Multi-criteria decision making (MCDM) algorithms play an important role in ensuring quality of service in an integrated HetNets (Heterogeneous Networks). The primary objective of this paper is to develop a multi-criteria vertical handoff decision algorithm (VHDA) for best access network selection in an integrated Wireless Local Area Network (WLAN)/Universal Mobile Telecommunications System (UMTS)/Worldwide Interoperability for Microwave Access (WiMAX) system. The proposed design consists of two parts, the first part is the evaluation of an Analytic Hierarchy Process (AHP) to decide the relative weights of handoff decision criteria and the second part computes the final score of the weights to rank network alternatives using Simple Additive Weighting (SAW). SAW ranks the network alternatives in a faster and simpler manner than AHP. The AHP-SAW mathematical model has been designed, evaluated and simulated for streaming video type of traffic. For other traffic type, such as conversational, background and interactive, only simulation results have been discussed and presented in brief. Simulation results reveal that the hierarchical modelling and computing provides optimum solution for access network selection in an integrated environment as obtained results prove to be an acceptable solution to what could be expected in real life scenarios.