Analysis of the M/G/1 Queueing System under the Triadic (N, D, J)-Policies

Abstract

We study the steady-state queue length and waiting time of the M/G/1 queue under the combined N-, D- and T- (multiple vacation) policies. We first derive the queue length PGF and the LSTs of the workload and waiting time. Then, the mean performance measures are derived. Finally some special cases and numerical experience are presented.

Key Words:

• D-policy
• M/G/1
• Min(N, D)-policy
• multiple vacations
• N-policy
• queue length
• T-policy
• waiting time
• workload

Additional information

Notes on contributors

Lee Ho Woo

Ho Woo Lee is currently a Full Professor at Department of Systems Management Engineering, Sungkyunkwan University, Suwon, Korea. He received his B.S. degree at Department of Industrial Engineering from Seoul National University, Seoul, Korea, M.S. and Ph.D. degrees at Department of Industrial and Systems Engineering from the Ohio State University, Columbus, Ohio, USA. His interested areas include queueing theory, stochastic modeling.

Won Joo Seo

Won Joo Seo is currently a senior researcher at Hyundai Information Technology, Seoul, Korea. He received his B.S. degree at Department of Mathematics and Department of Industrial Engineering (Double major) from Sungkyunkwan University, Suwon, Korea, M.S. and Ph.D. degrees at Department of Industrial Engineering, Graduate School, Sungkyunkwan University, Suwon, Korea.

Se Won Lee

Se Won Lee is currently a research Professor at Department of Systems Management Engineering, Sungkyunkwan University, Suwon, Korea. He received his B.S. degree at Department of Industrial Engineering from Sungkyunkwan University, Suwon, Korea, M.S. and Ph.D. degrees at Department of Industrial Engineering, Graduate School, Sungkyunkwan University, Suwon, Korea. His interested areas include queueing theory, stochastic modeling.