Mathematics and Statistics Vol. 8(2), pp. 225 - 232
DOI: 10.13189/ms.2020.080219
Reprint (PDF) (267Kb)

Stochastic Decomposition Result of an Unreliable Queue with Two Types of Services

Gautam Choudhury ¹, Akhil Goswami ², Anjana Begum ^1,*, Hemanta Kumar Sarmah ^2
1 Mathematical Sciences Division, Institute of Advanced Study in Science and Technology(IASST), Paschim Boragaon, Guwahati 781035, Assam, India
² Department of Mathematics, Gauhati University, Assam, India

ABSTRACT

The single server queue with two types of heterogeneous services with generalized vacation for unreliable server have been extended to include several types of generalizations to which attentions has been paid by several researchers. One of the most important results which deals with such types of models is the “Stochastic Decomposition Result”, which allows the system behaviour to be analyzed by considering separately distribution of system (queue) size with no vacation and additional system (queue) size due to vacation. Our intention is to look into some sort of united approach to establish stochastic decomposition result for two types of general heterogeneous service queues with generalized vacations for unreliable server with delayed repair to include several types of generalizations. Our results are based on embedded Markov Chain technique which is considerably a most powerful and popular method wisely used in applied probability, specially in queueing theory. The fundamental idea behind this method is to simplify the description of state from two dimensional states to one dimensinal state space. Finally, the results that are derived is shown to include several types of generalizations of some existing well- known results for vacation models, that may lead to remarkable simplification while solving similar types of complex models.

KEYWORDS
Stochastic Decomposition, Heterogenous Service, Generalized Vacation, Markov Chain

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Gautam Choudhury , Akhil Goswami , Anjana Begum , Hemanta Kumar Sarmah , "Stochastic Decomposition Result of an Unreliable Queue with Two Types of Services," Mathematics and Statistics, Vol. 8, No. 2, pp. 225 - 232, 2020. DOI: 10.13189/ms.2020.080219.

(b). APA Format:
Gautam Choudhury , Akhil Goswami , Anjana Begum , Hemanta Kumar Sarmah (2020). Stochastic Decomposition Result of an Unreliable Queue with Two Types of Services. Mathematics and Statistics, 8(2), 225 - 232. DOI: 10.13189/ms.2020.080219.