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An essential part of the provision of quality of service (QoS) is the reservation of bandwidth which is a scarce resource in a mobile ad hoc network. In this paper, we describe how to enhance the guarantees for bandwidth reservation in a Time Division Multiple Access (TDMA) based ad hoc network where the bandwidth is expressed in terms of the number of time slots. We devise a scheme for determining slots for transmission and reception of packets taking into account hidden and exposed terminal problems. We propose a QoS routing protocol that tries to identify multiple node-disjoint paths between a given source and a destination. In our protocol, the destination selects the paths that satisfy the bandwidth requirements of the flow. We study the effect of transmission range of nodes, node density, and the upper bound on the available slots on the bandwidth reservation success ratio.