On the extreme values of \(M/M/m\) queueing systems (Q2059046)

The paper under review considers a stationary and ergodic \(M/M/m\) queueing system. Let \(t_0=0, t_1, \dots\) be the arrival moments, and let \(W_n\) denote the waiting time of the \(n\)th arriving customer at the moment of arrival, \(W_0=0\). The author establishes asymptotic theorems for the probability distributions of the following characteristics: \(\overline{W}(t)=\sup_{0\leq t_k\leq t}W_k(s)\), \(\overline{W}_n=\overline{W}(t_n)=\max_{1\leq k\leq n}W_k\) as \(t\to\infty\) and \(n\to\infty\).