Time to Reach Buffer Capacity in a BMAP Queue

Abstract

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.

Keywords:

• Buffer overflow time
• BMAP/G/1/b queue
• Transient analysis

Mathematics Subject Classification:

• 68M20
• 90B22
• 60K25

ACKNOWLEDGMENTS

This material is based upon work supported by the Polish Ministry of Scientific Research and Information Technology under Grant No. 3 T11C 014 26.