Characterization of transport optimizers via graphs and applications to Stackelberg-Cournot-Nash equilibria

We introduce graphs associated to transport problems between discrete marginals, that allow to characterize the set of all optimizers given one primal optimizer. In particular, we establish that connectivity of those graphs is a necessary and sufficient condition for uniqueness of the dual optimizers. Moreover, we provide an algorithm that can efficiently compute the dual optimizer that is the limit, as the regularization parameter goes to zero, of the dual entropic optimizers. Our results find an application in a Stackelberg-Cournot-Nash game, for which we obtain existence and characterization of the equilibria

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. Keywords: Queueing, Fairness measures, Multi-server queue, Combined queue vs. separate queues, 2010 MSC: 60K25, 68M20, 60J2

The number of overtakes in an M/M/2 queue

The phenomenon of overtaking in queueing systems and queueing networks has been addressed by several authors with various motivations in the last decades. Nevertheless, up to now, for the relatively simple M/M/2/FCFS queue, the distribution of the number of overtakes a stationary customer suffers from was not known. In this paper, we characterize this distribution by its probability generating function. As a consequence, we derive the expectation (which is well-known) and the variance. Keywords: Queueing, Overtakes, Absorbing Markov chain, MSC: 60K25, 68M20, 60J1