A Mean-Value Analysis of Stochastic Petri Net Models of Slotted Rings

Andrew Coyle, Boudewijn R.H.M. Haverkort, William Henderson, Charles E.M. Pearce

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper, we analyse Stochastic Petri Net (SPN) models of slotted-ring networks. We show that a simple SPN model of a slotted-ring network, which exhibits a product-form solution, yields similar results to a more detailed SPN model that has to be analysed by numerical means. Furthermore, we demonstrate a Mean-Value Analysis (MVA) approach to calculate efficiently the results for the simple model. This MVA approach allows for the movement of groups of tokens (customers) rather than just individual customers, as traditional MVA schemes for queueing network models do. Also, the MVA allows for non-disjoint place invariants, whereas previous MVA schemes addressed disjoint place invariants only. From the MVAs, it can be concluded that slotted-rings have very attractive performance characteristics, even under overload conditions (there is no ldquothrashingrdquo). Also, we found that the choice of the slot size is a key factor in calibrating slotted-ring systems for optimal performance. Having a fast and reasonably accurate means available to evaluate the performance of slotted-ring systems, such as our proposed MVA, eases this calibration task. The proposed MVA for the product-form SPN models should therefore be regarded as a ldquoquick engineeringrdquo tool.
Original languageEnglish
Pages (from-to)203-227
Number of pages25
JournalTelecommunication systems
Volume6
Issue number2
DOIs
Publication statusPublished - 1996
Externally publishedYes

Fingerprint

Value engineering
Petri nets
Queueing networks
Calibration

Keywords

  • EWI-7879
  • IR-66560

Cite this

Coyle, Andrew ; Haverkort, Boudewijn R.H.M. ; Henderson, William ; Pearce, Charles E.M. / A Mean-Value Analysis of Stochastic Petri Net Models of Slotted Rings. In: Telecommunication systems. 1996 ; Vol. 6, No. 2. pp. 203-227.
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title = "A Mean-Value Analysis of Stochastic Petri Net Models of Slotted Rings",
abstract = "In this paper, we analyse Stochastic Petri Net (SPN) models of slotted-ring networks. We show that a simple SPN model of a slotted-ring network, which exhibits a product-form solution, yields similar results to a more detailed SPN model that has to be analysed by numerical means. Furthermore, we demonstrate a Mean-Value Analysis (MVA) approach to calculate efficiently the results for the simple model. This MVA approach allows for the movement of groups of tokens (customers) rather than just individual customers, as traditional MVA schemes for queueing network models do. Also, the MVA allows for non-disjoint place invariants, whereas previous MVA schemes addressed disjoint place invariants only. From the MVAs, it can be concluded that slotted-rings have very attractive performance characteristics, even under overload conditions (there is no ldquothrashingrdquo). Also, we found that the choice of the slot size is a key factor in calibrating slotted-ring systems for optimal performance. Having a fast and reasonably accurate means available to evaluate the performance of slotted-ring systems, such as our proposed MVA, eases this calibration task. The proposed MVA for the product-form SPN models should therefore be regarded as a ldquoquick engineeringrdquo tool.",
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author = "Andrew Coyle and Haverkort, {Boudewijn R.H.M.} and William Henderson and Pearce, {Charles E.M.}",
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A Mean-Value Analysis of Stochastic Petri Net Models of Slotted Rings. / Coyle, Andrew; Haverkort, Boudewijn R.H.M.; Henderson, William; Pearce, Charles E.M.

In: Telecommunication systems, Vol. 6, No. 2, 1996, p. 203-227.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A Mean-Value Analysis of Stochastic Petri Net Models of Slotted Rings

AU - Coyle, Andrew

AU - Haverkort, Boudewijn R.H.M.

AU - Henderson, William

AU - Pearce, Charles E.M.

N1 - Imported from research group DACS (ID number 441) M1 - 10.1007/BF02114294

PY - 1996

Y1 - 1996

N2 - In this paper, we analyse Stochastic Petri Net (SPN) models of slotted-ring networks. We show that a simple SPN model of a slotted-ring network, which exhibits a product-form solution, yields similar results to a more detailed SPN model that has to be analysed by numerical means. Furthermore, we demonstrate a Mean-Value Analysis (MVA) approach to calculate efficiently the results for the simple model. This MVA approach allows for the movement of groups of tokens (customers) rather than just individual customers, as traditional MVA schemes for queueing network models do. Also, the MVA allows for non-disjoint place invariants, whereas previous MVA schemes addressed disjoint place invariants only. From the MVAs, it can be concluded that slotted-rings have very attractive performance characteristics, even under overload conditions (there is no ldquothrashingrdquo). Also, we found that the choice of the slot size is a key factor in calibrating slotted-ring systems for optimal performance. Having a fast and reasonably accurate means available to evaluate the performance of slotted-ring systems, such as our proposed MVA, eases this calibration task. The proposed MVA for the product-form SPN models should therefore be regarded as a ldquoquick engineeringrdquo tool.

AB - In this paper, we analyse Stochastic Petri Net (SPN) models of slotted-ring networks. We show that a simple SPN model of a slotted-ring network, which exhibits a product-form solution, yields similar results to a more detailed SPN model that has to be analysed by numerical means. Furthermore, we demonstrate a Mean-Value Analysis (MVA) approach to calculate efficiently the results for the simple model. This MVA approach allows for the movement of groups of tokens (customers) rather than just individual customers, as traditional MVA schemes for queueing network models do. Also, the MVA allows for non-disjoint place invariants, whereas previous MVA schemes addressed disjoint place invariants only. From the MVAs, it can be concluded that slotted-rings have very attractive performance characteristics, even under overload conditions (there is no ldquothrashingrdquo). Also, we found that the choice of the slot size is a key factor in calibrating slotted-ring systems for optimal performance. Having a fast and reasonably accurate means available to evaluate the performance of slotted-ring systems, such as our proposed MVA, eases this calibration task. The proposed MVA for the product-form SPN models should therefore be regarded as a ldquoquick engineeringrdquo tool.

KW - EWI-7879

KW - IR-66560

U2 - 10.1007/BF02114294

DO - 10.1007/BF02114294

M3 - Article

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SP - 203

EP - 227

JO - Telecommunication systems

JF - Telecommunication systems

SN - 1018-4864

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ER -