Generating Optimal Thresholds in a Hysteresis Queue: Application to a Cloud Model

Reducing the energy consumption of a cloud system while guaranteeing a given quality of service level is a crucial problem encountered today by cloud providers. We consider an auto-scaling model where virtual machines are turned on and off depending on the queue's occupation (or thresholds). This model represents the variability of allocated resources (Virtual Machines or VMs) according to user demands. It can be studied using an hysteresis queuing model, which is represented by a multidimensional Markov chain, whose calculation of the stationary distribution becomes complex when the number of VMs grows. We adopt a cost-aware approach and define a mean cost computed as a reward function on the stationary distribution. This cost takes into account both the performance (for Service Level Agreement: SLA) and the use of the resources (for Energy). We propose efficient optimisation methods to find threshold values minimising the global cost. Because this mean cost is a non-convex function, the research of the optimal value is complex. We propose different optimisation methods: the first one, based on heuristics, coupled with aggregation of the Markov Chain to reduce the execution time and the second one which is a meta heuristic: the Simulated Annealing. Finally, we present a real case of a cloud system that we model and set parameter values to test our optimisation algorithms and show their relevance.