Stochastic Bounds for Switched Bernoulli Batch Arrivals Observed Through Measurements

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.

[1]  Herwig Bruneel,et al.  Discrete-time queues with correlated arrivals and constant service times , 1999, Comput. Oper. Res..

[2]  Enrique Hernández-Orallo,et al.  Network Performance Analysis based on Histogram Workload Models , 2007, 2007 15th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems.

[3]  Enrique Hernández-Orallo,et al.  Web server performance analysis using histogram workload models , 2009, Comput. Networks.

[4]  Wenhui Zhou,et al.  Discrete-time queue with Bernoulli bursty source arrival and generally distributed service times , 2008 .

[5]  Christoph Lindemann,et al.  Modeling IP traffic using the batch Markovian arrival process , 2003, Perform. Evaluation.

[6]  Akira Kato,et al.  Traffic Data Repository at the WIDE Project , 2000, USENIX Annual Technical Conference, FREENIX Track.

[7]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[8]  Marco Ajmone Marsan,et al.  Markov models of internet traffic and a new hierarchical MMPP model , 2005, Comput. Commun..

[9]  Enrique Hernández-Orallo,et al.  Network queue and loss analysis using histogram-based traffic models , 2010, Comput. Commun..

[10]  Wolfgang Fischer,et al.  The Markov-Modulated Poisson Process (MMPP) Cookbook , 1993, Perform. Evaluation.

[11]  Peter Buchholz,et al.  A MAP fitting approach with independent approximation of the inter-arrival time distribution and the lag correlation , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[12]  Mor Harchol-Balter,et al.  On the inapproximability of M/G/K: why two moments of job size distribution are not enough , 2010, Queueing Syst. Theory Appl..

[13]  Hind Castel-Taleb,et al.  Performance Analysis of a Queue by Combining Stochastic Bounds, Real Traffic Traces and Histograms , 2016, Comput. J..

[14]  Jean-Michel Fourneau,et al.  Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks , 2003, Perform. Evaluation.

[15]  P. Skelly,et al.  A histogram-based model for video traffic behavior in an ATM multiplexer , 1993, TNET.

[16]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[17]  Johanne Cohen,et al.  Accuracy vs. complexity: The stochastic bound approach , 2012, WODES.

[18]  Hind Castel-Taleb,et al.  Stochastic Bounds and Histograms for Network Performance Analysis , 2013, EPEW.

[19]  Yoshitaka Takahashi,et al.  Switched Batch Bernoulli Process (SBBP) and the Discrete-Time SBBP/G/1 Queue with Application to Statistical Multiplexer Performance , 1991, IEEE J. Sel. Areas Commun..