2019/04/11 by Fabrice Guillemin, Guillemin, Fabrice, Veronica Quintuna Rodriguez +3
Business, Management and Accounting · Computer Science · Mathematics · #68M20 #Advanced Queuing Theory Analysis #Algorithm #Batch processing #Cloud Computing and Resource Management #Cloud computing #Computer network #Computer science #Distributed computing #Distribution (mathematics) #Execution time #FOS: Computer and information sciences #Interconnection Networks and Systems #Mathematics #Operating system #Parallel computing #Performance (cs.PF) #Processor sharing #Queue #Real-time computing #Residual #cs.PF #msc:68M20
paper · pdf · doi:10.48550/arxiv.1904.05615
published in arXiv (Cornell University) (Cornell University) · Submitted for publication
arxiv created 2019/04/11 · arxiv updated 2019/04/12
The parallel execution of requests in a Cloud Computing platform, as for\nVirtualized Network Functions, is modeled by an M[X]/M/1 Processor-Sharing\n(PS) system, where each request is seen as a batch of unit jobs. The\nperformance of such paralleled system can then be measured by the quantiles of\nthe batch sojourn time distribution. In this paper, we address the evaluation\nof this distribution for the M[X]/M/1-PS queue with batch arrivals and\ngeometrically distributed batch size. General results on the residual busy\nperiod (after a tagged batch arrival time) and the number of unit jobs served\nduring this residual busy period are first derived. This enables us to provide\nan approximation for the distribution tail of the batch sojourn time whose\naccuracy is confirmed by simulation.\n