Simple Proof of Dynkin's Formula for Single-Server Systems and Polynomial Convergence Rates

A.Yu. Veretennikov, G.A. Zverkina

2014, v.20, №3, 479-504

ABSTRACT

An elementary rigorous justification of Dynkin's identity with an extended generator based on the idea of a complete probability formula is given for queueing systems with a single server and discontinuous intensities of arrivals and service. This formula is applied to the analysis of ergodicity and, in particular, to polynomial bounds of convergence rate to stationary distribution.

Keywords: Dynkin's formula,single-server model,stationary regime,convergence rate

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