First passage times: Busy periods and waiting times (Q1906588)

The authors consider a Markov process on the state space \(E = \{(i,j); i \geq 0, 1 \leq j \leq m\}\). The set of states \(\{(i,j); 1 \leq j \leq m\}\) is called the level \(i\), \(i \geq 0\). Denote by \(\tau\) the first passage time to level 0. The authors give a formula for Laplace transform of \(\tau\) and study computation problems for busy periods and waiting times for queues corresponding to Markov processes.