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With the interworking between a cellular network and wireless local area networks (WLANs), an essential aspect of resource management is taking advantage of the overlay network structure to efficiently share the multi-service traffic load between the interworked systems. In this study, we propose a new load sharing scheme for voice and elastic data services in a cellular/WLAN integrated network. Admission control and dynamic vertical handoff are applied to pool the free bandwidths of the two systems to effectively serve elastic data traffic and improve the multiplexing gain. To further combat the cell bandwidth limitation, data calls in the cell are served under an efficient service discipline, referred to as shortest remaining processing time (SRPT). The SRPT can well exploit the heavy-tailedness of data call size to improve the resource utilization. An accurate analytical model is developed to determine an appropriate size threshold so that data calls are properly distributed to the integrated cell and WLAN, taking into account the load conditions and traffic characteristics. It is observed from extensive simulation and numerical analysis that the new scheme significantly improves the overall system performance.