A method for delay analysis of interacting queues in multiple access systems

An approximate model for analyzing interacting queues is developed. This approximation models an N-dimensional infinite Markov chain by means of two Markov chains, one being one-dimensional and infinite and the other being N-dimensional and finite. The transition probabilities of each chain are expressed in terms of statistics of the other chain. The two chains are solved together iteratively to yield an approximation to the original N-dimensional infinite chain. The model is used to analyze systems of dependent queues which often arise in multiple access protocols. It is shown how this model can be used to analyze the ALOHA multiple access protocol as well as a previously proposed broadcast algorithm for a mesh network. The results compare very well with simulation.<
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