Abstract
In this work, we use the strong stability method to study the batch arrival queue after a perturbation of the batch size distribution. We show that, under some hypotheses, the characteristics of the batch arrival queueing system M X /M/1 may be approximated by the correspondent characteristics of the system M Geo /M/1.
After clarifying the conditions of approximation, we obtain stability inequalities with an exact computation of constants.
Acknowledgments
The authors thank the editor and the referees for their contributions.