Type of regression with nominal, ordinal, interval and ratio data
I think I'd try to model the rate at which the ambulances are released instead of the time it takes. That would let me use Poisson regression, which is the canonical type of GLM for rates (in R's GLM, set family = "poisson".) However, in order to use PR, the data needs to have its variance equal to its mean, or at least close to it.