Model of data-intensive support service

[alvinpoon]

Dear

I try to replicate the model from the article of "Dell’s SupportAssist customer adoption model". see attached model and the article.
I currently face 3 problems

1) I have almost done except 2 variables which I have no idea how to formulate according to the equation based on the equation description
see page 248 24. Attrition fraction γ = h(VE) ==> I am not sure how to formluate h(Ve)
see page 249 25. Attrition from adopters aA = (A/τ) ∙ h(VA) ==> I am not sure how to formluate h(VA)


2. I face the dimension inconsistency for 3 equation with the power functions, which vensim prompted me, for example
Error in units for the following equation:
Indicated resources = Resource per device unit * power ( Total devices with SA , Alpha )
Indicated resources --> $/month
Resource per device unit --> $/(month*device)
Total devices with SA --> device
Alpha --> Dmnl
Argument 1 of function power must be dimensionless


3) I cannot replicate the same base run output (page 231, Fig 7) as I almost followed all the equations to construct the models in the articl ( except the 2 variablesI mentioned earlier), I am not sure where went wrong. I think this model is compact and insightful model worth further studying about the data-intensive service's promotion strategy.

Thank you in advance for your time to look into the model and may give guidance how to make it.

PS the attached article is an open access article provided by System Dynamics Review vol 33, No 3-4 (July-December 2017): 219–253 for non-commercial use.

[tomfid]

1) It sounds like h(x) = 1-x, so you should be able to use y=1-Ve. That works, assuming Ve is dimensionless and defined over the [0,1] interval. I think there must be a mistake in the docs, because their statement that h(x)=1 and h(0)=.5 doesn't make sense. A more general approach might be to use a lookup, per #2 below.

2) I suspect that they may have defined the value units as equivalent to dimensionless, but in general, the right way to do this is to normalize with a reference value, like:

y = effect of Ve on attrition( Ve / Reference Ve )^Ve scale factor

This works for lookups, logs, powers, etc. and permits some experimentation with the shape via the scale factor (which should be 1 for their linear case however).

Another common option would be:

y = Ve scale*effect of Ve on attrition( Ve / Reference Ve ) + (1-Ve scale)

Again, the point of the scale factor is to permit experimentation with the slope of the lookup (in this case, you could only set Ve scale <= 1, but if you rearranged terms, you could also use steeper slopes).