This paper investigates the outage performance of an amplify-and-forward (AF) relay network with varying number of relays (RN-VR). In the previous works for the analysis of multi-relay networks, the number of available relays is always assumed to be fixed. Thus, the performance and diversity of the relay network is determined by the assumed number of available relays. However, under some practical cooperative system where many users in neighboring region share a restricted number of relays, the number of available relays may change due to the preoccupied relays by other users. Therefore, the performance and diversity of the relay networks cannot be represented as the previous analysis and, thus, a different investigation of this model is needed in this case. To investigate the suggested cooperative system, occupancy of each relay is modeled as a continuous time Markov on-off process to represent the varying number of relays and provide analytical insight. Based on this theoretical approach, we explore the outage performance of an AF relay network which is called RN-VR in a practical manner.