In this paper, we introduce and analyze a new cut-off priority scheme which provides a better grade-of-service to hand-off traffic while maintaining high throughput for the originating calls. A hysteresis control is used for additional robustness. The system model is found to have a general level-dependent quasi-birth-and-death (QBD) structure. An efficient solution methodology is used taking full advantage of the problem structure. Our model extends, generalizes and unifies the existing models for cut-off priority schemes in wireless cellular networks.

In this paper we introduce a general class of level-dependent quasi-birth-and-death (QBD) processes and their stationary solution. We obtain the complete characterization of their fundamental matrices in terms of minimal non-negative solution of the number of matrix quadratic equations. Our results provides a mixed-geometric solution for the stationary solution of level-dependent chains. Applications in overload control in communication networks are also discussed.