Quantum queued collisional models

We propose a general framework of queued collisional models, that combine stroboscopic quantum dynamics with queuing theory in classical stochastic processes. This framework generalizes existing approaches for quantum collisional models, recovering the deterministic and stochastic formulations in the appropriate limits. We illustrate the idea with a model where both the server and the queued ancillas are described by qubits, subject to either amplitude-damping noise or Rabi drives. We show how the queue parameters can predict whether or not a steady state is reached asymptotically, and how the overall dynamics is sensitive to the expected behavior of the queue. Finally, we discuss how a phase transition in the queue has physical consequences that can be explored by studying ensemble averages of the populations of the system.