Article

Skipping and Fetching: Insights on Non-conventional Product-Form Solutions

Authors:

Diletta Olliaro,

Gianfranco Balbo,

Matteo SerenoAuthors Info & Claims

Quantitative Evaluation of Systems: 20th International Conference, QEST 2023, Antwerp, Belgium, September 20–22, 2023, Proceedings

Pages 110 - 126

https://doi.org/10.1007/978-3-031-43835-6_8

Published: 20 September 2023 Publication History

Abstract

Complex models of computer systems are often difficult to study with numerical or analytical approaches because of the state space explosion problem. The class of product-form models is one of the most significant tools for overcoming this problem, and in many applications, this tool is the only way to perform a quantitative analysis.

In this paper, we study the duality between two different product-form models. The first consists of a queuing network with finite capacity waiting rooms governed by the skip-over policy. The second is a recently presented product-form model in which a job fetching policy is applied. To investigate the relationships between these two models, we first extend the fetching queuing model to allow for finite capacity warehouses and for a Repetitive Service Blocking with Random Destination (RS-RD) discipline. Subsequently, we represent their distinctive features in terms of Generalized Stochastic Petri Nets which precisely specify their semantics in a modular manner and provide clear and intuitive interpretations of these policies. With these two preliminary results, we prove that it is possible to structurally transform a model of one class into one of the other and vice versa, thus choosing the representation that is computationally more convenient to compute the performance measures of interest.

References

[1]

Marsan MA, Balbo G, Conte G, Donatelli S, and Franceschinis G Modelling with Generalized Stochastic Petri Nets 1995 Hoboken Wiley

[2]

Ajmone Marsan M, Balbo G, and Conte G A class of generalized stochastic petri nets for the performance evaluation of multiprocessor systems ACM Trans. Comput. Syst. 1984 2 2 93-122

[3]

Balbo G, Bruell SC, and Sereno M Product form solution for generalized stochastic petri nets IEEE Trans. Software Eng. 2002 28 10 915-932

[4]

Balsamo, S., Harrison, P.G., Marin, A.: A unifying approach to product-forms in networks with finite capacity constraints. In: SIGMETRICS 2010, Proceedings of the 2010 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, pp. 25–36. ACM (2010)

[5]

Balsamo S and de Nitto Persone V A survey of product form queueing networks with blocking and their equivalences Ann. Oper. Res. 1994 48 1 31-61

[6]

Baskett F, Chandy K, Muntz R, and Palacios F Open, closed and mixed networks of queues with different classes of customers J. ACM 1975 22 2 248-260

[7]

Boucherie RJ and van Dijk NM On the arrival theorem for product form queueing networks with blocking Perform. Eval. 1997 29 3 155-176

[8]

Chao X, Miyazawa M, and Pinedo M Queueing Networks: Customers, Signals and Product Form Solutions 1999 Hoboken Wiley

[9]

Chiola G, Ajmone Marsan M, Balbo G, and Conte G Generalized stochastic petri nets: a definition at the net level and its implications IEEE Trans. Software Eng. 1993 19 2 89-107

[10]

Ciardo G, Miner A, and Wan M Advanced features in SMART: the stochastic model checking analyzer for reliability and timing ACM SIGMETRICS Perform. Eval. Rev. 2009 36 4 58-63

[11]

Ciardo G, Muppala J, and Trivedi K On the solution of GSPN reward models Perform. Eval. 1991 12 4 237-253

[12]

Gates D and Westcott M Stationary states of crystal growth in three dimensions J. Stat. Phys. 1995 81 681-715

[13]

Gelenbe E Calzarossa MC and Tucci S G-networks: multiple classes of positive customers, signals, and product form results Performance Evaluation of Complex Systems: Techniques and Tools 2002 Heidelberg Springer 1-16

[14]

Harchol-Balter M Performance Modeling and Design of Computer Systems: Queueing Theory in Action 2013 Cambridge Cambridge Press

[15]

Harrison PG and Marin A Product-forms in multi-way synchronizations Comput. J. 2014 57 11 1693-1710

[16]

Jackson JR Networks of waiting lines Oper. Res. 1957 5 4 518-521

[17]

Jackson JR Jobshop-like queueing systems Manage. Sci. 1963 10 1 131-142

[18]

Kelly FP Reversibility and Stochastic Networks 1979 Hoboken Wiley

[19]

Lam SS Dynamic scaling and growth behavior of queueing network normalization constants J. ACM 1982 29 2 492-513

[20]

Marin A, Rossi S, and Olliaro D A product-form network for systems with job stealing policies SIGMETRICS Perform. Eval. Rev. 2023 50 4 2-4

[21]

Pittel BG Closed exponential networks of queues with saturation: the Jackson-type stationary distribution and its asymptotic analysis Math. Oper. Res. 1979 4 4 357-378

[22]

Sevcik KC and Mitrani I The distribution of queuing network states at input and output instants J. ACM 1981 28 2 358-371

[23]

Towsley DF Queuing network models with state-dependent routing J. ACM 1980 27 2 323-337

[24]

Van der Gaast J, De Koster R, Adan IJBF, and Resing JAC Capacity analysis of sequential zone picking systems Oper. Res. 2020 68 1 161-179

[25]

Zhang X, Xue Q, Li L, Fan E, Wu F, and Chen R Sustainable recycling and regeneration of cathode scraps from industrial production of lithium-ion batteries ACS Sustain. Chem. Eng. 2016 4 12 7041-7049

Cited By

Olliaro DCasale GMarin ARossi S(2024)A Product-form Network for Systems with Job Stealing PoliciesACM Transactions on Modeling and Performance Evaluation of Computing Systems10.1145/36438459:2(1-26)Online publication date: 3-Feb-2024
https://dl.acm.org/doi/10.1145/3643845

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Published In

cover image Guide Proceedings

Quantitative Evaluation of Systems: 20th International Conference, QEST 2023, Antwerp, Belgium, September 20–22, 2023, Proceedings

Sep 2023

376 pages

ISBN:978-3-031-43834-9

DOI:10.1007/978-3-031-43835-6

Editors:
Nils Jansen
Radboud University Nijmegen, Nijmegen, The Netherlands
,
Mirco Tribastone
IMT Lucca, Lucca, Italy

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 20 September 2023

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Cited By

Olliaro DCasale GMarin ARossi S(2024)A Product-form Network for Systems with Job Stealing PoliciesACM Transactions on Modeling and Performance Evaluation of Computing Systems10.1145/36438459:2(1-26)Online publication date: 3-Feb-2024
https://dl.acm.org/doi/10.1145/3643845

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