Analysis of a Single Server Queueing System Controlled by a Random Switch

Authors

  • Akshaya Ramesh Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamilnadu 600062, India
  • S. Udayabaskaran Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamilnadu 600062, India https://orcid.org/0000-0001-9056-0148

DOI:

https://doi.org/10.37256/cm.4220232123

Keywords:

single server queue, doubly stochastic environment, exhaustive service, random switch/set up time

Abstract

In this paper, a single server queueing system operating in a doubly stochastic environment is analysed. The random environment makes transitions among N levels controlled by a random switch which performs the task of assigning a job to the server. The queueing system resides in level k of the environment till the completion of the service of the last customer in the system and immediately reports to the random switch to get a new service job. The random switch generates a set up time and waits till a customer arrives and assigns a job to the server in any one of the N levels with a positive probability governed by a binomial distribution. In each level r of the environment, the queueing system behaves like M(λr)/M(μr)/1 queue subject to the condition that the server reports to the random switch immediately after performing exhaustive service for getting a new assignment. For this model, time-dependent state probabilities are explicitly found and the corresponding steady-state probabilities are deduced. Some key performance measures are also obtained. A numerical study is also made.

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Published

2023-03-30

How to Cite

1.
Ramesh A, Udayabaskaran S. Analysis of a Single Server Queueing System Controlled by a Random Switch. Contemp. Math. [Internet]. 2023 Mar. 30 [cited 2024 Mar. 4];4(2):189-201. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2123