Consider an M/M/1 queue where the arrival intensity \(\lambda\) (t) and the service intensity \(\mu\) (t), \(t\geq 0\), are time-dependent. The methods used to obtain especially asymptotic results are operator analytic techniques and a uniform acceleration for the queue length process. The latter means to investigate a sequence of systems with parameters \(\lambda\) (t)/\(\epsilon\), \(\mu\) (t)/\(\epsilon\), resp., \(\epsilon\) \(\downarrow 0.\)
The author defines a time dependent traffic intensity which is used to investigate times of over-saturation and under-saturation of the queue.