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In this paper a novel analytical model for the analysis of QoS in an Optical Burst Switching (OBS) network is described. This model is based on considering the Data Burst (DB) blocking probability at the optical node together with physical channel impairments like fiber cut between the nodes, for ensuring the QoS demanded. Here the primary importance is given for preventing the Data Burst (DB) loss while propagating from an ingress node to an egress node through intermediate switching nodes. At each node, prior information about the blocking probability in the immediate successor node and detection of fiber cuts between the nodes are required. So a non-homogenous Markov chain is used to find state of the node in relation to DB blocking probability after `n' states of the node. Upon detecting the fiber cut or probability of DB blocking in the immediate successor node, the present node invokes a Genetic algorithm to find the alternate shortest path for bypassing the immediate succeeding node in the specified light path. Furthermore, the blocking probability of DB with and without the Fiber Delay Lines (FDL) are considered and compared in this paper.