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The major issue in smart grid (SG) communications networks is the latency management of a vast amount of SG traffic in the access network that connects power substations to a large number of SG monitoring devices. There are three possible deployments for the SG access network considered by power industries: 1) a public access network with a mix of SG and human-to-human (H2H) traffic; 2) a private access network exclusively assigned to SG communications; and 3) a mix of private and public access networks, referred to as hybrid access networks. The SG communications traffic is classified as fixed-scheduling (FS) and event-driven (ED). The FS and ED traffic, generated by SG devices, occur on a periodic basis and as a response to electricity supply conditions, respectively. In this paper, we develop traffic models for public, private, and hybrid SG access networks based on queuing theory. By using these models, we derive an expression for the mean queuing delay for each traffic class in each network. We then propose an optimization problem to find the optimal partitioning of the SG traffic in a hybrid access network. The analytical results obtained from the proposed models agree very well with the simulation results.