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Recently, various analytical models have been proposed to analyze the performance of traditional EPONs. However, these analytical models are not readily applicable to analyze the performance of WDM EPON systems since they are aimed specifically at a single-channel EPON environment. Accordingly, this paper constructs an analytical framework comprising an M/M/1 queuing model and a recursive formulation to analyze the performance of the offline scheduling polling policy in a multi-channel WDM EPON network with differentiated services. The analytical results derived using this model for the mean queuing delay and mean queue length are found to be in good agreement with those obtained from computer simulations.