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This paper presents an Approximate Mean Value Analysis model of deflection routing in Shuffle-Loop Networks. In contrast to most previous work on deflection routing, the model makes no assumptions about traffic patterns, nor does it assume that messages that cannot be admitted to the network are lost. The technique allows the network to be modeled in its entirety: all processors, switches, and memory modules, and their steady-state interactions, are modeled explicitly. The results of the model are found to be in close agreement with the results of simulation experiments.