Abstract
Recently, Konstantopoulos and Zazanis (1992, 1994) and Brémaud and Lasgouttes (1993) derive the infinitesimal perturbation analysis (IPA) estimators 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. The problem here is how to treat the ‘catastrophic jumps’ on the sample path of the steady state and this is solved cleverly by using the Palm calculus. We deal with multi-class queues in this paper but our key formula is expected to be useful to any systems to which the SPA is applicable.
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Miyoshi, N. Smoothed Perturbation Analysis for Stationary Single-Server Queues with Multiple Customer Classes. Discrete Event Dynamic Systems 7, 275–293 (1997). https://doi.org/10.1023/A:1008206314658
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DOI: https://doi.org/10.1023/A:1008206314658