Manuscript Title:

AN ANALYTICAL FRAMEWORK FOR TRI-CUM BISERIAL AND PARALLEL QUEUEING MODEL CONNECTED WITH A COMMON SERVER

Author:

SACHIN KUMAR AGRAWAL, VIPIN KUMAR, PRATOSH KUMAR AWASTHI

DOI Number:

DOI:10.5281/zenodo.16309072

Published : 2025-07-23

About the author(s)

1. SACHIN KUMAR AGRAWAL - Assistant Professor, Department of Applied Sciences & Humanities, Moradabad Institute of Technology, Moradabad, Uttar Pradesh, India.
2. VIPIN KUMAR - Associate Professor, Department of Mathematics, Teerthankar Mahaveer University, Moradabad, Uttar Pradesh, India.
3. PRATOSH KUMAR AWASTHI - Assistant Professor, Department of Applied Sciences & Humanities, Moradabad Institute of Technology, Moradabad, Uttar Pradesh, India.

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Abstract

In this study, a queuing framework has been formulated to examine key performance characteristics of a multi-server system. The proposed model features two service facility servers, each comprising three individual servers, which are subsequently allied to a mutual exit server in a succession configuration. The first service facility incorporates a tri-cum biserial arrangement of its three servers, while the second facility has its three servers configured in parallel. Both the arrival and service processes are modeled as Poisson distributions. Performance metrics such as queue lengths, variances, waiting times, & system possibilities have been derived by means of a combination of statistical methods, generating function techniques, and fundamental calculus principles. A detailed parametric analysis is also led to validate the usefulness and robustness of the proposed modeling tactic.


Keywords

Queuing Model, Mean Queue Length, Variance, Probability, Poisson Law.