Superposition of Markov sources and long range dependence

This paper introduces a model to study the phenomenon of long range dependence. This model consists of an infinite superposition of independent Markovian ON/OFFsources. A condition for assuring long range dependence is given and the Hurst parameter together with the correlation decay is derived for a specific example. We also give a physical interpretation of the existing long range dependence by means of the Ising model.

[1]  Nina Taft,et al.  The Entropy of Cell Streams as a Traffic Descriptor in ATM Networks , 1995, Data Communications and their Performance.

[2]  Lars Onsager,et al.  Crystal Statistics. III. Short-Range Order in a Binary Ising Lattice , 1949 .

[3]  L. Onsager.  Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[4]  N. Duffield,et al.  Exponential upper bounds via martingales for multiplexers with Markovian arrivals , 1994 .

[5]  Egbert Falkenberg,et al.  On the asymptotic behaviour of the stationary distribution of Markov chains of M/G/1-type , 1994 .

[6]  Walter Willinger,et al.  Long-range dependence in variable-bit-rate video traffic , 1995, IEEE Trans. Commun..

[7]  F. Papangelou.  GIBBS MEASURES AND PHASE TRANSITIONS (de Gruyter Studies in Mathematics 9) , 1990 .

[8]  Hans-Otto Georgii,et al.  Gibbs Measures and Phase Transitions , 1988 .

[9]  Chris Blondia,et al.  A discrete-time ATM traffic model with long range dependence characteristics , 1997, PMCCN.

[10]  J. Fort,et al.  Stochastic Processes on a Lattice and Gibbs Measures , 1990 .

[11]  Parag Pruthi,et al.  An Application of Chaotic Maps to Packet Traffic Modelling , 1995 .

[12]  Jorma Virtamo,et al.  Broadband Network Traffic , 1996, Lecture Notes in Computer Science.

[13]  Nicolas D. Georganas,et al.  Analysis of an ATM buffer with self-similar ("fractal") input traffic , 1995, Proceedings of INFOCOM'95.

[14]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

[15]  W. Whitt,et al.  Asymptotics for steady-state tail probabilities in structured markov queueing models , 1994 .

[16]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[17]  Onno J. Boxma.  Fluid Queues and Regular Variation , 1996, Perform. Evaluation.

[18]  B. Kaufman.  Crystal Statistics: II. Partition Function Evaluated by Spinor Analysis. III. Short-Range Order in a Binary Ising Lattice. , 1949 .

[19]  Elliott H. Lieb,et al.  Two-Dimensional Ising Model as a Soluble Problem of Many Fermions , 1964 .

[20]  Erwin Kreyszig,et al.  Introductory Mathematical Statistics. , 1970 .

[21]  Piet Van Mieghem,et al.  The asymptotic behavior of queueing systems: Large deviations theory and dominant pole approximation , 1996, Queueing Syst. Theory Appl..

[22]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[23]  Herwig Bruneel,et al.  Some preliminary results on traffic characteristics and queueing behavior of discrete-time on-off sources , 1997 .

[24]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[25]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[26]  D. B. Davis,et al.  Sun Microsystems Inc. , 1993 .

[27]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[28]  Chris Blondia,et al.  The Correlation Structure of the Output of an ATM Multiplexer , 1997, Modelling and Evaluation of ATM Networks.

[29]  B. Conolly.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1991 .

[30]  E. Ising.  Beitrag zur Theorie des Ferromagnetismus , 1925 .

[31]  J. Kemeny,et al.  Denumerable Markov chains , 1969 .