Algebraic reasoning for timeliness-guided system design
Designing distributed systems to have predictable performance under all loads is difficult because of resource exhaustion, nonlinearity, and stochastic behaviour. Timeliness, defined as delivering results (sufficiently often) within a specified delay distribution, is a central aspect of predictable...
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| Vydané v: | Journal of logical and algebraic methods in programming Ročník 148; s. 101093 |
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01.01.2026
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| Abstract | Designing distributed systems to have predictable performance under all loads is difficult because of resource exhaustion, nonlinearity, and stochastic behaviour. Timeliness, defined as delivering results (sufficiently often) within a specified delay distribution, is a central aspect of predictable performance. In this paper, we consider the ΔQ Systems Development paradigm (ΔQSD, developed by PNSol), which computes timeliness by modelling systems observationally using so-called outcome expressions. An outcome expression is a compositional definition of a system's observed behaviour that shows the causal connections between its basic operations. Given the ΔQSD operations, we use outcome expressions to compute the stochastic behaviour of the whole system including its timeliness.
This paper defines and proves algebraic equivalences of outcome expressions with respect to timeliness. We prove the correctness of previously-known equivalences. We also introduce new equivalences and prove their correctness for outcome expressions containing probabilistic choice, failure, synchronisation (first-to-finish and last-to-finish), and sequential composition operators. We show how to incorporate failure as a first-class citizen in outcome expressions by developing the relevant mathematics based on the use of improper random variables. The paper shows the practical usefulness of algebraic equivalences by studying the design of a memory system containing a local cache, a networked read with timeout, and the ability to retry. We compute the delay and failure behaviour of several versions of this system, using the equivalences to simplify computations. This work is part of an ongoing project to disseminate and build tool support for ΔQSD, to make it available to the wider community of system designers.
•Design and analysis of large and/or distributed systems and their performance through use of symbolic reasoning.•Analytical modelling of delay-and-failure as a first-class object in system design, by use of ε-incomplete random variables.•Treating systems observationally to capture causality, allowing multiple levels of abstraction during design.•Using a stochastic approach to model system delay and failure behaviour hierarchically.•Extension of the ΔQSD paradigm with algebraic reasoning, proving equivalences for system design transformations. |
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| AbstractList | Designing distributed systems to have predictable performance under all loads is difficult because of resource exhaustion, nonlinearity, and stochastic behaviour. Timeliness, defined as delivering results (sufficiently often) within a specified delay distribution, is a central aspect of predictable performance. In this paper, we consider the ΔQ Systems Development paradigm (ΔQSD, developed by PNSol), which computes timeliness by modelling systems observationally using so-called outcome expressions. An outcome expression is a compositional definition of a system's observed behaviour that shows the causal connections between its basic operations. Given the ΔQSD operations, we use outcome expressions to compute the stochastic behaviour of the whole system including its timeliness.
This paper defines and proves algebraic equivalences of outcome expressions with respect to timeliness. We prove the correctness of previously-known equivalences. We also introduce new equivalences and prove their correctness for outcome expressions containing probabilistic choice, failure, synchronisation (first-to-finish and last-to-finish), and sequential composition operators. We show how to incorporate failure as a first-class citizen in outcome expressions by developing the relevant mathematics based on the use of improper random variables. The paper shows the practical usefulness of algebraic equivalences by studying the design of a memory system containing a local cache, a networked read with timeout, and the ability to retry. We compute the delay and failure behaviour of several versions of this system, using the equivalences to simplify computations. This work is part of an ongoing project to disseminate and build tool support for ΔQSD, to make it available to the wider community of system designers.
•Design and analysis of large and/or distributed systems and their performance through use of symbolic reasoning.•Analytical modelling of delay-and-failure as a first-class object in system design, by use of ε-incomplete random variables.•Treating systems observationally to capture causality, allowing multiple levels of abstraction during design.•Using a stochastic approach to model system delay and failure behaviour hierarchically.•Extension of the ΔQSD paradigm with algebraic reasoning, proving equivalences for system design transformations. |
| ArticleNumber | 101093 |
| Author | Haeri, Seyed Hossein Thompson, Peter W. Šinkarovs, Artjoms Apfelmus, Heinrich Davies, Neil J. Haveraaen, Magne Barash, Mikhail Chapman, James Hammond, Kevin Van Roy, Peter |
| Author_xml | – sequence: 1 givenname: Seyed Hossein surname: Haeri fullname: Haeri, Seyed Hossein email: hossein.haeri@iohk.io organization: Input Output Global, Brussels, Belgium – sequence: 2 givenname: Peter surname: Van Roy fullname: Van Roy, Peter email: pvr@info.ucl.ac.be organization: Université catholique de Louvain, Louvain-la-Neuve, Belgium – sequence: 3 givenname: Heinrich surname: Apfelmus fullname: Apfelmus, Heinrich email: apfelmus@quantentunnel.de organization: Cardano Stiftung, Zug, Switzerland – sequence: 4 givenname: Peter W. surname: Thompson fullname: Thompson, Peter W. email: Peter.Thompson@pnsol.com organization: Predictable Network Solutions Ltd. (PNSol), Stonehouse, UK – sequence: 5 givenname: Neil J. orcidid: 0000-0001-9462-8584 surname: Davies fullname: Davies, Neil J. email: Neil.Davies@pnsol.com organization: Predictable Network Solutions Ltd. (PNSol), Stonehouse, UK – sequence: 6 givenname: Magne surname: Haveraaen fullname: Haveraaen, Magne email: Magne.Haveraaen@uib.no organization: Department of Informatics, University of Bergen, Bergen, Norway – sequence: 7 givenname: Mikhail surname: Barash fullname: Barash, Mikhail email: mikhail.barash@uib.no organization: Department of Informatics, University of Bergen, Bergen, Norway – sequence: 8 givenname: Kevin surname: Hammond fullname: Hammond, Kevin email: kevin.hammond@iohk.io organization: Input Output Global, UK – sequence: 9 givenname: James surname: Chapman fullname: Chapman, James email: james.chapman@iohk.io organization: Input Output Global, UK – sequence: 10 givenname: Artjoms surname: Šinkarovs fullname: Šinkarovs, Artjoms email: artjoms.sinkarovs@iohk.io organization: Input Output Global, UK |
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| Cites_doi | 10.1016/j.scico.2019.102303 10.1145/321992.321997 10.1016/j.scico.2009.09.010 10.1109/TPDS.2019.2943339 10.3390/computers11030045 10.1016/j.scico.2018.08.007 10.1093/comjnl/bxh097 10.1016/j.scico.2010.09.007 10.1016/j.tcs.2020.02.020 10.1016/j.entcs.2005.10.040 10.1016/0304-3975(92)90182-F |
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| Keywords | Algebraic reasoning 60H99 90B99 03B99 Timeliness 68M99 System design ΔQSD |
| Language | English |
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