Paper ID:
IJSDIP_January 2025_VOLUME 13_ISSUE 1_77-82
Author's Name:
Dr.B.Sainath, Dr.U Nagi Reddy, Dr Y Raghunatha Reddy
Volume:
13
Issue:
Issue 1
Year:
2025
Pages:
77-82
Abstract
Markov chain models provide a compact mathematical framework for forecasting systems whose future state depends probabilistically on their current state. This article examines their role in stochastic-process forecasting and decision support through a focused review and a reproducible three-state numerical study. The illustrative system represents low, moderate, and high demand regimes with a time-homogeneous transition matrix estimated from controlled transition counts. Starting from probabilities (0.20, 0.50, 0.30), multi-step forecasts converge toward a stationary distribution of approximately (0.313, 0.441, 0.246). The expected demand index declines from 2.10 initially to 1.934 after twelve steps, showing how transient conditions settle toward long-run behavior. A Markov reward analysis further compares conservative, balanced, aggressive, and state-contingent actions. Over twelve periods, the state-contingent rule yields an illustrative cumulative expected reward of 128.67 units, compared with 96.07 for the best fixed balanced action. These calculations demonstrate how transition probabilities convert uncertainty into explicit forecasts and how forecasts can be linked to policy choice. Applications are discussed in inventory planning, credit migration, reliability, healthcare, customer behavior, energy, and queueing systems. The study also emphasizes limitations involving the first-order assumption, non-stationarity, state definition, sparse transitions, and estimation uncertainty. Markov chains are most valuable when their assumptions are tested, forecasts are updated, and decisions are evaluated against operational costs.
Keywords
Markov chain, stochastic processes, transition matrix, forecasting, stationary distribution, Markov reward model, decision-making systems.
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