Abstract
We consider Web services defined by orchestrations in the Orc language and two natural quality of services measures, the number of outputs and a discrete version of the first response time. We analyse first those subfamilies of finite orchestrations in which the measures are well defined and consider their evaluation in both reliable and probabilistic unreliable environments. On those subfamilies in which the QoS measures are well defined, we consider a set of natural related problems and analyse its computational complexity. In general our results show a clear picture of the difficulty of computing the proposed QoS measures with respect to the expressiveness of the subfamilies of Orc. Only in few cases the problems are solvable in polynomial time pointing out the computational difficulty of evaluating QoS measures even in simplified models.
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Notes
The expression “\(P(x)<x<Q\)” was encoded as “\(P(x) \;\mathbf{where} \; x:\in Q\)” and called asymmetric parallelism in Misra and Cook (2007).
In McIver and Morgan (2005, p. 20) the notation \(( prog _1@ p_1\mid \cdots \mid prog _k@ p_k)\) is used. We avoid \(\mid \), for probabilistic choice, as it represents the Orc operator parallel composition.
This definition can be seen as an adaptation of the law \(( prog _1\sqcap prog _2); prog _3 = prog _1; prog _3 \sqcap prog _2; prog _3 \) given in McIver and Morgan (2005, p. 323) to orchestrations.
As we are interested in counting problems we adapt the rule \( prog _1 ;( prog _2\sqcap prog _3)\sqsubseteq prog _1; prog _2 \sqcap prog _1; prog _3 \) given in McIver and Morgan (2005, p. 324) replacing \(\sqsubseteq \) by an equality.
We would like to warn the reader against the following, clearly false, “intuitive” approach: \(\Pr (\textsf {out} ( Tosses _n)>0)= Pr(\textsf {out} ( ParBlockingCoin _n)>0)\; \Pr (\textsf {out} ( BlockingCoin _n)>0) = (\big (1-(1/2)^n\big ) 1/2<1/2.\)
References
Aws service health dashboard. http://status.aws.amazon.com
Balcazar JL, Diaz J, Gabarro J (1995) Structural complexity I. EATCS series texts in theoretical computer science. Springer, Heidelberg
Cardoso J, Sheth AP, Miller JA, Arnold J, Kochut K (2004) Quality of service for workflows and web service processes. J Web Semant 1(3):281–308
Castro J, Gabarro J, Serna M, Stewart A (2015) The robustness of periodic orchestrations in uncertain evolving environments. In: Symbolic and quantitative approaches to reasoning with uncertainty—13th European conference, ECSQARU 2015, Compiegne, July 15–17
Dong JS, Liu Y, Sun J, Zhang X (2014) Towards verification of computation orchestration. Form Asp Comput 26(4):729–759
Fu Y, Vahdat A, Cherkasova L, Tang W (2002) Ete: passive end-to-end internet service performance monitoring. In: Proceedings of the general track of the annual conference on USENIX annual technical conference, ATEC ’02. USENIX Association, Berkeley, pp 115–130
Gabarro J, Serna M, Stewart A (2014) Analysing web-orchestrations under stress using uncertainty profiles. Comput J 57(11):1591–1615
Gao H, Miao H, Zeng H (2013) Predictive web service monitoring using probabilistic model checking. Appl Math Inf Sci 7(1):139–148
Gilly K, Quesada-Granja C, Alcaraz S, Juiz C, Puigjaner R (2009) A statistically customisable web benchmarking tool. Electron Notes Theor Comput Sci 232:89–99
Google apps status dashboard. http://www.google.com/appsstatus
Greifeneder J, Frey G (2005) Probabilistic delay time analysis in networked automation systems. In: Proceedings of 10th IEEE international conference on emerging technologies and factory automation, ETFA 2005. IEEE
Hoare T, Menzel G, Misra J (2005) A tree semantics of an orchestration language. In: Broy M, Grünbauer J, Harel D, Hoare T (eds) Engineering theories of software intensive systems, NATO science, vol 195. Springer, Dordrecht, pp 331–350
IPFW, Personal page at Purdue University Fort Wayne. http://users.ipfw.edu/jehle/courses/verbs/VERB.HTM
Kitchin D, Cook WR, Misra J (2006) A language for task orchestration and its semantic properties. In: Baier C, Hermanns H (eds) CONCUR 2006—concurrency theory, 17th international conference, LNCS, vol 4137. Springer, pp 477–491
Krushevskaja D, Sandler M (2013) Understanding latency variations of black box services. In: Proceedings of the 22nd international conference on World Wide Web, WWW ’13. International World Wide Web Conferences Steering Committee, Republic and Canton of Geneva, pp 703–714
McIver A, Morgan C (2005) Abstraction, refinement and proof for probabilistic systems. Springer, Berlin
Menasce DA (2002) Qos issues in web services. IEEE Internet Comput 6(6):72–75
Menasce DA, Almeida V (2001) Capacity planning for web services: metrics, models, and methods, 1st edn. Prentice Hall PTR, Upper Saddle River
Misra J, Cook W (2007) Computation orchestration: a basis for wide-area computing. Softw Syst Model 6(1):83–110
Papadimitriou CH (1994) Computational complexity. Addison Wesley, Reading
Rosario S, Benveniste A, Jard C (2010) Flexible probabilistic QoS management of orchestrations. Int J Web Serv Res 7(2):21–42
Stackoverflow. http://stackoverflow.com
Stewart A, Gabarro J, Keenan A (2013) Reasoning about orchestrations of web services using partial correctness. Form Asp Comput 25(6):833–846
Stewart A, Clint M, Harmer T, Kilpatrick P, Perrott R, Gabarro J (2008) Assessing the reliability and cost of web and grid orchestrations. In: Proceedings of the third international conference on availability, reliability and security, ARES 2008, March 4–7, Technical University of Catalonia, IEEE, Barcelona, pp 428–433
Stross R (2011) \(99.999\%\) reliable? Don’t hold your breath. http://www.nytimes.com/2011/01/09/business/09digi.html
Valiant LG (1979) The complexity of enumeration and reliability problems. SIAM J Comput 8(3):410–421
Vardoulakis D, Wand M (2008) A compositional trace semantics for orc. In: Lea D, Zavattaro G (eds) Coordination models and languages, 10th international conference, COORDINATION 2008, Oslo, LNCS, vol 5052. Springer, pp 331–346
Wehrman I, Kitchin D, Cook W, Misra J (2008) A timed semantics of Orc. Theor Comput Sci 402(2–3):234–248
Wheeler E (2011) Security risk management. Elsevier, Amsterdam
Yahoo. http://yahoo.com
Acknowledgements
The authors want to thank the anonymous referees for the careful reading that help us to improve the readability of the paper and correct several inaccuracies.
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J. Gabarro and M. Serna are partially supported by funds from the Spanish Ministry for Economy and Competitiveness (MINECO) and the European Union (FEDER funds) under Grant TIN2013-46181-C2-1-R (COMMAS) and also by SGR 2014:1034 (ALBCOM) from AGAUR, Generalitat de Catalunya. M. Serna is also supported by funds from the Spanish Ministry for Economy and Competitiveness (MINECO) under Grant MDM-2014-0445.
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Gabarro, J., Leon-Gaixas, S. & Serna, M. The computational complexity of QoS measures for orchestrations. J Comb Optim 34, 1265–1301 (2017). https://doi.org/10.1007/s10878-017-0146-9
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DOI: https://doi.org/10.1007/s10878-017-0146-9