Nonasymptotic Multicast Throughput and Delay in Multihop Wireless Networks

Abstract

Previous works on multicast capacity mainly focus on deriving asymptotic order results in large-scale wireless networks. While they can explore the general scaling laws of throughput capacity, it is also of great interest for practical concern to predict the exact achievable throughput in networks with an arbitrary finite number of nodes. In this paper, we investigate the nonasymptotic throughput and delay of multihop wireless networks for multicast applications wherein for each source node, $k$ nodes are randomly selected as receivers. It is challenging for the exact performance analysis since multicast transmission has a dynamic nature due to the following factors: 1) random distribution of nodes; 2) bursty traffic arrivals; and 3) different timescales for transient analysis. To tackle the problem, we propose an explicit analytical model and develop a multicast routing scheme, which accounts for these aspects. With our proposed model, we derive lower bound (LB) and upper bound (UB) on nonasymptotic multicast throughput and delay using stochastic network calculus. We show that the performance results hold for all timescales and network sizes and are strongly correlated to data burstiness and the number of receivers. While we investigate from a nonasymptotic point of view, our results can also cover the asymptotic scaling laws. Simulations are conducted to further verify the accuracy of the analytical bounds.