Abstract
This paper exhibits a primer on the use of modern system reliability techniques on several important topologies of small-cell deployment in multi-tier dense cellular networks. We synthesize a network into several subnetworks and use outage probability as a performance metric to formulate the small-cell deployment problem in the Boolean domain by means of an indicator function. The methodology employed herein includes disjointness for logically added expressions, arriving at a probability ready expression, and a transformation to the probability domain on a one-to-one basis by replacing indicator Boolean variables by their expectations and replacing logical operations by their arithmetical counterparts. This work also presents a systematic procedure of computing several reliability metrics such as the useful redundancy region, mean-time-to-failure, importance measures of the links, and quantification of uncertainty in system reliability as a function of uncertainties in link reliabilities by considering both identical and non-identical link failures. Non-linear algorithms are also tested on the optimization problem that minimizes system unreliability. We contribute to the important issue of analyzing small-cell deployment by providing exact system reliability metrics and hence open a new frontier for software defined networks controllers.