2009/10/15 by Young Myoung Ko, Ko, Young Myoung, Natarajan Gautam +1
Business, Management and Accounting · Decision Sciences · Mathematics · Social Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Transportation Planning and Optimization #math.PR
paper · pdf · doi:10.48550/arxiv.0910.2745
arxiv created 2009/10/15 · openalex publication_date 2009/10/15 · openalex created_date 2016/06/24 · arxiv updated 2016/09/08 · openalex updated_date 2026/07/28
In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be asymptotically exact, their effectiveness as approximations in the non-asymptotic regime needs to be investigated. We find that existing fluid and diffusion approximations might be either inaccurate under simplifying assumptions or computationally intractable. To address this concern, this paper focuses on developing a methodology based on adjusting the fluid model so that it provides exact mean queue lengths. Further, we provide a computationally tractable algorithm that exploits Gaussian density in order to obtain performance measures of the system. We illustrate the accuracy of our algorithm using a wide variety of numerical experiments.