Repair scheduling in wireless distributed storage with D2D communication

We consider distributed storage (DS) for a wireless network where mobile devices arrive and depart according to a Poisson random process. Content is stored in a number of mobile devices, using an erasure correcting code. When requesting a piece of content, a user retrieves the content from the mobile devices using device-to-device communication or, if not possible, from the base station (BS), at the expense of a higher communication cost. We consider the repair problem when a device that stores data leaves the network. In particular, we introduce a repair scheduling where repair is performed (from storage devices or the BS) periodically. We derive analytical expressions for the overall communication cost of repair and download as a function of the repair interval. We illustrate the analysis by giving results for maximum distance separable codes and regenerating codes. Our results indicate that DS can reduce the overall communication cost with respect to the case where content is only downloaded from the BS, provided that repairs are performed frequently enough. The required repair frequency depends on the code used for storage and the network parameters. In particular, minimum bandwidth regenerating codes require frequent repairs, while maximum distance separable codes give better performance if repair is performed less frequently. We also show that instantaneous repair is not always optimal.