New results on the single server queue with a batch markovian arrival process

David M. Lucantoni
1991 Communications in Statistics Stochastic Models  
The versatile Markovian point process was introduced by M. F. Neuts in 1979. This is a rich class of point processes which contains many familiar arrival process as very special cases. Recently, the Batch Markovian Arrival Process, a class of point processes which was subsequently shown tobe equivalent to Neuts' point process, has been studied using a more transparent notation. Recent results in the matrix-analytic approach to queueing theory have su.bstantially reduced the computational
more » ... ity of the algorithmic solution of single server queues with a general Markovian arrival process. We generalize these results to the single server queue with the batch arrival process and emphasize the resulting simplifications. Algorithms for the special cases of the PHIG/I and MMPPIGII queues are highlighted as these models are receiving renewed attention in the literature and the new algorithms proposed here are simpler than existing ones. In particular, the PHIG/I queue has additional structure which further enhances the efficiency of its algorithmic solution. Also, the two-state MMPPIGII queue, which has applications in communications modeling, has an extremely simple solution.
doi:10.1080/15326349108807174 fatcat:xona5d25yrdkdnc4k7nc4qx3xm