@article{Yiming2024, 
author = {Nurehemaiti Yiming},
title = {Dynamic analysis of the M/G/1 queueing system with multiple phases of operation},
year = {2024},
journal = {Networks and Heterogeneous Media},
volume = {19},
number = {3},
pages = {1231-1261},
keywords = {queueing system with multiple phases of operation, C0semigroup, operator spectrum, asymptotic behavior, time-evolving queue length},
url = {https://www.sciopen.com/article/10.3934/nhm.2024053},
doi = {10.3934/nhm.2024053},
abstract = {In this paper, we considered the M/G/1 queueing system with multiple phases of operation. First, we have proven the existence and uniqueness of the time-evolving solution for this queueing system. Second, by calculating the spectral distribution of the system operator, we proved that the solution converged at most strongly to its steady-state (static) solution. We also discussed the compactness of the system's corresponding semigroup. Additionally, we investigated the asymptotic behavior of dynamic indicators. Finally, to demonstrate the exponential convergence of the solution, we conducted some numerical analysis.}
}