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Although the IEEE 802.16 standard defines various QoS classes and their associated parameters, it does not define the scheduling, routing, and Call Admission Control (CAC) algorithms to be used in the network. It is left unstandardized for vendor differentiation. Currently, scalable distributed scheduling and routing algorithms are available for IEEE 802.16 mesh networks. But, the existing CAC algorithms are not entirely distributed and hence are not scalable. The algorithms not only create a bottleneck at the first hop nodes, but may also introduce an unbounded delay during the connection setup phase. In this paper, we propose an Instantaneous CAC algorithm which uses per-hop multi path routing for IEEE 802.16 mesh networks. Also, the proposed CAC algorithm eliminates the unbounded connection initiation delay and generates information for distributed routing tables. Finally, using extensive simulations, we compare the proposed protocol with Shortest Widest Efficient Bandwidth (SWEB) and Greedy Choice with Bandwidth Availability aware Defragmentation (GCAD). Simulations show that the proposed protocol eliminates the CAC delay and also improves the system throughput. The proposed protocol, reduces the number of packets (VBR and CBR) exceeding the delay requirements by about 15% and the connection delay by about 40%.