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A Markovian Queueing System for Modeling a Smart Green Base Station

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Computer Performance Engineering (EPEW 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9272))

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Abstract

We investigate a model to assess the performance of a base station (BS) fully powered by renewable energy sources. The BS is modeled as a three-queue system where two of them are coupled. One represents accumulated energy, the second is the data queue and the third one serves as a reserve energy queue. This smart BS is able to dynamically adjust its coverage area (thereby controlling the traffic intensity) and to generate signals to the reserve energy queue that trigger the movement of energy units to the main energy buffer. Given the randomness of renewable energy supply and the internal traffic intensity control, our queueing model is operated in a finite state random environment. Using the matrix analytic formalism we construct a five-dimensional Markovian model to study the performance of the BS. The stationary distribution of the system state is obtained and key performance metrics are calculated. A small numerical example illustrates the model and a simplified product-form approximation is proposed.

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References

  1. Akar, N., Oguz, N.C., Sohraby, K.: A novel computational method for solving finite QBD processes. Stoch. Models 16(2), 273–311 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chao, X., Miyazawa, M., Pinedo, M.: Queueing Networks: Customers, Signals and Product Form Solutions. Wiley (1999)

    Google Scholar 

  3. De Cuypere, E., De Turck, K., Fiems, D.: Stochastic modelling of energy harvesting for low power sensor nodes. In: Proc. of QTNA 2012 (2012)

    Google Scholar 

  4. De Cuypere, E., De Turck, K., Fiems, D.: Performance analysis of a kitting process as a paired queue. Mathematical Problems in Engineering, 10 (2013)

    Google Scholar 

  5. Elhafsi, E.H., Molle, M.: On the solution to QBD processes with finite state space. Stoch. Anal. and Appl. 25(4), 763–779 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gaver, D.P., Jacobs, P.A., Latouche, G.: Finite birth-and-death models in randomly changing environments. Adv. Appl. Prob. 16(4), 715–731 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gelenbe, E.: G-networks with triggered customer movement. J. Appl. Prob. 30(3), 742–748 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gelenbe, E.: A sensor node with energy harvesting. ACM Sigmetrics Perform. Evaluation Review 42(2), 37–39 (2014)

    Article  Google Scholar 

  9. Gelenbe, E., Marin, A.: Interconnected wireless sensors with energy harvesting. In: Remke, A., Manini, D., Gribaudo, M. (eds.) ASMTA 2015. LNCS, vol. 9081, pp. 87–99. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  10. Harrison, P., Marin, A.: Product-forms in multi-way synchronizations. Comp. Journal 57(11), 1693–1710 (2014)

    Article  Google Scholar 

  11. Jones, G.L., Harrison, P.G., Harder, U., Field, A.J.: Fluid queue models of battery life. In: Proc. of MASCOTS 2011, pp. 278–285 (2011)

    Google Scholar 

  12. Jones, G.L., Harrison, P.G., Harder, U., Field, A.J.: Fluid queue models of renewable energy storage. In: Proc. of VALUETOOLS 2012, pp. 224–225 (2012)

    Google Scholar 

  13. Kim, C., Dudin, A., Dudin, S., Dudina, O.: Analysis of an \(MMAP/PH_1\), \(PH_2/N/\infty \) queueing system operating in a random environment. Int. J. Appl. Math. Comput. Sci. 24(3), 485–501 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  15. Latouche, G.: Queues with paired customers. J. Appl. Prob. 18(3), 684–696 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  16. Neuts, M.F.: Matrix-geometric solutions in stochastic models: An Algorithmic Approach. The John Hopkins University Press (1981)

    Google Scholar 

  17. Takahashi, M., Osawa, H., Fujisawa, T.: On a synchronization queue with two finite buffers. Queueing Systems 36(1–3), 107–123 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wimmer, R., Derisavi, S., Hermanns, H.: Symbolic partition refinement with automatic balancing of time and space. Perform. Evaluation 67(9), 816–836 (2010)

    Article  Google Scholar 

  19. Ye, J., Li, S.Q.: Folding algorithm: A computational method for finite QBD processes with level-dependent transitions. IEEE Trans. Comm. 42(2/3/4), 625–639 (1994)

    Article  Google Scholar 

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Correspondence to Alain Jean-Marie .

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Dimitriou, I., Alouf, S., Jean-Marie, A. (2015). A Markovian Queueing System for Modeling a Smart Green Base Station. In: Beltrán, M., Knottenbelt, W., Bradley, J. (eds) Computer Performance Engineering. EPEW 2015. Lecture Notes in Computer Science(), vol 9272. Springer, Cham. https://doi.org/10.1007/978-3-319-23267-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-23267-6_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23266-9

  • Online ISBN: 978-3-319-23267-6

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