Stochastic model for cell movement in a knockout switch in computer networks

Abstract

In computer networks, switching is used as a juncture to provide a path to a message to pass on. The knockout switch is a specially designed architecture having equal number of input and output lines. An input cell, in this switch, passes through several stages like filters, concentrators and shifters (or queue). The cell may be under unicasting or multicasting depending upon the number of tokens of output lines allotted. This paper considers the random movement of a cell, inside the design of knockout switch, up to the output line. A Markov chain model is proposed to explain the transitions on various states of filter, concentrator and shifter. The outgoing probability is computed using the number of transitions performed by the cell. Several theorems and corollaries are derived for explaining the behavior of the cell movement. The expected number of transitions are computed keeping various situational constraints. A simulation study is performed to support the derived theorems under the model.