Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes

Lucia Cloth; Henrik Bohnenkamp; Boudewijn Haverkort

doi:10.1007/3-540-44804-7_10

Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes

Lucia Cloth, Henrik Bohnenkamp, Boudewijn Haverkort

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an elegant notation for stochastic prefixes not containing any decisions. Furthermore, they allow for the computation of performance measures. The derivation of the so called k-th occurrence times is shown in detail.

Original language	English
Title of host publication	Process Algebra and Probabilistic Methods. Performance Modelling and Verification
Subtitle of host publication	Joint International Workshop, PAPM-PROBMIV 2001, Aachen, Germany, September 12-14, 2001. Proceedings
Editors	Luca de Alfaro, Stephen Gilmore
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	152-167
Number of pages	16
ISBN (Electronic)	978-3-540-44804-4
ISBN (Print)	978-3-540-42556-4
DOIs	https://doi.org/10.1007/3-540-44804-7_10
Publication status	Published - 2001
Event	Joint International Workshop on Process Algebra and Probabilistic Methods & Probabilistic Methods in Verification, PAPM-PROBMIV 2001 - Aachen, Germany Duration: 12 Sept 2001 → 14 Sept 2001

Workshop

Workshop	Joint International Workshop on Process Algebra and Probabilistic Methods & Probabilistic Methods in Verification, PAPM-PROBMIV 2001
Abbreviated title	PAPM-PROBMIV
Country/Territory	Germany
City	Aachen
Period	12/09/01 → 14/09/01

Keywords

n/a OA procedure

Access to Document

10.1007/3-540-44804-7_10

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Cloth, L., Bohnenkamp, H., & Haverkort, B. (2001). Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes. In L. de Alfaro, & S. Gilmore (Eds.), Process Algebra and Probabilistic Methods. Performance Modelling and Verification: Joint International Workshop, PAPM-PROBMIV 2001, Aachen, Germany, September 12-14, 2001. Proceedings (pp. 152-167). Springer. https://doi.org/10.1007/3-540-44804-7_10

Cloth, Lucia ; Bohnenkamp, Henrik ; Haverkort, Boudewijn. / Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes. Process Algebra and Probabilistic Methods. Performance Modelling and Verification: Joint International Workshop, PAPM-PROBMIV 2001, Aachen, Germany, September 12-14, 2001. Proceedings. editor / Luca de Alfaro ; Stephen Gilmore. Berlin, Heidelberg : Springer, 2001. pp. 152-167

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title = "Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes",

abstract = "In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an elegant notation for stochastic prefixes not containing any decisions. Furthermore, they allow for the computation of performance measures. The derivation of the so called k-th occurrence times is shown in detail.",

keywords = "n/a OA procedure",

author = "Lucia Cloth and Henrik Bohnenkamp and Boudewijn Haverkort",

year = "2001",

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booktitle = "Process Algebra and Probabilistic Methods. Performance Modelling and Verification",

publisher = "Springer",

address = "Germany",

note = "Joint International Workshop on Process Algebra and Probabilistic Methods & Probabilistic Methods in Verification, PAPM-PROBMIV 2001, PAPM-PROBMIV ; Conference date: 12-09-2001 Through 14-09-2001",

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Cloth, L, Bohnenkamp, H & Haverkort, B 2001, Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes. in L de Alfaro & S Gilmore (eds), Process Algebra and Probabilistic Methods. Performance Modelling and Verification: Joint International Workshop, PAPM-PROBMIV 2001, Aachen, Germany, September 12-14, 2001. Proceedings. Springer, Berlin, Heidelberg, pp. 152-167, Joint International Workshop on Process Algebra and Probabilistic Methods & Probabilistic Methods in Verification, PAPM-PROBMIV 2001, Aachen, Germany, 12/09/01. https://doi.org/10.1007/3-540-44804-7_10

Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes. / Cloth, Lucia; Bohnenkamp, Henrik; Haverkort, Boudewijn.
Process Algebra and Probabilistic Methods. Performance Modelling and Verification: Joint International Workshop, PAPM-PROBMIV 2001, Aachen, Germany, September 12-14, 2001. Proceedings. ed. / Luca de Alfaro; Stephen Gilmore. Berlin, Heidelberg: Springer, 2001. p. 152-167.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an elegant notation for stochastic prefixes not containing any decisions. Furthermore, they allow for the computation of performance measures. The derivation of the so called k-th occurrence times is shown in detail.

AB - In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an elegant notation for stochastic prefixes not containing any decisions. Furthermore, they allow for the computation of performance measures. The derivation of the so called k-th occurrence times is shown in detail.

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BT - Process Algebra and Probabilistic Methods. Performance Modelling and Verification

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Cloth L, Bohnenkamp H, Haverkort B. Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes. In de Alfaro L, Gilmore S, editors, Process Algebra and Probabilistic Methods. Performance Modelling and Verification: Joint International Workshop, PAPM-PROBMIV 2001, Aachen, Germany, September 12-14, 2001. Proceedings. Berlin, Heidelberg: Springer. 2001. p. 152-167 doi: 10.1007/3-540-44804-7_10

Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes

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