A ProcessorSharing model for the Performance of Virtualized Network Functions The parallel execution of requests in a Cloud Computing platform, as for Virtualized Network Functions, is modeled by an MXM1 ProcessorSharing (PS) system, where each request is seen as a batch of unit jobs. The performance of such paralleled system can then be measured by the quantiles of the batch sojourn time distribution. In this paper, we address the evaluation of this distribution for the MXM1PS queue with batch arrivals and geometrically distributed batch size. General results on the residual busy period (after a tagged batch arrival time) and the number of unit jobs served during this residual busy period are first derived. This enables us to provide an approximation for the distribution tail of the batch sojourn time whose accuracy is confirmed by simulation.

Evaluating Performance of Active Containers on PaaS Fog under Batch Arrivals: A Modeling Approach Modelbased performance evaluation of largescale PaaS Fog Datacenter requires to develop a hierarchical model, which is usually composed of a series of monolithic models. This paper proposes an approximate analytic modeling approach to evaluate the performance of a pool of active containers on a PaaS Fog physical node under batch task arrivals, by using an MmathrmxGmmK queue. We describe the details of the proposed model and the formulas for calculating performance measures of interest. Experiment results indicate that the proposed approach (including the model and the formulas) can approximately capture the system behaviors even when the task servicetime distribution has a large coefficient of variation (u003e1.5).