Abstract

Call blocking probabilities (CBP) are a key index of quality of service assessment in multi-rate networks. We focus on the CBP calculation in single link loss models where calls of each service-class come from finite sources and compete for the available link bandwidth under the complete sharing policy. We review the Engset multi-rate loss model (EnMLM) and the single-retry loss model for finite sources (f-SRM) in which blocked calls of a service-class may immediately retry once, in order to be connected in the system, with reduced bandwidth and increased service time requirements. We extend the f-SRM to the multi-retry loss model for finite sources (f-MRM) to cover multiple retrials. Furthermore, we propose the single- and multi-threshold finite source models (f-STM, f-MTM) in which calls, prior to being blocked, may adjust their traffic requirements according to a common set of thresholds, which indicate the occupied link bandwidth. Moreover, we generalize the above-mentioned models with the connection-dependent threshold model for finite sources (f-CDTM), in which each service-class may have its own set of thresholds. The proposed models do not have a product form solution and therefore we resort to approximate but recursive formulas for the calculation of the link occupancy distribution, which is essential for the CBP calculation. The link occupancy distribution calculation is more complex than that in the corresponding infinite source models, since it requires enumeration and processing of the state space. To this end, we propose a new method for the state space determination, applicable to the proposed models. Furthermore, we present the f-CDTM for service-classes of a mixture of finite and infinite sources. Finally, we evaluate the models’ accuracy by comparing the analytical with simulation CBP results.

Keywords: Call blocking; Loss model; Finite population; Recurrent formula; Thresholds

Article Outline

1. Introduction

2. Review of the Engset multi-rate loss model and single-retry model for finite sources

2.1. The Engset multi-rate loss model (EnMLM) – the analytical model

2.1.1. State space determination – link occupancy distribution

2.2. The single-retry model for finite sources (f-SRM) – the analytical model

2.2.1. A new method for the state space determination and the calculation of the link occupancy distribution

3. The proposed multi-retry model for finite sources (f-MRM)

3.1. The multi-retry model for finite sources (f-MRM) – the analytical model

4. The proposed threshold models for finite sources

4.1. The single-threshold model for finite sources (f-STM) – the analytical model

4.1.1. A new method for the state space determination and the calculation of the link occupancy distribution

4.2. The multi-threshold model for finite sources (f-MTM) – the analytical model

4.3. The connection-dependent threshold model for finite sources (f-CDTM) – the analytical model

5. Generalization of the f-CDTM to service-classes with a mixture of finite and infinite sources

6. Numerical examples – evaluation

7. Conclusion

Acknowledgements

Appendix A. f-SRM – state space determination

Appendix B. f-STM – state space determination

References

Vitae

Part of this work appeared in the Proceedings of the First International Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks (HET-NETs’03), Ilkley, West Yorkshire, UK, July 21–23, 2003.