On the exact simulation of functionals of stationary Markov chains Original Research Article

In performance evaluation domain, simulation is an alternative when numerical analysis fail. To avoid the burn-in time problem, this paper presents an adaptation of the perfect simulation algorithm [Random Struct. Algorithms 9 (1996) 223] to finite ergodic Markov chain with arbitrary structure. Simulation algorithms are deduced and provide samplings of functionals of the steady-state without computing the state coupling, it speeds up the algorithm by a significant factor. Based on a sparse representation of the Markov chain, the aliasing technique improves highly the complexity of the simulation. Moreover, with small adaptations, it builds a transition function algorithm that ensures coupling.