Abstract
We generalise to non stationary traffics an approach that we have previously proposed to derive performance bounds of a queue under histogram-based input traffics. We use strong stochastic ordering to derive stochastic bounds on the queue length and the output traffic. These bounds are valid for transient distributions of these measures and also for the steady-state distributions when they exist. We provide some numerical techniques under arrivals modelled by a Switched Batch Bernoulli Process (SBBP). Unlike approximate methods, these bounds can be used to check if the Quality of Service constraints are satisfied or not. Our approach provides a tradeoff between the accuracy of results and the computational complexity and it is much faster than the histogram-based simulation proposed in the literature.
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Aït-Salaht, F., Castel-Taleb, H., Fourneau, J.-M., Pekergin, N.: Stochastic bounds and histograms for network performance analysis. In: Balsamo, M.S., Knottenbelt, W.J., Marin, A. (eds.) EPEW 2013. LNCS, vol. 8168, pp. 13–27. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40725-3_3
Aït-Salaht, F., Castel Taleb, H., Fourneau, J.-M., Pekergin, N.: Performance analysis of a queue by combining stochastic bounds, real traffic traces and histograms. Comput. J. 59(12), 1817–1830 (2016)
Aït-Salaht, F., Cohen, J., Castel Taleb, H., Fourneau, J.M., Pekergin, N.: Accuracy vs. complexity: the stochastic bound approach. In: 11th International Workshop on Discrete Event Systems, pp. 343–348 (2012)
Fischer, W., Hellstern, K.M.: The Markov-modulated Poisson process (MMPP) cookbook. Perform. Eval. 18, 149–171 (1992)
Gupta, V., Harchol-Balter, M., Dai, J.G., Zwart, B.: On the inapproximability of M/G/K: why two moments of job size distribution are not enough. Queueing Syst. 64(1), 5–48 (2010)
Gusak, O., Dayar, T., Fourneau, J.-M.: Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks. Perform. Eval. 53(1), 43–69 (2003)
Hashida, O., Takahashi, Y., Shimogawa, S.: Switched batch Bernoulli process (SBBP) and the discrete-time SBBP/G/1 queue with application to statistical multiplexer performance. IEEE J. Select. Areas Commun. 9(3), 394–401 (1991)
Hernández-Orallo, E., Vila-Carbó, J.: Network performance analysis based on histogram workload models. In: MASCOTS, pp. 209–216 (2007)
Hernández-Orallo, E., Vila-Carbó, J.: Web server performance analysis using histogram workload models. Comput. Netw. 53(15), 2727–2739 (2009)
Hernández-Orallo, E., Vila-Carbó, J.: Network queue and loss analysis using histogram-based traffic models. Comput. Commun. 33(2), 190–201 (2010)
Horváth, G., Telek, M., Buchholz, P.: A map fitting approach with independent approximation of the inter-arrival time distribution and the lag correlation. In: QEST, pp. 124–133. IEEE Computer Society (2005)
Klemm, A., Lindemann, C., Lohmann, M.: Traffic modelling of IP networks using the batch Markovian arrival process. Perform. Eval. 54(25), 149–173 (2003)
Muller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, New York (2002)
Muscarielloa, L., Melliaa, M., Meoa, M., Ajmone, M.M., Lo Cignob, R.: Markov models of internet traffic and a new hierarchical MMPP model. Comput. Commun. 28, 1835–1851 (2005)
Skelly, P., Schwartz, M., Dixit, S.S.: A histogram-based model for video traffic behaviour in an ATM multiplexer. IEEE/ACM Trans. Netw. 1(4), 446–459 (1993)
Sony, K.C., Cho, K.: Traffic data repository at the wide project. In: Proceedings of USENIX 2000 Annual Technical Conference: FREENIX Track, pp. 263–270 (2000)
Stewart, W.: Introduction to the numerical Solution of Markov Chains. Princeton University Press, New Jersey (1995)
Wittevrongel, S., Bruneel, H.: Discrete-time queues with correlated arrivals and constant service times. Comput. Oper. Res. 26, 93–108 (1999)
Zhou, W., Wang, A.: Discrete-time queue with Bernoulli bursty source arrival and generally distributed service times. Appl. Math. Model. 3, 2223–2240 (2013)
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Aït-Salaht, F., Castel-Taleb, H., Fourneau, JM., Pekergin, N. (2017). Stochastic Bounds for Switched Bernoulli Batch Arrivals Observed Through Measurements. 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_1
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DOI: https://doi.org/10.1007/978-3-319-61428-1_1
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