Fluid approximation of closed queueing networks with discriminatory processor sharing

As a multi-class variant of the classical egalitarian processor-sharing (EPS) discipline, discriminatory processor sharing (DPS) provides a suitable paradigm to model systems where share exists to control the service access of heterogeneous jobs. Although DPS is a more fine-grained scheduling discip...

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Bibliographic Details
Published in:Performance evaluation 2020-06, Vol.139, p.102094, Article 102094
Main Authors: Zhu, Lulai, Casale, Giuliano, Perez, Iker
Format: Article
Language:English
Subjects:
Closed queueing networks
Discriminatory processor sharing
Fluid approximation
Response time distributions
Transient and steady-state analysis
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Summary:As a multi-class variant of the classical egalitarian processor-sharing (EPS) discipline, discriminatory processor sharing (DPS) provides a suitable paradigm to model systems where share exists to control the service access of heterogeneous jobs. Although DPS is a more fine-grained scheduling discipline than EPS, the behavior of closed queueing networks (QNs) with DPS remains poorly understood. We propose in this paper a fluid approach to transient and steady-state analysis of closed QNs comprising delay and DPS stations. Our reference model features an arbitrary routing topology, phase-type service time distributions and class switching. The proposed approach has been validated against simulation for both transient and steady-state analysis. Moreover, we introduce a refined method for approximating response time distributions at either station or system level through transient analysis, showing its improvement upon prior art in handling non-exponentially distributed service times.
ISSN:0166-5316
1872-745X
DOI:10.1016/j.peva.2020.102094