A Stochastic Model Approach for Reaching Probabilities of Message Flow in Space-Division Switches

In computer networks messages are transmitted through switches in order to reach destinations. Cross point switches are the simplest technique which requires one-to-one connection between input and output. The limitation of a cross bar switch technology is that if numbers of lines are large then cross point increases in huge amount consequently increasing the dimension of the switch. Space division switches are used to route the calls, which implies betterment over the cross bar technology. Actually it is built up of several smaller rectangular crossbars. This takes the advantage over the crossbar switches that less cross points are needed in the space division switches. The limitations of space division switches are that if more the number of cross points then there is increase the outgoing reaching probabilities of messages but the cost and overheads is also high with lesser cross points the congestion increases. In this paper we considered the architecture of a three crossbar space-division switch and assumed a Markov chain model for the transitional analysis of message flow. With the help of simulation study it is concluded that the impact of reaching probabilities for the different values of parameters must be kept in mind while designing this switch by designers.