Giuliano Casale
ABSTRACT
Run-time resource allocation requires the availability of system performance models that are both accurate and inexpensive to solve. We here propose a new methodology for run-time performance evaluation based on a class of closed queueing networks. Compared to exponential product-form models, the proposed queueing networks also support the inclusion of resources having first-come first-served scheduling under non-exponential service times. Motivated by the lack of an exact solution for these networks, we propose a fixed-point algorithm that approximates performance indexes in linear time and linear space with respect to the number of requests considered in the model. Numerical evaluation shows that, compared to simulation, the proposed models solved by fixed-point iteration have errors of about 1%-6%, while, on the same test cases, exponential product-form models suffer errors even in excess of 100%. Execution times on commodity hardware are of the order of a few seconds or less, making the proposed methodology practical for run-time decision-making.
- S. Asmussen and F. Koole. Marked point processes as limits of Markovian arrival streams. J. Appl. Prob., 30:365--372, 1993.Google Scholar
Cross Ref
- M. Bertoli, G. Casale, and G. Serazzi. User-friendly approach to capacity planning studies with Java Modelling Tools. In Proc. of SIMUTools 2009, pages 1--9. ACM, 2009. Google ScholarDigital Library
- D. Bini, B. Meini, S. Steffé, and B. Van Houdt. Structured Markov chains solver: software tools. In Proc. of SMCTOOLS Workshop. ACM, 2006, http://win.ua.ac.be/~vanhoudt/. Google ScholarDigital Library
- G. Bolch, S. Greiner, H. de Meer, and K. S. Trivedi. Queueing Networks and Markov Chains. 2nd ed., Wiley and Sons, 2006. Google ScholarDigital Library
- J. P. Buzen. Computational algorithms for closed queueing networks with exponential servers. Comm. of the ACM, 16(9):527--531, 1973. Google ScholarDigital Library
- G. Casale. A note on stable flow-equivalent aggregation in closed networks. Queueing Systems, 60(3-4):193--202, 2008. Google ScholarDigital Library
- G. Casale, N. Mi, and E. Smirni. Bound analysis of closed queueing networks with workload burstiness. In Proc. of ACM SIGMETRICS 2008, pp. 13--24. ACM Press, 2008. Google ScholarDigital Library
- G. Casale, N. Mi, L. Cherkasova, and E. Smirni. Dealing with burstiness in multi-tier applications: new models and their parameterization. IEEE Trans. Software Eng., to appears. Google ScholarDigital Library
- G. Casale, M. Tribastone. Fluid Analysis of Queueing in Two-Stage Random Environments. in Proc. of QEST, Aachen, Germany, Sep 2011. Google ScholarDigital Library
- P. Courtois. Decomposability, instabilities, and saturation in multiprogramming systems. Comm. of the ACM, 18(7):371--377, 1975. Google ScholarDigital Library
- D. L. Eager, D. Sorin, and M. K. Vernon. AMVA techniques for high service time variability. In Proc. of ACM SIGMETRICS, pages 217--228. ACM Press, 2000. Google ScholarDigital Library
- E. Gelenbe and I. Mitrani. Analysis and Synthesis of Computer Systems. Academic Press, London, 1980.Google Scholar
- A. Heindl. Traffic-Based Decomposition of General Queueing Networks with Correlated Input Processes. Ph.D. Thesis, Shaker Verlag, Aachen, 2001.Google Scholar
- A. Heindl, G. Horvath, and K. Gross. Explicit Inverse Characterizations of Acyclic MAPs of Second Order. Proc. of EPEW, Springer LNCS 4054, 108--122, 2006. Google ScholarDigital Library
- H. Kobayashi. Application of the diffusion approximation to queueing networks I: equilibrium queue distributions. Journal of the ACM, 21(2):316--328, 1974. Google ScholarDigital Library
- E. D. Lazowska, J. Zahorjan, G. S. Graham, and K. C. Sevcik. Quantitative System Performance. Prentice-Hall, 1984. Google ScholarDigital Library
- T. Marian, M. Balakrishnan, K. Birman, and R. van Renesse. Tempest: Soft state replication in the service tier. In DSN, pages 227--236. IEEE Computer Society, 2008.Google ScholarCross Ref
- N. Mi, Q. Zhang, A. Riska, E. Smirni, and E. Riedel. Performance impacts of autocorrelated flows in multi-tiered systems. Perform. Eval., 64(9-12):1082--1101, 2007. Google ScholarDigital Library
- M. F. Neuts. The caudal characteristic curve of queues. Adv. Appl. Prob., 18:221--254, 1986.Google ScholarCross Ref
- M. F. Neuts. Structured Stochastic Matrices of M/G/1 Type and Their Applications. Marcel Dekker, New York, 1989.Google Scholar
- B. Pittel. Closed exponential networks of queues with saturation: the Jackson-type stationary distribution and its asymptotic analysis. Math. Oper. Res., 4:357--378, 1979.Google ScholarDigital Library
- M. Reiser. A queueing network analysis of computer communication networks with window flow control. IEEE Trans. on Communications, 27(8):1199--1209, 1979.Google ScholarCross Ref
- A. Riska and E. Smirni. MAMsolver: A matrix analytic methods tool. In Proc. of TOOLS, pp. 205--211. Springer-Verlag, 2002, http://www.cs.wm.edu/MAMSolver/. Google ScholarDigital Library
- A. Riska, V. Diev, and E. Smirni. An EM-based technique for approximating long-tailed data sets with PH distributions. Perform. Eval., 55(1-2):147--164, Jan. 2004. Google ScholarDigital Library
- R. Sadre and B. R. Haverkort. Fifiqueues: Fixed-point analysis of queueing networks with finite-buffer stations. In Proc. of MMB, pages 77--80, 1999.Google Scholar
- W. Whitt. The queueing network analyzer. The bell system tech. journal, 62(9):2779--2815, Nov. 1983.Google Scholar
- J. Zahorjan, E. D. Lazowska, and R. L. Garner. A decomposition approach to modelling high service time variability. Perform. Eval., 3:35--54, 1983.Google ScholarCross Ref
- Z. Zheng and M. R. Lyu. Collaborative reliability prediction of service-oriented systems. In Proc. of ACM ICSE, pp. 35--44, May 2010. Google ScholarDigital Library
Index Terms
- A class of tractable models for run-time performance evaluation
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