Perfect Generation, Monotonicity and Finite Queueing Networks

Perfect generation, also called perfect or exact simulation, provides a new technique to sample steady-state and avoids the burn-in time period. When the simulation algorithm stops, the returned state value is in steady-state. Initiated by Propp and Wilson in the context of statistical physics, this technique is based on a coupling from the past scheme that, provided some conditions on the system, ensures convergence in a finite time to steady-state. This approach has been successfully applied in various domains including stochastic geometry, interacting particle systems, statistical physics, networking.The aim of this tutorial is to introduce the concept of perfect generation and discuss about the algorithmic design of perfect samplers. To improve the efficiency of such samplers, structural properties of models such as monotonicity are enforced in the algorithm to improve drastically the complexity. Such samplers could then been used in brute force to estimate low probability events in finite queueing networks.