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Closed-form mathematical expressions of network performances, such as the mean packet delay, are useful for evaluating a communication network during the design process. This paper provides derivations of closed-form expressions of the mean packet delay for the gated service and the limited service of dynamic bandwidth allocation in Ethernet passive optical networks (EPONs). Based on the M/G/1 queueing analysis framework of a multiuser cyclic polling system, we derive the mean packet delay expressions by modifying the expressions for the reservation time component of the total delay. Results from simulation experiments confirm that our analysis can accurately predict the mean packet delay. Finally, we extend the analysis to demonstrate how the limited service can protect packets transmitted by a light-load user from having excessive delays due to high traffic loads from other users in the same EPON. The analytical results indicate that, in selecting the maximum length of a scheduling cycle for the limited service, there is a tradeoff between the mean packet delay under uniform traffic and the guaranteed upper bound on the mean packet delay under nonuniform traffic.