Optimal job splitting in parallel processor sharing queues

The main barrier to the sustained growth of wireless communications is the Shannon limit that applies to the channel capacity. A promising means to realize high-capacity enhancements is the use of multi-path communication solutions to improve reliability and network performance in areas that are covered by a multitude of overlapping wireless access networks. Despite the enormous potential for capacity enhancements offered by multi-path communication techniques, little is known about how to effectively exploit this. Motivated by this, we study a model where jobs are split and downloaded over N multiple parallel networks, each of which is modeled as a processor sharing (PS) queue. Each job is fragmented, according to a fixed splitting rule  and re-assembled at the receiving end. The complex correlation structure between the sojourn times at the PS nodes makes an exact detailed mathematical analysis of the model impossible. Therefore, in this paper we propose a simple and fast approximation for the splitting rule that minimizes the expected job-download time. Our approximation is validated extensively by simulations. The results show that the outcomes are extremely accurate over a wide range of parameter combinations.