Analytical and Stochastic Modeling Techniques and Applications

We discuss the application of an efficient numerical algorithm to sensitivity analysis of the GI/M/1 queue. Specifically, we use a numerical approach based on the Taylor series expansion to examine the robustness of the GI/M/1 queue to some specific perturbations in the arrival process: linear and non-linear perturbations. For each kind of perturbation we approximately compute the sensitivity of the main characteristics of the GI/M/1 queue corresponding to the case where the arrival processes are lightly different from that of the nominal queue. Numerical examples are presented to illustrate the accuracy of the proposed approach.

[1]  Pierre Semal,et al.  Histogram based bounds and approximations for production lines , 2009, Eur. J. Oper. Res..

[3]  Armand M. Makowski,et al.  Queueing models for systems with synchronization constraints , 1989, Proc. IEEE.

[4]  Ren Asmussen,et al.  Fitting Phase-type Distributions via the EM Algorithm , 1996 .

[5]  A. Bobbio,et al.  A benchmark for ph estimation algorithms: results for acyclic-ph , 1994 .

[6]  C. Commault,et al.  Sparse representations of phase-type distributions , 1999 .

[7]  Johannes Gehrke,et al.  Gossip-based computation of aggregate information , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[8]  Tadashi Dohi,et al.  A refined EM algorithm for PH distributions , 2011, Perform. Evaluation.

[9]  Gábor Horváth,et al.  On the canonical representation of phase type distributions , 2009, Perform. Evaluation.

[10]  Harry G. Perros,et al.  Open Networks of Queues with Blocking: Split and Merge Configurations: , 1986 .

[11]  M. Telek,et al.  Moment Bounds for Acyclic Discrete and Continuous Phase Type Distributions of Second Order , 2002 .

[12]  J. Walrand,et al.  Monotonicity of Throughput in Non-Markovian Networks. , 1989 .

[13]  C. Leake.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[14]  Evgenia Smirni,et al.  Interarrival Times Characterization and Fitting for Markovian Traffic Analysis , 2007, Numerical Methods for Structured Markov Chains.

[15]  Derek L. Eager,et al.  Bound hierarchies for multiple-class queuing networks , 1986, JACM.

[16]  Yves Dallery,et al.  Manufacturing flow line systems: a review of models and analytical results , 1992, Queueing Syst. Theory Appl..

[17]  R. Smythe,et al.  First-passage percolation on the square lattice. I , 1977, Advances in Applied Probability.

[18]  Koichi Nakade.  New bounds for expected cycle times in tandem queues with blocking , 2000, Eur. J. Oper. Res..

[19]  F. Baccelli,et al.  Comparison properties of stochastic decision free Petri nets , 1992 .

[20]  Miklós Telek,et al.  PhFit: A General Phase-Type Fitting Tool , 2002, Computer Performance Evaluation / TOOLS.

[21]  Ramin Sadre,et al.  Fitting World Wide Web request traces with the EM-algorithim , 2001, SPIE ITCom.

[22]  Y. L. Tong.  The multivariate normal distribution , 1989 .

[23]  Peter Buchholz,et al.  Multi-class Markovian arrival processes and their parameter fitting , 2010, Perform. Evaluation.

[24]  Panagiotis Papadimitratos,et al.  Vehicular communication systems: Enabling technologies, applications, and future outlook on intelligent transportation , 2009, IEEE Communications Magazine.

[25]  Michael A. Johnson,et al.  Matching moments to phase distri-butions: mixtures of Erlang distribution of common order , 1989 .

[26]  Anja Feldmann,et al.  Fitting mixtures of exponentials to long-tail distributions to analyze network performance models , 1997, Proceedings of INFOCOM '97.

[27]  Wallace J. Hopp,et al.  Factory physics : foundations of manufacturing management , 1996 .

[28]  Peter Buchholz,et al.  A novel approach for fitting probability distributions to real trace data with the EM algorithm , 2005, 2005 International Conference on Dependable Systems and Networks (DSN'05).

[29]  A. Horváth,et al.  Matching Three Moments with Minimal Acyclic Phase Type Distributions , 2005 .

[30]  Peter Buchholz,et al.  Stochastic Petri nets with matrix exponentially distributed firing times , 2010, Perform. Evaluation.