Studying pensions funds through an infinite servers nodes network: A theoretical problem

Abstract

This study intends to present a representation of a pensions fund through a stochastic network with two infinite servers nodes. With this representation it is allowed to deduce an equilibrium condition of the system with basis on the identity of the random rates expected values, for which the contributions arrive to the fund and the pensions are paid by the fund. In our study a stochastic network is constructed where traffic is represented. This network allows to study the equilibrium in the system and it is admissible to get a balance to a pensions fund. A specific case is studied. When the arrivals from outside at nodes A and B are according to a Poisson process, with rates λA and λB, respectively, the system may be seen as a two nodes network where the first node is a M/G/∞ queue and second a Mt/G/∞ queue. For this case in the long term the conditions of equilibrium are as follows: mAλAαA = mB(ρλA + λB)αB. In this formula it is established a relationship among the two nodes. Several examples are given in the study.