Asymptotic study of a busy period in a retrial queue

In this work, we propose two approaches to study the convergence in distribution of the busy period of the M/G/1 retrial queue. The first approach rely on the modeling of Artalejo and Falin (1996) and an invariance principle for independent random variables. In the second one, we use the evolution of the system in terms of idle periods and busy periods of the server and we conclude too with an Holderian invariance principle.