Linganisha mbinu

	Uigaji wa Matukio Diskriti wa Kistohastiki	Mfumo wa Markov
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1960s–1970s	1906
Mwanzilishi	Banks, Carson, Nelson, Nicol; Law, A. M.	Andrei Markov
Aina	Stochastic simulation model	Probabilistic state-transition model
Chanzo asilia	Banks, J., Carson, J. S., Nelson, B. L., & Nicol, D. M. (2010). Discrete-Event System Simulation (5th ed.). Prentice Hall. ISBN: 9780136062127	Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. ISBN: 9780521633963
Majina mbadala	Stochastic DES, SDES, Probabilistic DES, Monte Carlo DES	Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process
Zinazohusiana	6	5
Muhtasari	Stochastic Discrete-Event Simulation (Stochastic DES) models complex systems by advancing simulated time from one discrete event to the next, drawing event durations and inter-arrival times from fitted probability distributions. It is the standard technique for analyzing queues, manufacturing lines, healthcare pathways, and logistics networks under uncertainty, producing output statistics with confidence intervals.	A Markov Model represents a system as a finite set of states and specifies the probability of moving from one state to another at each time step. By capturing only the current state — not the full history — it enables tractable analysis of complex dynamic processes across health economics, engineering reliability, operations research, and social-science modeling.