Time to reach buffer capacity in a BMAP queue

In this paper a detailed study is presented on the first time to reach buffer capacity in a queue with batch arrivals and general service time distribution. A flexible analytical model of the input stream, which is the Batch Markovian Arrival Process (BMAP), is assumed. The results include the explicit formula for the Laplace transform of the distribution of the first buffer overflow time and discussion of its computational aspects. In addition, the popular special case of the BMAP queue, which is the batch Poisson arrival queue, is studied. Theoretical results are illustrated via numerical calculations based on IP traffic data.