Transient queue length and busy period of the BMAP/PH/1 queue
Abstract
We derive in this paper the transient queue length and the busy period distributions in the single server queue with phase-type (PH) services times and a batch Markovian arrival process (BMAP). These distributions are obtained by the uniformization technique which gives simple recurrence relations. The main advantage of this technique is that it leads to stable algorithms for which the precision of the result can be given in advance.