In a communication network where resources are shared between Instantaneous Request (IR) and Book- Ahead (BA) connections, activation of future BA connections causes preemption of many on-going IR connections upon resource scarcity. A solution to this problem is to reroute the preempted calls via alternative feasible paths, which often does not ensure acceptably low disruption of service. In this paper, a new rerouting strategy is proposed that uses the destination node to initiate the rerouting and thereby reduces the rerouting time, which ultimately improves the service disruption time. Simulations on a widely used network topology suggest that the proposed rerouting scheme achieves more successful rerouting rate with lower service disruption time, while not compromising other network performance metrics like utilization and call blocking rate.