Waiting time and idle time of uncertain queueing system

Abstract

Uncertain queueing system is a waiting line in which the interarrival times and service times are both modeled by uncertain variables. This paper investigates four important performance characteristics of uncertain queueing system, including waiting time, idle time, total idle time and total busy time. The analytical formulas of uncertainty distributions of those performance characteristics are also derived separately.

Keywords:

• Uncertain queueing system
• waiting time
• idle time
• busy time
• uncertainty theory

Acknowledgments

The support by Grant No. 61873329 of National Natural Science Foundation in China is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China Grant No. 61873329.

Notes on contributors

Yang Liu

Yang Liu received the B.S. degree from Harbin Institute of Technology, Harbin, China, in 2018. He is currently a Ph.D. candidate at Department of Mathematical Sciences, Tsinghua University, Beijing, China. Mr. Liu's current research interests include uncertain statistics, uncertain renewal processes and uncertain differential equations.

Baoding Liu

Baoding Liu received his B.S. degree in 1986 from Nankai University, and his M.S. degree in 1989 and Ph.D. degree in 1993 from Chinese Academy of Sciences. He joined Tsinghua University as Associate Professor in 1996 and was appointed Professor of Mathematics in 1998. He is currently a professor with the Department of Mathematical Sciences, Tsinghua University, Beijing, China. Dr. Liu's research led to the development of uncertainty theory that is a branch of mathematics concerned with the analysis of belief degree.