We study the repair problem in distributed storage systems where storage nodes are connected through packet erasure channels and some nodes are dedicated to repair [termed as dedicated-for-repair (DR) storage nodes]. We first investigate the minimum required repair-bandwidth in an asymptotic setup, in which the stored file is assumed to have an infinite size. The result shows that the asymptotic repair-bandwidth over packet erasure channels with a fixed erasure probability has a closed-form relation to the repair-bandwidth in lossless networks. Next, we show the benefits of DR storage nodes in reducing the repair bandwidth, and then we derive the necessary minimal storage space of DR storage nodes. Finally, we study the repair in a nonasymptotic setup, where the stored file size is finite. We study the minimum practical-repair-bandwidth, i.e., the repair-bandwidth for achieving a given probability of successful repair. A combinatorial optimization problem is formulated to provide the optimal practical-repair-bandwidth for a given packet erasure probability. We show the gain of our proposed approaches in reducing the repair-bandwidth.