ASIP tandem queues with consumption

Yaron Yeger*, Onno Boxma, Jacques Resing, Maria Vlasiou

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

The Asymmetric Inclusion Process (ASIP) tandem queue is a model of stations in series with a gate after each station. At a gate opening, all customers in that station instantaneously move to the next station unidirectionally. In our study, we enhance the ASIP model by introducing the capability for individual customers to independently move from one station to the next, and by allowing both individual customers and batches of customers from any station to exit the system. The model is inspired by the process by which macromolecules are transported within cells. We present a comprehensive analysis of various aspects of the queue length in the ASIP tandem model. Specifically, we provide an exact analysis of queue length moments and correlations and, under certain circumstances, of the queue length distribution. Furthermore, we propose an approximation for the joint queue length distribution. This approximation is derived using three different approaches, one of which employs the concept of the replica mean-field limit. Among other results, our analysis offers insight into the extent to which nutrients can support the survival of a cell.

Original languageEnglish
Article number102380
JournalPerformance evaluation
Volume163
DOIs
Publication statusPublished - Jan 2024

Keywords

  • Asymmetric Inclusion Process (ASIP)
  • Replica mean-field limit
  • Vesicular transport hypothesis

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