Describe the finite and infinite M/M/1 queuing models with examples and their waiting time distribution

The M/M/1 queuing model is a fundamental model in the study of stochastic processes and queueing theory. It describes a system with a single server where arrivals follow a Poisson process and service times are exponentially distributed. The notation “M/M/1” stands for: Markovian (Poisson) arrival process / Markovian (exponential) service process / 1 server. The model is characterized by two key parameters: λ (arrival rate) and μ (service rate).

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