Linganisha mbinu

	Uigaji wa Mfumo wa Msafara wa Stochastiki	Uigizaji wa Matukio Maalum (DES)
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1953	1960s (formalized); modern computational form from 1970s onward
Mwanzilishi	Kendall, D. G.	Banks, Carson, Nelson & Nicol (textbook lineage); foundational work by Tocher & Conway (1960s)
Aina	Stochastic simulation — waiting-line system analysis	Stochastic process simulation
Chanzo asilia	Kendall, D. G. (1953). Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. The Annals of Mathematical Statistics, 24(3), 338–354.	Banks, J., Carson, J.S., Nelson, B.L. & Nicol, D.M. (2010). Discrete-Event System Simulation (5th ed.). Pearson. ISBN: 978-0136062127
Majina mbadala	SQS, Probabilistic Queueing Simulation, Stochastic Queue Modeling, Random Queueing Simulation	DES, event-driven simulation, Ayrık Olay Simülasyonu (DES)
Zinazohusiana	6	4
Muhtasari	Stochastic Queueing Simulation models waiting-line systems where arrival and service processes follow probability distributions rather than fixed rates. By simulating thousands of random events, it estimates performance measures — mean waiting time, queue length, server utilization — under realistic uncertainty, making it the standard tool for designing and evaluating service systems from hospitals to call centers.	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.