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 crosspoin...

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Bibliographic Details
Published in:Applied mathematics and computation 2007-01, Vol.184 (2), p.235-269
Main Authors: Shukla, D., Gadewar, Surendra, Pathak, R.K.
Format: Article
Language:English
Subjects:
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Computer systems performance. Reliability
Exact sciences and technology
Graph theory
Markov Chain model
Markov processes
Mathematics
Probability and statistics
Probability theory and stochastic processes
Reaching probabilities
Sciences and techniques of general use
Software
Space division switches
States
Transition probabilities
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.05.215