Public Safety Networks (PSNs) provide assistance before- and post-disaster events. With the help of technological advances, PSNs are able to cope with both natural and man-made disasters, protecting people, environment and property. Effective communications, better situational awareness, lower response times and greater emergency efficiency are essential to an effective response to emergencies and disasters. Long Term Evolution (LTE) has been chosen to be the key technology for public safety networks. In this study, a performance model is presented for the PSN frameworks which use cooperative devices with LTE device to device (D2D) communications features. Mobile stations that are out of cellular network coverage range use D2D communications, where mobile stations which are in a healthy area can act as relay nodes to provide information about the location of potential victims to a central system. Since relay nodes have the potential to become bottlenecks for relatively high scale disasters, the interaction between the relay node and the base station is critically considered in this study. The analytical model and solution are suitable for assessing the quality of service for PSNs with similar infrastructures. Results obtained from the analytical model are presented comparatively with those from discrete event simulations for validation. The maximum discrepancy between the results obtained from the analytical model and the simulation results is less than 1.4%, which is within the confidence interval of the simulation.