Decision making under uncertain and dependent system rates in service systems

•Develops optimal staffing methods for service systems with dependent uncertain arrival, service, and abandonment rates.•Develops Markov chain Monte Carlo methods for estimating the joint probability distribution of the system rates.•Extends the augmented nested sampling algorithm to discrete state spaces.•Provides evidence that ignoring dependence between system rates leads to over – or under-staffing.•Provides evidence that assuming fixed rates always yields lower staffing levels when high fluctuations in the system rates are present.