### Journals Information

Mathematics and Statistics Vol. 10(5), pp. 981 - 987
DOI: 10.13189/ms.2022.100509
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## Mathematical Analysis of Priority Bi-serial Queue Network Model

Deepak Gupta 1, Aarti Saini 1,*, A.K.Tripathi 2
1 Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), India
2 Mathematics Department, MMDU, India

ABSTRACT

One of the most comprehensive theories of stochastic models is queueing theory. Through innovative analytical research with broad applicability, advanced theoretical models are being developed. In the present research, we would like to investigate at a queuing network model with low and high priority users and different server transition probabilities. The two service channels used in this study, and , are connected to the same server, . Customers with low and high priorities are invited by the server . The objective of the research is to design a model that helps in minimizing congestion in different systems. Poisson distribution is used to characterize both the arrival and service patterns. The functioning of this system takes place in a stochastic domain. The differential difference equations have been established, and the consistency of behaviour of the system has been examined. The generating function approach, the law of calculus, and a statistical formula are used to assess the model's performance. Numerical analyses and graphical presentations are used to show the model's outcomes. The results of the model are displayed graphically and through numerical analyses. This model can be used in a number of real situations, including administration, manufacturing, hospitals, banking systems, etc. In such situations, the present study is quite beneficial for understanding the system and redesigning it.

KEYWORDS
Priority, Bi-series Channel, Graphical Analyze, Queue Length, Stochastic Environment

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Deepak Gupta , Aarti Saini , A.K.Tripathi , "Mathematical Analysis of Priority Bi-serial Queue Network Model," Mathematics and Statistics, Vol. 10, No. 5, pp. 981 - 987, 2022. DOI: 10.13189/ms.2022.100509.

(b). APA Format:
Deepak Gupta , Aarti Saini , A.K.Tripathi (2022). Mathematical Analysis of Priority Bi-serial Queue Network Model. Mathematics and Statistics, 10(5), 981 - 987. DOI: 10.13189/ms.2022.100509.