The impact of breakdowns disciplines and repeated attempts on performances of Small Cell Networks

This paper aims at presenting an approach to study performance and reliability of Small Cell Networks, taking into account the retrial phenomenon, the finite number of customers (mobiles) served in a cell and the random breakdowns of the base station channels. We consider the classical disciplines namely, active and dependent breakdowns and moreover we propose new breakdowns disciplines, in which we give to the interrupted customers due to a channel failure, a higher priority compared to other customers. To this end, we use the Generalized Stochastic Petri Nets (GSPNs) model as a support. However, one of the major drawbacks of this high-level formalism in performance evaluation of large networks is the state space explosion problem which increases when considering repeated calls and multiple unreliable channels. Hence, the novelty of this investigation is the presentation, for the different breakdowns disciplines with and without priority, of an approach which allows a direct computing of the infinitesimal generator describing the customers behavior and the channels allocation in as small cell, neither generating nor storing the reachability set. In addition, we develop the formulas of the main stationary performance and reliability indices, as a function of the network parameters, the stationary probabilities and independently of the reachability set markings. Through numerical examples, we discuss the effect of retrials, breakdowns disciplines and the priority on performances.