Ultra-wideband (UWB) technology is expected to provide high data rate services for future wireless personal area networks (WPANs). The WiMedia Alliance recently has launched its standard for UWB-based WPANs, where the distributed reservation protocol (DRP) is specified to allow the channel time being reserved in a distributed manner. In view of the urgent need of using DRP to support high data rate multimedia applications, we investigate the delay performance of DRP in this paper. Since the negotiation of channel time is fully distributed without centralized coordination, the reserved channel time may be non-evenly spaced. In addition, the channel dynamics due to shadowing that is notable in indoor environments can greatly affect the protocol performance. In this paper, we study the delay performance of DRP under different reservation patterns and take into account the dynamics of UWB shadowing channel. The system is modeled as a discrete-time single server queue with vacation, which can be represented by the quasi-birth and death (QBD) process and solved by the well-established matrix-geometric approach. We use numerical results to validate the accuracy of the mathematical modeling. The proposed analytical model can be useful to understand the actual performance of DRP, thereby further performance improvement can be guided.