Improving the Mean-Field Fluid Model of Processor Sharing Queueing Networks for Dynamic Performance Models in Cloud Computing

Abstract

Resource management in cloud computing is a difficult problem, as one needs to balance between adequate service to clients and cost minimization in a dynamic environment of interconnected components. To make correct decisions in such an environment, good performance models are necessary. A common modeling methodology is to use networks of queues, but as these are prohibitively expensive to evaluate for many applications, approximation methods for key metrics are frequently employed. One such method-that provides both transient solutions and short, scalable computation times-is the fluid model, which approximates the dynamics of the mean queue lengths using a system of ordinary differential equations. However, finding a fluid model that can adequately approximate an arbitrary queueing network is in general difficult. In the paper, we extend the state of the art with the following three contributions. First, we show that for any mixed multiclass queueing network of processor sharing and delay queues with phase-type service time distributions, such a fluid model can be found via the meanfield approximation. Furthermore, we propose an improved model based on smoothing of the processor share function that improves the performance of certain systems. Finally, using the smoothed mean-field model, we introduce an accurate closed-form approximation of the response time CDF over any subset of classes and queues.