2021/04/19 by Fabrice Guillemin, Alain Simonian, Guillemin, Fabrice +5
Business, Management and Accounting · Computer Science · #68M20 #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #FOS: Mathematics #Interconnection Networks and Systems #Network Traffic and Congestion Control #Performance (cs.PF) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2104.09273
openalex publication_date 2021/04/19 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28
In this paper, we exploit results obtained in an earlier study for the Laplace transform of the sojourn time Ω of an entire batch in the M[X]/M/1 Processor Sharing (PS) queue in order to derive the asymptotic behavior of the complementary probability distribution function of this random variable, namely the behavior of P(Ω>x) when x tends to infinity. We precisely show that up to a multiplying factor, the behavior of P(Ω>x) for large x is of the same order of magnitude as P(ω>x), where ω is the sojourn time of an arbitrary job is the system. From a practical point of view, this means that if a system has to be dimensioned to guarantee processing time for jobs then the system can also guarantee processing times for entire batches by introducing a marginal amount of processing capacity.