Ranking flexibility structures in queueing systems

We consider the problem of comparing flexibility structures in queueing systems. We find that an important issue in evaluating flexibility is that one cannot separately consider the design of a flexibility structure and the choice of a server scheduling policy. We propose a policy that leverages flexibility in a more predictable (and typically more effective) manner than several common policies and find that the proposed policy is a useful basis for comparisons. In terms of evaluating flexibility, we take as a starting point the CF index of Iravani, Kolfal, and van Oyen (2011) and find that by breaking it down to its components, we are able to identify scenarios in which the CF index may incorrectly compare flexibility structures in systems with heterogeneous variability in the underlying interarrival time and service requirement distributions. For such scenarios, we propose a distribution-dependent metric for performing the ranking. A consequence of our observations is the ability to construct partial rankings that appear to be relatively insensitive to the underlying distributions.