A Prediction Model for Delta Interconnection Network

The Delta Interconnection Network is a digit controlled multistage interconnection network .It can be made up with simple switching elements that do not have logical processing or buffering capabilities. A 2x2 switching elements has two inputs and two outputs. Every cell comes into the delta network from any input port of processors and destined for any output port to memories, which shows random behaviour of cell transmission. In this paper we study the 8X8 delta network for predicting the outgoing chances of cells from sources to destinations in transmission process. For explaining the behavior of cell transmission we derive various outgoing probabilities and theorems using the Markov chain model technique. A simulation study is performed to support the outcomes of derived theorems under the assumed model.

[1]  Emanuel Parzen,et al.  Stochastic Processes , 1962 .

[2]  Chang C. Y. Dorea,et al.  Approximation results for non-homogeneous markov chains and some applications , 2004 .

[3]  Ted H. Szymanski,et al.  Markov chain analysis of packet-switched banyans with arbitrary switch sizes, queue sizes, link multiplicities and speedups , 1989, IEEE INFOCOM '89, Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies.

[4]  Arif Merchant,et al.  A Markov chain approximation for the analysis of banyan networks , 1991, SIGMETRICS '91.

[5]  Philip Heidelberger,et al.  Fast simulation of packet loss rates in a shared buffer communications switch , 1995, TOMC.

[6]  Maurizio Naldi Internet access traffic sharing in a multi-operator environment , 2002, Comput. Networks.

[7]  Rami G. Melhem,et al.  Distributed, dynamic control of circuit-switched Banyan networks , 1998, Proceedings of the First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processing.

[8]  Mohamed N. El-Derini,et al.  Structure and performance evaluation of a replicated banyan network based ATM switch , 1999, Proceedings IEEE International Symposium on Computers and Communications (Cat. No.PR00250).

[9]  J. Medhi,et al.  Stochastic Processes , 1982 .

[10]  Pierre L'Ecuyer,et al.  Estimating small cell-loss ratios in ATM switches via importance sampling , 2001, TOMC.

[11]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[12]  M. Ufuk Çaglayan,et al.  Design and Performance Evaluation of a Banyan Network Based Interconnection Structure for ATM Switches , 1997, IEEE J. Sel. Areas Commun..

[13]  Achille Pattavina,et al.  Performance analysis of ATM Banyan networks with shared queueing—part I: random offered traffic , 1994, TNET.

[14]  John Lygeros,et al.  Stabilization of a class of stochastic differential equations with Markovian switching , 2005, Syst. Control. Lett..

[15]  Daniel M. Dias,et al.  Analysis and Simulation of Buffered Delta Networks , 1981, IEEE Transactions on Computers.

[16]  Jean-Luc Dekeyser,et al.  An Interconnection Networks Comparative Performance Evaluation Methodology: Delta and Over-Sized Delta Networks , 2003, PDCS.

[17]  Diwakar Shukla,et al.  A stochastic model for space-division switches in computer networks , 2007, Appl. Math. Comput..

[18]  Diwakar Shukla,et al.  Stochastic model for cell movement in a knockout switch in computer networks , 2007, J. High Speed Networks.

[19]  Yih-Chyun Jenq,et al.  Performance Analysis of a Packet Switch Based on Single-Buffered Banyan Network , 1983, IEEE J. Sel. Areas Commun..