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Multi-sink wireless sensor networks (WSNs) have been deployed for an ever-widening range of applications, especially due to their low power consumption and reliability. In most applications, the sensor data must be sent to the Internet or core network, so the issue arises of providing a backhaul for WSN traffic. Passive optical networks (PONs), a next-generation access network technology, are well suited to form such a backhaul. In this paper, a new structure is proposed which converges multi-sink WSNs and PONs. It is analyzed and modelled through queueing theory. Based on this analytical model, a DBA algorithm is proposed to optimize the allocation of grant sizes. Numerical results show that the proposed algorithm outperforms other proposals for such a converged network.