Analysis of a tandem queuing system with blocking and group service in the second node

ABSTRACT

In this paper, we study a tandem queuing system in which the arrivals occur according to a versatile Markovian point process. The buffer sizes in the first and second nodes are, respectively, infinite and finite. We incorporate the impatience of the customers in both the nodes. The service times in both nodes are assumed to be of phase type. While the services in the first node are offered on a first-come-first-served basis, we assume that in the second node the services are provided in batches of varying sizes based on two pre-determined thresholds. The system is studied as a multi-dimensional continuous time Markov chain and a few illustrative numerical examples are reported.

KEYWORDS:

• Tandem queuing system
• MAP
• group service
• algorithmic analysis

Acknowledgements

The authors highly appreciate the valuable comments by the anonymous reviewers that significantly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Notes on contributors

S. A. Dudin

S. A. Dudin was graduated from Belarusian State University in 2007. In 2010, he earned PhD degree in Belarusian State University in System Analysis, Control and Information Processing and works currently as leading scientific researcher of Research Laboratory of Applied Probabilistic Analysis in Belarusian State University. His main fields of interests are queueing systems with correlated arrival flows and controlled tandem models. He published the monograph and over 100 papers including more than 75 papers cited in Scopus.

A. N. Dudin

A. N. Dudin has got PhD degree in Probability Theory and Mathematical Statistics in 1982 from Vilnius University and Doctor of Science degree in 1992 from Tomsk University. He is Head of Laboratory of Applied Probabilistic Analysis in Belarusian State University. He is author of more than 450 publications including 5 books and more than 130 papers in top level Journals. He coedited more than ten volumes of the Springer series. In 2013, he received Scopus Award Belarus for outstanding contribution to the field of Mathematics. He is the Chairman of Belarusian Winter Workshops in Queueing Theory which are held since 1985 and the Chairman of IPC of the conference named after A.F. Terpugov since 2014. He was invited for lecturing and research to USA, UK, Germany, France, the Netherlands, Japan, Korea, India, Russia, China, Italy, and Sweden.

O. S. Dudina

O. S. Dudina was graduated from Belarusian State University in 2007. In 2010, she earned PhD degree in Belarusian State University in Probability Theory and Mathematical Statistics. Her PhD dissertation got Award as the best dissertation of the year in Republic of Belarus in Natural Sciences. She works as leading scientific researcher of Research Laboratory of Applied Probabilistic Analysis in Belarusian State University. Her main fields of interests are queueing tandem queueing models with correlated arrival flows, non-markovian queueing systems. She published the monograph and over 100 papers including more than 65 papers cited in Scopus.

S. R. Chakravarthy

S. R. Chakravarthy, a Distinguished Faculty (Kettering's Faculty and Alumni Honor Wall), retired as a Professor in the Departments of Industrial and Manufacturing Engineering & Mathematics at Kettering University, Flint, Michigan. Srinivas Chakravarthy's research interests are in the areas of algorithmic probability, queuing, reliability, inventory, and simulation. He has published more than 135 papers in leading journals and his recent contributions include a 2-volume book on Matrix-Analytic Methods in Queues, published by ISTE-Wiley, 2022.