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The IEEE 802.16 standard (commonly known as WiMax) has emerged as a broadband wireless technology covering large geographical area while providing high speed data rates with native Quality of Service (QoS) support. In this paper, we study mesh mode of operation of WiMax with centralized scheduling for UGS and RTPS service classes. We briefly discuss two known routing algorithms (to find the path of a request) and propose two new routing algorithms. We present a novel scheduling and Call Admission Control (CAC) algorithm for UGS and RTPS service class. The scheduling and CAC algorithm make sure that each and every packet of admitted request strictly meets its delay and jitter constraints. Since an RTPS request can change its data rate requirement, we propose an efficient algorithm for computing extra bandwidth request for RTPS service class which perform much better in terms of average packet delay and packet drop percentage compared to some simple algorithms. We present simulation results comparing our scheduling algorithm with two other algorithms proposed in the literature. We also present results which show that our scheduling does provide strict QoS guarantee for every packet.