How do I map SSIS 2012 Package Variables to Parameters?
I am bit too late to answer this question but I would like to make a point about Parameter role in package deployment model 

It says'


  In general, if you are deploying a package using the package deployment model, you should use configurations instead of parameters.
  
  When you deploy a package that contains parameters using the package
  deployment model and then execute the package, the parameters are not
  called during execution. If the package contains package parameters
  and expressions within the package use the parameters, the resulting
  values are applied at runtime. If the package contains project
  parameters, the package execution may fail.


Here is a beautiful answer about setting up variables for different environment configurations.