ABSTRACT
This chapter discusses the M/M/1 queue where the first "M" means "Poisson arrivals", and the second "M" means "service times". It treats other useful variants to develop techniques for modelling stochastic models using Level Crossing (LC): e.g., M/M/1 with service time depending on waiting time. The LC method focuses on sample-path rate balance across an arbitrary state-space level, because of the basic level crossing theorems state that sample-path downcrossing rates correspond to very simple mathematical expressions of the continuous part of the probability density function in the state space. The main advantage of LC is that it avoids a great deal of algebra in deriving integral equations for pdfs of r.v.s of interest, especially in complex models.
