The expected discrimination frequency for two-server queues

Fairness measures for queues were introduced for measuring the individual satisfaction of human customers with respect to the waiting experience. The measure which performs best in some sense is the expected discrimination frequency (DF). In contrast to competing fairness measures, up to now, the DF has not been thoroughly analysed for multi-server systems. In particular, there are no results concerning the question whether or not in terms of the DF, combined queues are fairer than separate queues. In this note, we prove that under Markovian assumptions, combined queues are fairer and, furthermore, that this statement does not remain true for general queueing systems.