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6. Ergodic Theorems for Queuing Systems

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Author
Dmitrii Silvestrov
Published in
Coupling and Ergodic Theorems for Semi-Markov-Type Processes II
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into ergodic theorems for M/G-type queuing systems, focusing on explicit upper bounds for convergence rates. It introduces a queuing system where service distributions depend on the queue length, providing detailed analysis and explicit upper bounds for power and exponential moments of the busy period duration. The chapter explores the ergodic properties of the system, presenting theorems that establish the convergence of the queue process to its stationary distribution. Additionally, it derives explicit upper bounds for moments of regeneration times and transition periods using polynomial and exponential test functions. The chapter concludes with a discussion on the stability and ergodic relations of the queue process, offering insights into the behavior of such systems under various conditions. Readers will gain a comprehensive understanding of the mathematical framework underlying these queuing systems and the practical implications of the derived bounds.
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previous chapter Semi-Markov Processes with Discrete State Spaces and Embedded Regenerative Processes
next chapter Semi-Markov Processes with General State Spaces with Atoms
Title
Ergodic Theorems for Queuing Systems
Author
Dmitrii Silvestrov
Copyright Year
2025
Book
Coupling and Ergodic Theorems for Semi-Markov-Type Processes II

Print ISBN: 978-3-031-89314-8

Electronic ISBN: 978-3-031-89315-5

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-89315-5_6
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