On busy period and sojourn time distributions in the M/G/1-EPS queue with catastrophes

We derive the Laplace-Stiltjes transforms of busy period and sojourn time distributions in the M/G/1 queue with egalitarian processor sharing (EPS) and the possibility of (external) catastrophes. Each arrival of the catastrophes immediately removes all the positive jobs (and hence unfinished work) in this non work-conserving queueing system. One of the main results is obtained by means of the so-called method of decomposition into delay elements introduced by the first author.