Heavy-traffic limits for Discriminatory Processor Sharing models with joint batch arrivals

P. Vis, R. Bekker, R. D. van der Mei*, R. Núñez-Queija

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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Abstract

We study the performance of Discriminatory Processor Sharing (DPS) systems, with exponential service times and in which batches of customers of different types may arrive simultaneously according to a Poisson process. We show that the stationary joint queue-length distribution exhibits state-space collapse in heavy traffic: as the load ρ tends to 1, the scaled joint queue-length vector (1−ρ)Q converges in distribution to the product of a deterministic vector and an exponentially distributed random variable, with known parameters. The result provides new insights into the behavior of DPS systems. It shows how the queue-length distribution depends on the system parameters, and in particular, on the simultaneity of the arrivals. The result also suggests simple and fast approximations for the tail probabilities and the moments of the queue lengths in stable DPS systems, capturing the impact of the correlation structure in the arrival processes. Numerical experiments indicate that the approximations are accurate for medium and heavily loaded systems.

Original languageEnglish
Pages (from-to)136-141
Number of pages6
JournalOperations Research Letters
Volume48
Issue number2
Early online date31 Jan 2020
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • Batch arrivals
  • Discriminatory Processor Sharing
  • Heavy traffic
  • Joint queue-length distribution

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