Linganisha mbinu

	Mfumo wa Markov wa Kistokastiki	Uigizaji wa Matukio Maalum (DES)
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1993	1960s (formalized); modern computational form from 1970s onward
Mwanzilishi	Markov, A. A. (probabilistic extension developed by Sonnenberg & Beck and others)	Banks, Carson, Nelson & Nicol (textbook lineage); foundational work by Tocher & Conway (1960s)
Aina	Probabilistic state-transition model with Monte Carlo uncertainty propagation	Stochastic process simulation
Chanzo asilia	Sonnenberg, F. A., & Beck, J. R. (1993). Markov models in medical decision making: A practical guide. Medical Decision Making, 13(4), 322–338.	Banks, J., Carson, J.S., Nelson, B.L. & Nicol, D.M. (2010). Discrete-Event System Simulation (5th ed.). Pearson. ISBN: 978-0136062127
Majina mbadala	Probabilistic Markov Model, Stochastic Markov Chain, SMM, Monte Carlo Markov Model	DES, event-driven simulation, Ayrık Olay Simülasyonu (DES)
Zinazohusiana	6	4
Muhtasari	A Stochastic Markov Model is a simulation technique that represents a system as a set of mutually exclusive health or decision states, moves a cohort (or individual agents) through those states using probabilistically sampled transition parameters, and aggregates outcomes across thousands of Monte Carlo iterations to produce full probability distributions over costs, outcomes, or rankings rather than single point estimates.	Discrete-Event Simulation (DES) is a computational modeling paradigm in which the state of a system changes only at a countable sequence of points in time — the events. Between events nothing changes, so the simulation clock jumps directly from one event to the next. Formalized through the foundational textbooks of Banks, Carson, Nelson and Nicol and of Law in the 1960s–2000s, DES has become the standard tool for analyzing queuing systems, healthcare patient flows, manufacturing lines, and logistics networks where entities move through resources over time.