Linganisha mbinu

	Uigizaji wa Matukio Maalum (DES)	M/M/c Queue: Kielelezo cha Msongamano chenye Seva Nyingi
Nyanja	Uigaji	Utafiti wa Operesheni
Familia	Process / pipeline	Regression model
Mwaka wa asili	1960s (formalized); modern computational form from 1970s onward	1998
Mwanzilishi	Banks, Carson, Nelson & Nicol (textbook lineage); foundational work by Tocher & Conway (1960s)	Queueing-theory tradition; Gross & Harris
Aina	Stochastic process simulation	Multi-server Markovian queueing model
Chanzo asilia	Banks, J., Carson, J.S., Nelson, B.L. & Nicol, D.M. (2010). Discrete-Event System Simulation (5th ed.). Pearson. ISBN: 978-0136062127	Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9
Majina mbadala	DES, event-driven simulation, Ayrık Olay Simülasyonu (DES)	Multi-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu
Zinazohusiana	4	3
Muhtasari	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.	The M/M/c queue is a multi-server stochastic model in which customers arrive according to a Poisson process at rate λ, are served by c identical servers each with exponentially distributed service times at rate μ, and wait in a single common queue when all servers are busy. Systematized within classical queueing theory and thoroughly treated by Gross and Harris (1998), it extends the simpler M/M/1 model to settings with parallel servers, making it the foundational tool for capacity planning in service systems.