Sojourn times in fluid queues with independent and dependent input and output processes

Gábor Horváth, M. Telek

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Markov Fluid Queues (MFQs) are the continuous counterparts of quasi birth-death processes, where infinitesimally small jobs (fluid drops) are arriving and are being served according to rates modulated by a continuous time Markov chain. The fluid drops are served according to the First-Come-First- Served (FCFS) discipline. The queue length process of MFQs can be analyzed by efficient numerical methods developed for Markovian fluid models. In this paper, however, we are focusing on the sojourn time distribution of the fluid drops. In the first part of the paper we derive the phase-type representation of the sojourn time when the input and output processes of the queue are dependent. In the second part we investigate the case when the input and output processes are independent. Based on the age process analysis of the fluid drops, we provide smaller phase-type representations for the sojourn time than the one for dependent input and output processes.

Original languageEnglish
Pages (from-to)160-181
Number of pages22
JournalPerformance Evaluation
Volume79
DOIs
Publication statusPublished - 2014

Fingerprint

Fluid Queue
Sojourn Time
Fluids
Dependent
Output
Fluid
Representation Type
Birth-death Process
Continuous-time Markov Chain
Queue Length
Fluid Model
Queue
Numerical Methods
Markov processes
Numerical methods

Keywords

  • Age process
  • Markov fluid model
  • Phase type representation

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Software
  • Modelling and Simulation

Cite this

Sojourn times in fluid queues with independent and dependent input and output processes. / Horváth, Gábor; Telek, M.

In: Performance Evaluation, Vol. 79, 2014, p. 160-181.

Research output: Contribution to journalArticle

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