)/ϵ)))
This is an exponential association, also known as a “limits to growth” or
transitional, equation. If the travel
times are normally distributed, then 1+δ is the (one tailed) Z-Score of the
percentile of reliability. If reliability
is 95%, then δ=.645
The value of ε is such that 99.99994%, 5 Sigma, of the transition must take place between TTI =1 and TTI=1+δ. The theoretical value for a 95% reliability is ε = 0.102815.
TTI, the Travel Time Index, is the Mean Time divided by
the Free Flow Time, FFT. PI, the Planning Index is the Mean Time plus the Extra Time
Added in order to be 95% reliable, divided by the Free Flow Time. The Planning Index and the Travel Time Index
is recorded for various metropolitan area and reported in the FHWA’s Urban Congestion
Reports. The Extra Time Added to be 95% reliable
divided by the Mean Time is the Buffer Index, BI. The relationship between the Planning Index,
the Buffer Index, and the Travel Time Index is thus:
PI = TTI*(1+BI).
A non-linear regression of the 156 reported values in the FHWA's Urban Congestion Reports for the Third Quarter of the Federal Fiscal Year, the period including
April, May, and June, for 2017, 2018 and 2019, yields the following result.
PI = TTI*(1+δ*(1-exp(-(TTI-1)/ε)))
with a coefficient of determination, r2, of 0.964,
where:
δ =0.602
+/- 0.001; and
ε =0.113
+/- 0.007
One of the data points, which is an outlier to the
regression, is for San Juan, Puerto Rico.
If the data for San Juan is removed, then the regression becomes
PI = TTI*(1+δ*(1-exp(-(TTI-1)/ε)))
with a coefficient of determination, r2, of 0.934,
where:
δ = 0.621 +/- 0.008; and
ε = 0.121 +/- 0.005.
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