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Wireless sensor networks (WSNs) are being deployed for an ever-widening range of applications, particularly due to their low power consumption and reliability. In most applications, the sensor data must be sent over the Internet or core network, which results in the WSN backhaul problem. Passive optical networks (PONs), a next-generation access network technology, are well suited form a backhaul which interfaces WSNs to the core network. In this paper a new structure is proposed which converges WSNs and PONs. It is modelled and analyzed through queuing theory by employing two M/M/1 queues in tandem. Numerical results show how the WSN and PON dimensions affect the average queue length, thus serving as a guideline for future resource allocation and scheduling of such a converged network.