From Classical to Retrial Systems: A Unified View of Large Deviations in Queueing Theory

Author(s)	Padmapriya V.K, Dr. Sandeep Sharma
Country	India
Abstract	Queueing theory, a vital branch of applied probability and stochastic processes, provides mathematical tools for analyzing service systems where entities compete for limited resources. Among its extensions, the study of large deviations serves as a fundamental mechanism to quantify the exponential decay of probabilities associated with rare events in such systems. This paper presents a unified mathematical framework for examining large deviations in both classical and retrial queueing models. The analysis begins with classical queueing models, particularly the M/M/1 and M/G/1 systems, whose steady-state behavior is governed by Markovian processes. The study then extends to retrial queueing systems, where arriving customers who encounter a busy server join an orbit and attempt service again after a random time interval. The presence of retrials introduces non-Markovian dynamics and a new layer of complexity in the system’s probabilistic structure.
Published In	Volume 6, Issue 1, January-February 2024
Published On	2024-01-05

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