The transient BMAP\(/G/1\) queue. (English) Zbl 0801.60083

Authors’ abstract: We derive the two-dimensional transforms of the transient workload and queue-length distributions in the single-server queue with general service times and a batch Markovian arrival process (BMAP). This arrival process includes the familiar phase-type renewal process and the Markov modulated Poisson process as special cases, as well as superpositions of these processes, and allows correlated interarrival times and batch sizes. Numerical results are obtained via two-dimensional transform inversion algorithms based on the Fourier- series method. From the numerical examples we see that predictions of system performance based on transient and stationary performance measures can be quite different.


60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
Full Text: DOI