Mathematics and Statistics Vol. 11(2), pp. 315 - 324
DOI: 10.13189/ms.2023.110210
Reprint (PDF) (320Kb)

Performance Analysis of A Single Server Queue Operating in A Random Environment - A Novel Approach

Akshaya Ramesh , S. Udayabaskaran ^*
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, India

ABSTRACT

In this paper, we consider a single server queueing system operating in a random environment subject to disaster, repair and customer impatience. The random environment resides in any one of N + 1 phases 0, 1, 2, · · · ,N + 1. The queueing system resides in phase k, k = 1, 2, · · · ,N for a random interval of time and the sojourn period ends at the occurrence of a disaster. The sojourn period is exponentially distributed with mean . At the end of the sojourn period, all customers in the system are washed out, the server goes for repair/set up and the system moves to phase 0. During the repair time, customers join the system, become impatient and leave the system. The impatience time is exponentially distributed with mean . Immediately after the repair, the server is ready for offering service in phase i with probability , k = 1, 2, · · · ,N. In the k−level of the environment, customers arrive according to a Poisson process with rate and the service time is exponential with mean . Explicit expressions for time-dependent state probabilities are found and the corresponding steady-state probabilities are deduced. Some new performance measures are also obtained. Choosing arbitrary values of the parameters subject to the stability condition, the behaviour of the system is examined. For the chosen values of the parameters, the performance measures indicated that the system did not exhibit much deviation by the presence of several phases of the environment.

KEYWORDS
Single Server Queue, Random Environment, Disasters, Repair/set up, Impatience

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Akshaya Ramesh , S. Udayabaskaran , "Performance Analysis of A Single Server Queue Operating in A Random Environment - A Novel Approach," Mathematics and Statistics, Vol. 11, No. 2, pp. 315 - 324, 2023. DOI: 10.13189/ms.2023.110210.

(b). APA Format:
Akshaya Ramesh , S. Udayabaskaran (2023). Performance Analysis of A Single Server Queue Operating in A Random Environment - A Novel Approach. Mathematics and Statistics, 11(2), 315 - 324. DOI: 10.13189/ms.2023.110210.