Partial Server Pooling in Redundancy Systems Partial sharing allows providers to possibly pool a fraction of their resources when full pooling is not beneficial to them. Recent work in systems without sharing has shown that redundancy can improve performance considerably. In this paper, we combine partial sharing and redundancy by developing partial sharing models for providers operating multiserver systems with redundancy. Two MMN queues with redundant service models are considered. Copies of an arriving job are placed in the queues of servers that can serve the job. Partial sharing models for canceloncomplete and cancelonstart redundancy models are developed. For canceloncomplete, it is shown that the Pareto efficient region is the full pooling configuration. For a cancelonstart policy, we conjecture that the Pareto frontier is always nonempty and is such that at least one of the two providers is sharing all of its resources. For this system, using bargaining theory the sharing configuration that the providers may use is determined. Mean response time and probability of waiting are the performance metrics considered.

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.