Markov-modulated PH/G/1 queueing systems (Q811028)

The authors study a queue in which the arrival process and the service times depend on the state of an underlying Markov chain on a countable state space. The interarrival time has a phase type distribution, the service time is general, and, given the states of the Markov chain, independent of the arrival process. By using properties of Markov- additive processes, the authors derive the busy period process, waiting time and idle time, and then study the special case of a Markov-modulated \(E_ K/G/1\). All the proofs and techniques draw from a previous paper [Queueing Syst. 5, No.1-3, 215-245 (1989; Zbl 0694.60087)] and from \textit{G. J. K. Regterschot} and \textit{J. H. A. de Smit} [Math. Oper. Res. 11, 465-483 (1986; Zbl 0619.60093)].