Network-Layer Performance Analysis of Multihop Fading Channels

A fundamental problem for the delay and backlog analysis across multihop paths in wireless networks is how to account for the random properties of the wireless channel. Since the usual statistical models for radio signals in a propagation environment do not lend themselves easily to a description of the available service rate, the performance analysis of wireless networks has resorted to higher-layer abstractions, e. g., using Markov chain models. In this paper, we propose a network calculus that can incorporate common statistical models of fading channels and obtain statistical bounds on delay and backlog across multiple nodes. We conduct the analysis in a transfer domain, where the service process at a link is characterized by the instantaneous signal-to-noise ratio at the receiver. We discover that, in the transfer domain, the network model is governed by a dioid algebra, which we refer to as the algebra. Using this algebra, we derive the desired delay and backlog bounds. Using arguments from large deviations theory, we show that the bounds are asymptotically tight. An application of the analysis is demonstrated for a multihop network of Rayleigh fading channels with cross traffic at each hop.