On an M/G/1 quorum queueing system under T-policy

Abstract

We study in this paper an M/G/1 quorum queueing system under T-policy. First, we consider the system size stochastic process embedded at departure epoch times and show that it is an ergodic Markov chain. Then, we consider the system size stochastic process at arbitrary instants of time and show that it is an ergodic semi-regenerative process. We derive the steady-state distribution for both processes. Various system characteristics of related processes (idle and busy periods) are also obtained and special cases are discussed.

Keywords:

• queue
• quorum
• T-policy
• embedded Markov chain
• semi-regenerative process
• steady-state distribution
• AMS Subject Classification:
• primary 60K10;
• 60K25;
• secondary 90B22;
• 90B25

Acknowledgements

I thank an anonymous referee for bringing to my attention reference 11, for correcting numerous mistakes, and for making many suggestions that greatly enhanced the readability and quality of the paper.