International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

A Widely Indexed Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

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Mathematical Modeling of Rare Events in Queueing Theory: Comparative Evaluation of Classical and Retrial Systems

Author(s) Padmapriya V.K, Dr. Sandeep Sharma
Country India
Abstract This paper provides a comprehensive examination of rare-event phenomena in queueing theory through a comparative evaluation of classical and retrial systems. Rare events, characterized by their low probability yet high impact, often manifest as excessive waiting times, service congestion, or system overloads. The study integrates analytical modeling and simulation-based approaches to analyze these phenomena, using frameworks grounded in stochastic processes, large deviation theory, and Markovian formulations. The research further explores the dynamics introduced by retrial systems, where customers reattempt service after finding servers busy—a feature that fundamentally alters system stability and rare-event probability structures. Through mathematical derivations and empirical validation, the study demonstrates that while classical queueing systems provide analytical tractability, retrial systems offer greater resilience under high-load conditions due to self-regulating feedback mechanisms. Advanced simulation methods, such as importance sampling, splitting, and cross-entropy techniques, are employed to estimate rare-event probabilities efficiently. The findings highlight that retrial systems can distribute congestion over time, thereby mitigating system failure risks. These insights have substantial implications for designing reliable communication networks, computer systems, and service infrastructures.
Published In Volume 6, Issue 4, July-August 2024
Published On 2024-07-09
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E-ISSN 2582-2160
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