Abstract
In this article, we consider the problem of load balancing (LB), but, unlike the approaches that have been proposed earlier, we attempt to resolve the problem in a fair manner (or rather, it would probably be more appropriate to describe it as an \epsilon -fair manner because, although the LB can, probably, never be totally fair, we achieve this by being "as close to fair as possible"). The solution that we propose invokes a novel stochastic learning automaton (LA) scheme, so as to attain a distribution of the load to a number of nodes, where the performance level at the different nodes is approximately equal and each user experiences approximately the same Quality of the Service (QoS) irrespective of which node that he/she is connected to. Since the load is dynamically varying, static resource allocation schemes are doomed to underperform. This is further relevant in cloud environments, where we need dynamic approaches because the available resources are unpredictable (or rather, uncertain) by virtue of the shared nature of the resource pool. Furthermore, we prove here that there is a coupling involving LA's probabilities and the dynamics of the rewards themselves, which renders the environments to be nonstationary. This leads to the emergence of the so-called property of "stochastic diminishing rewards." Our newly proposed novel LA algorithm \epsilon -optimally solves the problem, and this is done by resorting to a two-time-scale-based stochastic learning paradigm. As far as we know, the results presented here are of a pioneering sort, and we are unaware of any comparable results.