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IEEE 802.16e amendments for the mesh mode do not specify particular QoS mechanisms. However, each Mesh Subscriber Station (MSS) transmits its own traffic and forwards the traffic of its children while each traffic flow has its particular QoS constraints. As all forwarded traffics use the same link, one MSS may experience starvation or act selfishly. Besides, the MSS's mobility adds important complexity as all the affected flows need to be re-routed, re-admitted and re-scheduled while respecting their original QoS requirements. In this paper, we adopt the concept of assigning five virtual nodes to each MSS reflecting the five QoS classes of IEEE 802.16e and we propose scheduling the uplink transmissions of the real-time Polling Service (rtPS) traffic class by adopting the Genetic Algorithms concept. We define the priority assigner component which communicates with the scheduler of the mesh BS in order to set and update flows' priority and we optimize the time spent by a flow in the queue while implementing the mobility constraints within the mutation function.