Quasi-stationary distributions for queueing and other models

2022/02/11 by Phil. Pollett, Pollett, Phil.
Business, Management and Accounting · Decision Sciences · Mathematics · #(60J27) #(60K25 #60J80) #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2202.05428

openalex publication_date 2022/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note presents conjectures on polynomial/algebraic/sub-exponential convergence of transition probabilities for λ-null recurrent and λ-transient Markov chains in continuous time. The only known positive examples are in queueing, branching, and related models. Implications for the existence of limiting conditional distributions for λ-transient chains are discussed.

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