Stochastic decomposition of the M/M/1 queue with environment dependent working vacation
Abstract
We consider an M/M/1 queue with n types of working vacation. After a non zero busy period if the server finds the system empty, it opts for one of the n types of working vacation depending on the environment. On vacation completion epoch finding an empty system, it remains in the respective vacation. We demonstrate the stochastic decomposition structure of the queue length and waiting time of this M/M/1 queue and obtain the distribution of the additional queue length and additional delay.
Copyright © 2021 S. Jaya, B. Lakshmi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. Jaya, B. Lakshmi, Stochastic decomposition of the M/M/1 queue with environment dependent working vacation, J. Math. Comput. Sci. 11 (2021), 8008–8020. https://doi.org/10.28919/jmcs/6708
BibTeX
@article{Jaya2021,
author = {Jaya, S. and Lakshmi, B.},
title = {Stochastic decomposition of the M/M/1 queue with environment dependent working vacation},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {8008--8020},
doi = {10.28919/jmcs/6708}
}