On tandem blocking queues with a common retrial queue

K. Avrachenkov*, U. Yechiali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider systems of tandem blocking queues having a common retrial queue. The model represents dynamics of short TCP transfers in the Internet. Analytical results are available only for a specific example with two queues in tandem. We propose approximation procedures involving simple analytic expressions, based on mean value analysis (MVA) and on fixed point approach (FPA). The mean sojourn time of a job in the system and the mean number of visits to the orbit queue are estimated by the MVA which needs as an input the fractions of blocked jobs in the primary queues. The fractions of blocked jobs are estimated by FPA. Using a benchmark example of the system with two primary queues, we conclude that the approximation works well in the light traffic regime. We note that our approach becomes exact if the blocking probabilities are fixed. Finally, we consider two optimization problems regarding minimizing mean total sojourn time of a job in the system: (i) finding the best order of queues and (ii) allocating a given capacity among the primary queues.

Original languageEnglish
Pages (from-to)1174-1180
Number of pages7
JournalComputers and Operations Research
Volume37
Issue number7
DOIs
StatePublished - Jul 2010

Funding

FundersFunder number
Euro-NF Network of Excellence

    Keywords

    • Fixed point approach
    • Mean value analysis
    • Retrial networks

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