Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment

2014/05/19 by Eleni Vatamidou, Vatamidou, Eleni, Ivo Adan +7
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Simulation Techniques and Applications #math.PR

paper · pdf · doi:10.48550/arxiv.1405.4853

Full version (including Appendices) of the paper to be published at a Special Issue of Stochastic Models (Issue 30.4). arXiv admin note: substantial text overlap with arXiv:1405.0138

arxiv created 2014/05/19 · openalex publication_date 2014/05/19 · arxiv updated 2014/05/21 · openalex created_date 2019/01/01 · openalex updated_date 2026/07/28

Abstract

We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples.

Citations

• Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment

Related

• Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment
• Uniform Approximations for the M/G/1 Queue with Subexponential Processing Times
• Heavy-traffic analysis of the M^X/semi-Markov/1 queue
• Heavy-tailed queues in the Halfin-Whitt regime
• Delay Stability Regions of the Max-Weight Policy under Heavy-Tailed Traffic