Simple proof of Dynkin's formula for single-server systems and polynomial convergence rates

2013/06/30 by Alexander Yu. Veretennikov, Galina A. Zverkina · 1 citation
Mathematics · #math.PR #msc:60K25 #msc:90B22

paper · pdf

published as Markov Processes and Related Fields. 2014. Vol. 20. No. 3. P. 479-504 · 27 pages, a few typos corrected, a few references added in comparison to the first version

arxiv created 2013/10/23 · arxiv updated 2014/12/15

Abstract

An elementary and rigorous justification of Dynkin's identity with an extended infinitesimal operator based on the idea of a complete probability formula is given for queueing systems with a single server and discontinuous intensities of arrivals and serving.

Cited by

• On recurrence and availability factor for single--server system with general arrivals

Related

• The join-the-shortest-queue system in the Halfin-Whitt regime: rates of convergence to the diffusion limit
• New Look at Finite Single Server Queue with Poisson Input and Semi-Markov Service Times
• The M/M/Infinity Service System with Ranked Servers in Heavy Traffic
• The Limit of Stationary Distributions of Many-Server Queues in the Halfin-Whitt Regime
• On Pollaczek-Khinchine Formula for Peer-to-Peer Networks