Exact convergence order of the Lr-quantization error for Markov-type measures

Let E be a graph-directed set associated with a di-graph G. Let μ be a Markov-type measure on E. Assuming a separation condition for E, we determine the exact convergence order of the Lr-quantization error for μ. This result provides us with accurate information on the asymptotics of the quantization error, especially when the quantization coefficient is infinite.