Wireless 3-hop Networks with Stealing Revisited: A Kernel Approach

Abstract

Wireless multi-hop networks are an important type of networks, which have been studied in the literature by several researchers. For example, in a recent study, Guillemin et al. (2013) obtained exact tail asymptotics for the two stationary marginal distributions for wireless 3-hop networks with stealing based on boundary value problems. Efficient algorithms and good approximations for system performance could be derived based on this asymptotic property. However, it has been pointed out (see Fayolle and Iasnogorodski, 2014) that the key boundary value problem proposed in Guillemin et al. (2013) is incorrect, and an erratum by the authors has been published, Guillemin et al. (2014), with further details to appear in the near future. In this paper, we revisit this wireless 3-hop network with stealing. Using a different approach, the kernel method, we obtain exact tail asymptotics not only for the marginal distributions, but also for the joint distributions, which matches exactly with the results in Guillemin et al. (2013) (and Guillemin et al., 2011). Based on this result, impact of stealing can be clearly revealed.

Keywords:

• Wireless networks with stealing
• stationary distribution
• Kernel method
• exact tail asymptotics

Acknowledgments

The authors would like to thank the two referees for their helpful comments which result in the improvement of this work. This work was partially supported through NSERC Discovery grants, the Guangxi Natural Science Foundation (Nos. 2012GXNSFBA053010, 2014GXNSFCA118001) and the National Natural Science Foundation of China (No. 11361007).