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The mobile broadband revolution with its rapidly increasing traffic volumes has resulted in a number of challenges, including ubiquitous network coverage, high bandwidth, and reliable services for reasonable price, etc.. To address these challenges, the Evolved Packet System is proposed as the evolution of the packet core network. While resource management and load balancing issue in Evolved Packet System (EPS) is mentioned in standard, relatively little discussions focus on the scheme design for load information monitoring and evaluation. Furthermore, as the system utility is one of the major considerations for system service provider, how to design the load balancing algorithm to maximize the joint system utility in the integration scenario of multiple access gateways and heterogeneous access networks is an important issue worthy of study. In this paper, an IASA load balancing mechanism is proposed which performs load status monitoring and evaluation for access gateways and heterogeneous networks and an optimal load balancing algorithm to maximize the joint utility of integrated heterogeneous networks is also proposed. The system utilities of access networks are modeled mathematically and the optimal handoff user number is obtained through solving the optimization problem. Numerical results demonstrate the network utility varying with the number of users in it, and the optimal handoff user number can be obtained corresponding to the maximum of the joint network utility.