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Markovian Queue with Garbage Collection

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Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2017)

Abstract

Garbage collection is a fundamental component of memory management in several software frameworks. We present a general two-dimensional Markovian model of a queue with garbage collection where the input process is Markov-modulated and the memory consumption can be modeled with discretisation. We derive important performance measures (also including garbage collection-related measures like mean garbage collection cycle length). The model is validated via measurements from a real-life data processing pipeline.

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References

  1. Ganglia monitoring system. http://ganglia.sourceforge.net/. Accessed 08 May 2017

  2. Apache Storm. http://storm.apache.org/. Accessed 08 May 2017

  3. Bacon, D.F., Cheng, P., Rajan, V.T.: The metronome: a simpler approach to garbage collection in real-time systems. In: Meersman, R., Tari, Z. (eds.) OTM 2003. LNCS, vol. 2889, pp. 466–478. Springer, Heidelberg (2003). doi:10.1007/978-3-540-39962-9_52

    Chapter  Google Scholar 

  4. Balsamo, S., Dei Rossi, G.-L., Marin, A.: Optimisation of virtual machine garbage collection policies. In: Al-Begain, K., Balsamo, S., Fiems, D., Marin, A. (eds.) ASMTA 2011. LNCS, vol. 6751, pp. 70–84. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21713-5_6

    Chapter  Google Scholar 

  5. Blackburn, S.M., Cheng, P., McKinley, K.S.: Oil and water? High performance garbage collection in Java with MMTk. In: Proceedings of the 26th International Conference on Software Engineering. IEEE Computer Society (2004)

    Google Scholar 

  6. Bolch, G., et al.: Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications. Wiley, Hoboken (2006)

    Book  Google Scholar 

  7. Brodie-Tyrrell, W.: Surf: an abstract model of distributed garbage collection. Dissertation (2008)

    Google Scholar 

  8. Bux, W., Iliadis, I.: Performance of greedy garbage collection in flash-based solid-state drives. Perform. Eval. 67(11), 1172–1186 (2010)

    Article  Google Scholar 

  9. Detlefs, D., et al.: Garbage-first garbage collection. In: Proceedings of the 4th International Symposium on Memory Management. ACM (2004)

    Google Scholar 

  10. Gribaudo, M., Telek, M.: Fluid models in performance analysis. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 271–317. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72522-0_7

    Chapter  MATH  Google Scholar 

  11. Jones, R., Lins, R.D.: Garbage Collection: Algorithms for Automatic Dynamic Memory Management. Wiley, New York (1996)

    MATH  Google Scholar 

  12. Jones, G.L., et al.: Fluid queue models of battery life. In: 2011 IEEE 19th Annual International Symposium on Modelling, Analysis, and Simulation of Computer and Telecommunication Systems. IEEE (2011)

    Google Scholar 

  13. Kwon, O., et al.: FeGC: an efficient garbage collection scheme for flash memory based storage systems. J. Syst. Softw. 84(9), 1507–1523 (2011)

    Article  Google Scholar 

  14. Latouche, G., Ramaswami, V.: Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM, Philadelphia (1999)

    Book  Google Scholar 

  15. Li, Y., Lee, P.P.C., Lui, J.C.S.: Stochastic modeling and optimization of garbage collection algorithms in solid-state drive systems. Queueing Syst. 77(2), 115–148 (2014)

    Article  MathSciNet  Google Scholar 

  16. Lowry, M.C.: A new approach to the train algorithm for distributed garbage collection. Dissertation (2004)

    Google Scholar 

  17. Kressner, D., Macedo, F.: Low-rank tensor methods for communicating Markov processes. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 25–40. Springer, Cham (2014). doi:10.1007/978-3-319-10696-0_4

    Chapter  Google Scholar 

  18. Medhi, J.: Stochastic Models in Queueing Theory. Academic Press, Cambridge (2002)

    MATH  Google Scholar 

  19. Nazarathy, Y., Weiss, G.: A fluid approach to job shop scheduling: theory, software and experimentation. J. Sched. 13, 509–529 (2009)

    Article  Google Scholar 

  20. Neuts, M.: Matrix-Geometric Solutions in Stochastic Models. An Algoritheoremic Approach. The Johns Hopkins University Press, Baltimore (1981)

    Google Scholar 

  21. Norcross, S.J.: Deriving distributed garbage collectors from distributed termination algorithms. Dissertation, University of St Andrews (2004)

    Google Scholar 

  22. Plainfossé, D., Shapiro, M.: A survey of distributed garbage collection techniques. In: Baler, H.G. (ed.) IWMM 1995. LNCS, vol. 986, pp. 211–249. Springer, Heidelberg (1995). doi:10.1007/3-540-60368-9_26

    Chapter  Google Scholar 

  23. Schoeberl, M.: Real-time garbage collection for Java. In: Ninth IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC 2006). IEEE (2006)

    Google Scholar 

  24. Lakatos, L., Szeidl, L., Telek, M.: Introduction to Queueing Systems with Telecommunication Applications. Springer, New York (2013)

    Book  Google Scholar 

  25. Van Houdt, B.: A mean field model for a class of garbage collection algorithms in flash-based solid state drives. In: ACM SIGMETRICS Performance Evaluation Review. vol. 41, no. 1. ACM (2013)

    Google Scholar 

  26. Van Houdt, B.: Performance of garbage collection algorithms for flash-based solid state drives with hot/cold data. Perform. Eval. 70(10), 692–703 (2013)

    Article  Google Scholar 

  27. Wilson, P.R.: Uniprocessor garbage collection techniques. In: Bekkers, Y., Cohen, J. (eds.) IWMM 1992. LNCS, vol. 637, pp. 1–42. Springer, Heidelberg (1992). doi:10.1007/BFb0017182

    Chapter  Google Scholar 

  28. Yang, Y., Zhu, J.: Analytical modeling of garbage collection algorithms in hotness-aware flash-based solid state drives. In: 2014 30th Symposium on Mass Storage Systems and Technologies (MSST). IEEE (2014)

    Google Scholar 

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Acknowledgment

We would like to thank Miklós Telek and Gábor Horváth for their valuable help and insight. This research is partially supported by the OTKA K123914 project.

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Correspondence to Illés Horváth .

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Horváth, I., Finta, I., Kovács, F., Mészáros, A., Molontay, R., Varga, K. (2017). Markovian Queue with Garbage Collection. In: Thomas, N., Forshaw, M. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2017. Lecture Notes in Computer Science(), vol 10378. Springer, Cham. https://doi.org/10.1007/978-3-319-61428-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-61428-1_8

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