Smoothed perturbation analysis estimates for stationary multi-class queues

Recently, Konstantopoulos and Zazanis and Bremaud and Lasgouttes derive the infinitesimal perturbation analysis estimator for the stationary and ergodic G/G/1 queue using Palm calculus, where neither regenerative structure nor convex property are required and the strong consistency is ensured by ergodic theorem. This work has been motivated by them and derives the smoothed perturbation analysis (SPA) estimator on the stationary and ergodic framework. We deal with multi-class queues in this paper but our key formula is expected to be useful to the systems to which the SPA is applicable