A stochastic model for space-division switches in computer networks

In computer networks, calls are routed through switches in order to reach at destinations. The simplest types of them are crosspoint switches which require one-to-one connection between inputs and outputs. If it assumed that all lines fully duplex and there are no self-connections, so many crosspoints are needed to provide the proper connectivity. To reduce this factor, space-division switches are designed to provide better connectivity under the condition of limited space. In this paper, we assume a Markov chain based stochastic model with the unit step transition probability matrix to examine the functioning and properties of space-division switches. The connectivity of system under this model is studied using a simulation procedure. Expressions for various connectivity probabilities are derived for the different stages of the space-division switching elements and simulation is performed for K-dependent and L-dependent Markov models.