Queueing Network Realization of an Epidemiological Model for Efficient Evaluation of Computer Transmitted Infections

Abstract This paper reexamines an epidemiological model with 4 population groups (vigilant/non-vigilant susceptible/infectious) built to study the effect of user vigilance on computer transmitted infections (CTIs) in computer networks. The model serves as an example through which a model conversion process is delineated, which aims at enhancing computational efficiency in the evaluation of the global prevalence of CTIs. More specifically, the conventional node-centric networked Markov chain (NCMC) is remodeled as a population-centric Markov chain (PCMC) to reduce the state-space size from an exponential to a polynomial function of the number of computing nodes N in a strongly connected network, where external attack and internal spread processes are aggregated. The PCMC is then realized as a closed queueing network of 4 M/M/N/N queueing nodes, corresponding to the 4 population groups. The results of evaluating the evolution of mean populations for the 4-population network of up to 150,000 computing nodes show that the queueing network realization slows the growth of computational complexity from exponential to linear with respect to the network size without resorting to mean field approximations. The paper briefly discusses on how the queueing network framework can accommodate node-centric Markov chains (NCMCs) of arbitrary directed networks of heterogeneous nodes, and its potential to significantly reduce the complexity in the evaluation of mean population dynamics for the more general class of large networks.